Benchmarking StreamLine Dynamic · 2020-03-26 · Benchmarking StreamLine Dynamic test cases Farzad...

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Benchmarking StreamLine Dynamic Traffic Assignment model: theoretical test cases Farzad FakhraeiRoudsari Wei Huang Chris Tampère RA-2015-010 30/09/2015

Transcript of Benchmarking StreamLine Dynamic · 2020-03-26 · Benchmarking StreamLine Dynamic test cases Farzad...

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Benchmarking StreamLine Dynamic Traffic Assignment model: theoretical test cases

Farzad FakhraeiRoudsari Wei Huang Chris Tampère

RA-2015-010

30/09/2015

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Steunpunt Verkeersveiligheid | RA-2015-010

© Steunpunt Verkeersveiligheid Wetenschapspark 5 bus 6 | 3590 Diepenbeek

Consortium UHasselt, KU Leuven en VITO

Niets uit deze uitgave mag worden verveelvoudigd en/of openbaar gemaakt zonder uitdrukkelijk te verwijzen naar de bron.

Dit rapport kwam tot stand met de steun van de Vlaamse Overheid, programma ‘Steunpunten voor Beleidsrelevant Onderzoek’. In deze tekst komen onderzoeksresultaten van de auteur(s) naar voor en niet die van de Vlaamse Overheid. Het Vlaams Gewest kan niet aansprakelijk gesteld worden voor het gebruik dat kan worden gemaakt van de meegedeelde gegevens.

Het Steunpunt Verkeersveiligheid 2012-2015 voert in opdracht van de Vlaamse overheid beleidsondersteunend Wetenschappelijk onderzoek uit over verkeersveiligheid. Het Steunpunt Verkeersveiligheid is een samenwerkingsverband tussen de Universiteit Hasselt, de KU Leuven en VITO, de Vlaamse Instelling voor Technologisch Onderzoek.

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Contents

Contents ................................................................................................................................................ III

List of Figures ........................................................................................................................................ V

List of Tables........................................................................................................................................ VII

Summary ................................................................................................................................................ 8

Samenvatting ......................................................................................................................................... 9

Introduction .......................................................................................................................................... 10

Methodology ........................................................................................................................................ 11

Structure of the document .................................................................................................................. 12

1 Uninterrupted flow propagation model ...................................................................................... 13

1.1 Free flow propagation ............................................................................................................ 16

1.1.1 Free flow propagation without queue at the origin ........................................................................... 16

1.1.2 Free flow propagation with queue at the origin ................................................................................ 22

1.2 Stationary bottleneck and demand is too high over entire time domain................................ 25

1.3 Stationary bottleneck and demand is too high only during some peak between t1 and t2..... 34

1.4 Temporary bottleneck during an incident between t3 and t4 when demand OD is constant 37

1.5 Speed limit modeling ............................................................................................................. 41

1.6 Variable speed limit ............................................................................................................... 41

1.7 Shoulder lane modeling ......................................................................................................... 43

1.8 Detector modeling.................................................................................................................. 48

1.9 Output visualization ............................................................................................................... 48

1.10 Retrieve output ...................................................................................................................... 48

1.11 Travel times result ................................................................................................................. 48

2 Uninterrupted corridor (merges and diverges) ......................................................................... 54

2.1 Single merge model behavior where the receiving link’s capacity is the constraint .............. 58

2.2 Single merge model behavior while having congestion spillback from downstream bottleneck 66

2.3 Single diverge model behavior where the receiving link’s capacity is the constraint and while having congestion spillback from downstream bottleneck ................................................................. 70

2.4 Consistency of turning rates at a diverge node ..................................................................... 76

2.5 Route travel time outputs ....................................................................................................... 78

2.6 Turning flows output .............................................................................................................. 78

2.7 Ramp metering control on on-ramp ....................................................................................... 78

3 Signalized intersection ................................................................................................................ 81

3.1 Single turn movement ............................................................................................................ 85

3.1.1 Single turn movement with under-saturation flow ............................................................................ 85

3.1.2 Single turn movement with over-saturation flow .............................................................................. 87

3.1.3 Single turn movement with spillback from downstream bottleneck .................................................. 90

3.2 Diverging turn movement ...................................................................................................... 93

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3.2.1 Diverging turn movement with under-saturation flow ....................................................................... 93

3.2.2 Diverging turn movement with over-saturation flow ......................................................................... 95

3.2.3 Diverging turn movement with spillback from downstream bottleneck ............................................. 97

4 Route Choice .............................................................................................................................. 102

4.1 Stochastic Route Choice ..................................................................................................... 105

4.1.1 Same travel cost ............................................................................................................................ 106

4.1.2 Route with cost a bit higher than the other one (under saturated) ................................................. 108

4.1.3 Over saturation with travel cost difference ..................................................................................... 110

Conclusion ......................................................................................................................................... 117

Reference ........................................................................................................................................... 118

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List of Figures

Figure 1: Demand pattern and maximum network capacity for free flow without queue at the origin .. 17

Figure 2: Speed of the links when connectors speed are set to 90km/h .............................................. 20

Figure 3: Speed of the links when connectors speed are set to 50km/h .............................................. 20

Figure 4: Speed of the links when connectors speed are set to 90km/h and anticipation factor (Nue) is set to 140 km2/h ..................................................................................................................................... 21

Figure 5: Flow propagation in free flow condition network .................................................................... 21

Figure 6: Demand pattern and maximum network capacity for free flow with queue at the origin ...... 22

Figure 7: Speed pattern when connectors speed are set to 90 km/h.................................................... 23

Figure 8: Speed pattern when connectors speed are set to 50 km/h.................................................... 23

Figure 9: Flow propagation when queue is at the origin ....................................................................... 24

Figure 10: Density correlation by disaggregating the link ..................................................................... 25

Figure 11: Flow propagation with stationary bottleneck ........................................................................ 26

Figure 12: Flow propagation with stationary bottleneck ........................................................................ 29

Figure 13: Density pattern in stationary bottleneck with default parameters ........................................ 30

Figure 14: Flow - Density (left) and Speed – Density (right) for link 5 (bottleneck) ............................... 30

Figure 15: Flow – Density (left) and Speed - Density (right) for link 6 (bottleneck downstream) ......... 31

Figure 16: Density pattern in stationary bottleneck when anticipation parameter is zero .................... 32

Figure 17: Flow - Density (left) and Speed – Density (right) for link 5 (bottleneck) .............................. 32

Figure 18: Density pattern in stationary bottleneck when anticipation parameter is zero .................... 33

Figure 19: Flow - Density (left) and Speed – Density (right) for link 5 (bottleneck) .............................. 33

Figure 20: Flow - Density (left) and Speed – Density (right) for link 4 (upstream link of bottleneck) ... 34

Figure 21: Flow propagation with stationary bottleneck and peak demand ......................................... 35

Figure 22: Flow propagation in stationary bottleneck with peak demand ............................................. 36

Figure 23: Space – Time diagram when link 5 is stationary bottleneck with peak demand .................. 37

Figure 24: Speed difference with capacity reduction alternatives ......................................................... 38

Figure 25: Flow propagation with temporary bottleneck ...................................................................... 39

Figure 26: Flow propagation in temporary bottleneck ........................................................................... 40

Figure 27: Space – Time diagram when link 5 is temporary bottleneck .............................................. 41

Figure 28: Space – Time diagram when VSL is not activated .............................................................. 43

Figure 29: Space – Time diagram when VSL is activated ................................................................... 43

Figure 30: The effect of shoulder lane running ...................................................................................... 46

Figure 31: Space – Time diagram without shoulder lane running ......................................................... 47

Figure 32: Space – Time diagram with shoulder lane running ............................................................. 47

Figure 33: Travel time with (light blue line) and without (dark blue line) shoulder lane ........................ 48

Figure 34: Flow propagation in single merge for test 2.1.1, at time 7:15 (above) and last time step of demand feeding (below) ........................................................................................................................ 59

Figure 35: Space-Time plot for highway (left) and second on-ramp ..................................................... 60

Figure 36: Flow propagation in single merge for test 2.1.2, at free flow stage (above) and last time step of demand feeding (below) .................................................................................................................... 61

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Figure 37: Space-Time plot for highway (left) and second on-ramp ..................................................... 62

Figure 38: Flow propagation in single merge for test 2.1.3, at free flow stage (above) and last time step of demand feeding (below) .................................................................................................................... 63

Figure 39: Space-Time plot for highway (left) and second on-ramp ..................................................... 64

Figure 40: Flow propagation in single merge for test 2.1.4, at free flow stage (above) and last time step of demand feeding (below) .................................................................................................................... 65

Figure 41: Space-Time plot for highway (left) and second on-ramp ..................................................... 66

Figure 42: Flow propagation in single merge with congestion triggered by spillback from downstream bottleneck for test 2.2.1, at free flow stage (above) and last time step of demand feeding (below) ..... 67

Figure 43: Sending flow at merging point A (left) and C (right) ............................................................. 68

Figure 44: Space-Time plot for highway (top left), first on-ramp (top right) and second on-ramp (bottom ) .............................................................................................................................................................. 68

Figure 45: Flow propagation in single merge with congestion triggered by spillback from downstream bottleneck for test 2.2.2, at free flow stage (above) and last time step of demand feeding (below) ..... 69

Figure 46: Space-Time plot for highway (top left), first on-ramp (top right) and second on-ramp (bottom ) .............................................................................................................................................................. 70

Figure 47: Flow propagation in simple diverge at free flow stage for test 2.3.1 .................................... 71

Figure 48: Space-Time plot for highway (left) and off-ramp (right) ....................................................... 72

Figure 49: Flow propagation in single diverge for test 2.3.2, at free flow stage (above) and last time step of demand feeding (below) .................................................................................................................... 73

Figure 50: Space-Time plot for highway (left) and off-ramp (right) ....................................................... 73

Figure 51: Flow propagation in single diverge with congestion triggered by spillback from downstream bottleneck for test 2.3.3 after one hour simulation (above) and end of demand profile (below) ........... 76

Figure 52: flow propagation with different demand pattern for test 2.4.1 .............................................. 77

Figure 53: Cumulative of the flow arriving at each destination .............................................................. 78

Figure 54: Ramp metering scheme in StreamLine ................................................................................ 79

Figure 55: Network layout for signalized intersection ............................................................................ 84

Figure 56: Flow propagation for single intersection at under-saturated condition for test 3.1.1 ........... 86

Figure 57: Travel cost (min) for O1D3 in test 3.1.1 ............................................................................... 87

Figure 58: Flow propagation for single intersection at under-saturated condition for test 3.1.2 ........... 88

Figure 59: Turn cost and flow for test 3.1.2 ........................................................................................... 89

Figure 60: Travel route cost of test 3.1.2 ............................................................................................... 89

Figure 61: Space – Time diagram for test 3.1.3, left figure is speed and right is density ..................... 91

Figure 62: Turn cost and flow for test 3.1.3 ........................................................................................... 92

Figure 63: Route travel time for test 3.1.3 ............................................................................................. 92

Figure 64: Turn cost and flow for test 3.2.1 ........................................................................................... 94

Figure 65: Route travel time for test 3.2.1 ............................................................................................. 95

Figure 66: Space – time plot for O1D3 in test 3.2.2, the left figure is speed and right one is density .. 96

Figure 67: Route travel cost for test 3.2.2 ............................................................................................. 97

Figure 68: Space – time diagram for O1D3 for test 3.2.3, left shows speed, right shows density ........ 98

Figure 69: Turn flow and cost for route O1D3 in test 3.2.3 ................................................................... 99

Figure 70: Travel cost (left) and route fractions (right) for test 4.1.1 ................................................... 107

Figure 71: Abnormal speed reduction by having short downstream link............................................. 109

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Figure 72: Travel cost (left) and route fractions (right) for test 4.1.2 ................................................... 109

Figure 73: Travel cost (left) and route fractions (right) for test 4.1.3 ................................................... 111

Figure 74: Travel cost (left) and route fractions (right) when beginning of collection interval is used to calculate the route cost ........................................................................................................................ 112

Figure 75: Travel cost (left) and route fractions (right) when end of collection interval is used to calculate the route cost ....................................................................................................................................... 112

List of Tables

Table 1: Network properties .................................................................................................................. 17

Table 2: Network properties .................................................................................................................. 26

Table 3: Network properties .................................................................................................................. 35

Table 4: Network properties .................................................................................................................. 38

Table 5: Network properties .................................................................................................................. 42

Table 6: Demand pattern ....................................................................................................................... 42

Table 7: Network Properties .................................................................................................................. 44

Table 8: Demand pattern ....................................................................................................................... 45

Table 9: Demand profile and adjusted supply properties for test 2.1.1 ................................................. 58

Table 10: Demand profile and adjusted supply properties for test 2.1.2 ............................................... 60

Table 11: Demand profile and adjusted supply properties for test 2.1.3 ............................................... 62

Table 12: Demand profile and adjusted supply properties for test 2.1.4 ............................................... 64

Table 13: Demand profile and adjusted supply properties for test 2.2.1 ............................................... 66

Table 14: Demand profile and adjusted supply properties for test 2.2.2 ............................................... 69

Table 15: Demand profile and adjusted supply properties for test 2.3.1 ............................................... 71

Table 16: Demand profile and adjusted supply properties for test 2.3.2 ............................................... 72

Table 17: Demand profile and adjusted supply properties for test 2.3.3 ............................................... 74

Table 18: Demand profile and adjusted supply properties for test 2.4.1 ............................................... 77

Table 19: Supply characteristics of the signalized intersection toy network ......................................... 84

Table 20: Intersection’s properties ........................................................................................................ 84

Table 21: Demand profile for test 3.1.1 ................................................................................................. 85

Table 22: Demand and supply modification for test 3.1.3 ..................................................................... 90

Table 23: Demand profile for test 3.2.1 ................................................................................................. 93

Table 24: Demand profile for test 3.1.2 ................................................................................................. 95

Table 25: Demand and supply modification for test 3.1.3 ..................................................................... 97

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Summary

An aspect of road traffic safety that is less intensely researched is the rerouting or network effect. When measures are taken to improve traffic safety, usually the effect is measured at the location where the measure was activated. However, because most measures also affect the throughput and hence the attractivity of the route, measures might in addition cause rerouting effects either away from or towards the location where the safety measure was taken. While doing so, also safety effects can be exported to or imported from alternative roads

Dynamic Traffic Management (DTM) measures can be aimed at improving safety, efficiency or both. Either way, they will have cause rerouting, intended or as a side-impact. It is thus important to ex-ante evaluate the impact of DTM on the network level. Given that DTM is usually aimed at mitigating congestion effects, an adequate modeling of the dynamics of traffic in networks is crucial in such evaluation. However, existing modeling instruments do not always comply with this requirement. Static models lack the time dimension, whereas microsimulators are impractical (if not unable) for modeling larger networks. That is why the use of macroscopic dynamic traffic assignment (DTA) models is being explored.

There are several components affecting the outcome of dynamic network evaluations such as dynamic traffic demand known as dynamic origin-destination, Dynamic Network Loading (DNL) which propagates traffic demand given network characteristics, resulting among others in route travel times and Route Choice (RC) component that uses the route travel times to calculate route choice fractions. The combination of last two components known as Dynamic Traffic Assignment (DTA) that is consistent with both DNL and RC and obtained by an iterative process between these two components. The inability to provide high quality in one of these components makes the prediction simply impossible. Therefore, it is essential to measure and in-depth analysis the capability of DTA modeling software that can adequately describe traffic dynamics and behavioral processes in a network. It is vital to have an accurate DTA model that would realistically describe network flow distributions, to capture the effects of congestion as well as route choices. To achieve this, a benchmarking of the DTA modeling software of DAT.Mobility (NL) called OmniTRANS with StreamLine framework is conducted (in a complementary report, the TRE (Traffic Real-time Equilibrium) component of Visum software of PTV AG and Sistema is benchmarked using the same methodology).The main focus of this benchmarking was done for Dynamic Network Loading and Route choice components. Since dynamic traffic demand is an exogenous input for DTA, this is not relevant for this study. In this benchmarking, several test cases have been defined, where DNL and RC components were scattered into several sub problem and different aspects of the DNL and RC have been analyzed. In the first two cases, we explore the propagation model under different conditions. These test series brought depth analysis the functionality of propagation model and influences of the demand and supply interaction with flow propagation. Delay is the most important measure of effectiveness (MOE) at a signalized intersection because it relates to the amount of lost travel time, fuel consumption, and the frustration and discomfort of drivers. To understand it, modeling of the traffic flow at signalized intersections is explored and analyzed under different demand and supply conditions. This test enables us to understand how signalizations are taken into account in the signalized intersection also the calculation and definition of the delay in non-congested condition or when the queue spillovers the intersection. Modeling route choice behavior is essential to appraise traveler’s perceptions of route characteristics, to forecast traveler’s behavior under hypothetical scenarios, to predict future traffic conditions on transportation networks and to understand traveler’s reaction and adaptation to sources of information. Therefore, route choice component is analyzed where stochastic and deterministic models are activated under different scenarios. The sensitivity of the RC model to the overlapping of paths and functionality of the model under gridlock condition are also explored. Beside these technical analyzes, robustness, consistency, accountability and ease of use of StreamLine/OmniTRANS within each test case are explored.

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Samenvatting

Een minder intensief onderzocht aspect van verkeersveiligheid zijn netwerkeffecten door herroutering. Wanneer men maatregelen treft ter verhoging van de lokale verkeersveiligheid, wordt het effect ook veelal geëvalueerd rondom de plaats van deze maatregelen. Veel van deze maatregelen hebben echter ook een invloed op doorstroming en daarmee op de attractiviteit van een route. Hierdoor is het heel plausibel dat routes zich verleggen, doordat het meer of minder aantrekkelijk wordt om langs de aangepaste locatie te rijden. Als verkeersstromen zich aldus verleggen, kunnen ook verkeersveiligheidseffecten geïmporteerd of geëxporteerd worden naar alternatieve routes, waar de veiligheid kan toe- of afnemen. Men kan zich dit het beste voorstellen wanneer een ingreep voor verkeersveiligheid filevorming zou veroorzaken en daardoor verkeer door een woonwijk zou gaan sluipen.

Maatregelen van dynamisch verkeersmanagement (DVM) kunnen bedoeld zijn ter verhoging van verkeersveiligheid, van efficiëntie of beide. Hoe dan ook kunnen zij – bedoeld of onbedoeld – herroutering als gevolg hebben. Daarom is het van belang om DVM maatregelen ex-ante te evalueren op netwerkniveau en niet alleen lokaal. Omdat veel DVM maatregelen bedoeld zijn om congestievorming te beïnvloeden, is een correcte weergave van congestie bij zulke ex-ante evaluatie van groot belang. Echter, de momenteel meest gebruikte verkeersmodellen voldoen niet op dit aspect. Statische modellen missen de tijdsdimensie; microsimulatie is dan weer onpraktisch, zo niet onmogelijk voor grote netwerken. Dat verklaart de interesse in een nieuw instrument: macroscopische dynamische toedelingsmodellen (DTA naar het Engelse Dynamic Traffic Assignment).

Er zijn in DTA modellen verschillende componenten die de uitkomst van de dynamische netwerkanalyses beïnvloeden, waaronder de dynamische verkeersvraag (in de vorm van een herkomst-bestemmingstabel), de dynamische afwikkelingscomponent (DNL) en het routekeuzemodel. Indien één van deze componenten niet voldoet, worden de voorspellingen van het DTA model onbruikbaar. Een gedegen analyse van DTA software (relatief nieuw op de markt) is daarom onmisbaar alvorens deze in te zetten voor de analyse van DVM. Met dit doel voor ogen, is een grondige studie verricht naar twee van de nieuwste softwarepakketten voor DTA modellering: het TRE model van PTV/Sistema en het StreamLine model van DAT.mobility. Dit rapport beschrijft de analyseresultaten van het StreamLine model; in een complementair rapport wordt de analyse van StreamLine gerapporteerd. De focus van deze analyses ligt bij de DNL (dynamic network loading) component die de fysieke verschijnselen van verkeerspropagatie en filevorming in een netwerk beschrijft, en bij het routekeuzemodel, dat voorspelt hoe reizigers in een netwerk hun route kiezen in functie van de veranderlijke weerstanden (door de op- en afbouw van files en vertragingen bij knelpunten en kruispunten). De analyses gebeuren aan de hand van een reeks testcases. De eerste twee daarvan onderzoeken de verkeersafwikkeling (DNL) in diverse types knelpunten en bij diverse vormen van dynamische verkeersvraag en capaciteitsbeperkingen. Vervolgens testen we de modellering van kruispunten en met name de capaciteitsbeperkingen en vertragingen die de conflicterende stromen en de verkeersregeling veroorzaken. Tenslotte kijken een paar tests naar de routekeuze onder welgekozen gecontroleerde omstandigheden, wat uiteraard van belang is bij het voorspellen van herrouteringseffecten. Theoretisch maakt men onderscheid tussen deterministische en stochastische keuzemodellen, al naargelang de populatie van bestuurders in hun routekeuze als een homogene dan wel heterogene groep wordt verondersteld. Bekende pijnpunten van routekeuzemodellen, zoals de invloed van overlap in de routes en het mogelijk ontstaan van gridlock door de interactie tussen routekeuze en congestieterugslag krijgen bijzondere aandacht. Tenslotte wordt tijdens de tests naast zuiver technische analyse, ook gekeken naar het gebruiksgemak van de software, de consistentie en soliditeit van de resultaten en naar de in- en uitvoermogelijkheden die de software biedt.

Uit de analyses blijkt dat StreamLine op veel tests voldoet, maar met name in de verkeersafwikkeling moeilijk controleerbaar is en soms inconsistenties laat zien. Dit komt doordat gekozen is voor een relatief complex tweede orde verkeersafwikkelingsmodel. Los daarvan zijn routekeuze, maar ook gebruiksaspecten als de visualisatie en interface solide en laten gebruik voor praktische netwerken toe.

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Introduction

As a part of the SPRINT (policy support research center on traffic safety), Project 5.3 considers the “Impact of infrastructural measures on traffic safety”, focusing more specifically on the impact of Dynamic Traffic Management measures. Because such measures are often directly or indirectly affecting traffic flow efficiency, they may cause substantial rerouting by drivers, which may have safety consequences as well, as discussed next.

An aspect of road traffic safety that is less intensely researched is the rerouting or network effect. When measures are taken to improve traffic safety, usually the effect is measured at the location where the measure was activated. For example: an intersection is converted to a roundabout, after which the safety statistics of that intersection before and after conversion are monitored; speed on an artery is reduced by lowering the speed limit and installing speed bumps and the accident statistics on that road are analyzed; a motorway’s capacity is increased by allowing shoulder lane running, after which the number of accidents is carefully monitored.

What is disregarded in this practice is that the measure might cause rerouting effects either away from or towards the location where the safety measure was taken. Usually there is not only the safety impact, but also the road or intersection becomes more or less attractive because driving speed or comfort are affected (positively or negatively). Traffic flows may therefore divert to alternative routes, or inversely the alternative routes may be abandoned in favor of the location where the measure was taken (e.g. in the case of the shoulder lane running). While doing so, also safety effects can be exported to or imported from alternative roads: the artery may now seem safer, but as speeds are lower and traffic partially reroutes to minor roads through residential areas, safety there might be negatively affected. Despite the seemingly positive local effect, rerouting may induce negative safety effects with negative net effect on network safety. In the example of shoulder lane running, the motorway that was previously so congested that traffic during the peaks massively rerouted over the regional and local networks, may now attract that traffic again. Even if more accidents on the motorway may be registered, this could possibly be counterbalanced by safer regional and local roads.

The conclusion of this is clear: not only for efficiency, livability and environmental reasons, but also for safety analyses it is important to understand and predict rerouting effects induced by measures on the operational level. This is another reason why planning models need to be continuously improved. One major improvement in regional network traffic models is the transition from static to dynamic modeling that is possible nowadays as after years of development and piloting in academic context, dynamic traffic assignment (DTA) software is currently reaching the state of maturity that allows large-scale practical applications.

Verkeerscentrum Vlaanderen (the Flemish traffic center) takes this challenge. For a series of measures in the regional network around Antwerp, they prepare a DTA model that will be used to evaluate a series of traffic measures, as a complement to their multimodal static transport planning model. Because of the high level of congestion (hence also: rerouting), a dynamic model is indispensable for some analyses. However, up to date, no systematic and in-depth comparison of the latest DTA software is available.

The aim of this report it therefore to contribute to this transition of DTA from laboratory to practice by benchmarking new DTA software. In this part of this study, the StreamLine model of DAT.Mobility (NL) is analyzed. A second part of this study benchmarks the TRE software of PTV and Sistema and is reported in a separate report.

The authors wish to thank Katia Organe, Patrick Deknudt and Leen De Valck of Verkeerscentrum Vlaanderen and Bruno Villé and Jan Decoster of Mint NV for the constructive discussions and feedback that helped improving the results of our study substantially. Also the fast and useful cooperation and communication with the helpdesk of DAT.Mobility is herewith acknowledged.

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Methodology

The benchmarking of the StreamLine for DTA is done in two parts.

One part considered the ability to calculate efficiently the traffic state in large realistic networks. Also usability aspects like the quality of the GUI, import-export facilities etc were tested. This work was done by Mint NV consultancy and is not reported in this document.

The other part consists of a series of theoretical benchmark problems. For such problems, the desired theoretical outcome is known (sometimes even analytically). They enable to observe separately crucial behavior of the model, the algorithm, or the way in which the network was configured. In more complex networks, these aspects are so tightly intertwined that it is impossible to judge if the results are theoretically consistent, and if not, what the problem might be. These theoretical benchmark cases are the subject of this report.

The benchmark problems in this report are targeted at the following aspects: propagation of traffic (congestion) in motorway corridors and over signalized intersections; route choice modeling and convergence to equilibrium. For each of the cases, in a separate chapter the following aspects are reported: the motivation, theoretical background and challenges, scenario of the test, results, discussion, and answer by the software developers are reported.

First and basic fundamental question in DTA is related to propagation and queue formation and evolution. Queue formation and dissipation occur frequently in any motorway network with peak load, where the bottleneck can be caused by different reasons. Therefore, it is important that the model can propagate the demand correctly into the network and build correct queues that also dissipate precisely. To check the propagation model, first test case is developed where several scenarios have been conducted to model the stationary and temporary bottleneck with different demand profiles. In this test case, supply and demand properties are adjusted to control queue formation and dissipation. By doing so, correct amount and severity of spillback upstream and flow reduction downstream can be observed. Besides checking for consistency with fundamental aspects in traffic flow theory, numerical stability and accuracy of the model are explored.

In most parts of the network, especially in highways (off-ramp and on-ramp intersections), delay is the result of congestion originated from discontinuities: merges and diverges. Thus, they are crucial point to trigger congestion and spill back to traffic that does not pass the cause of the congestion, but intended to leave the network upstream of the bottleneck. Hence, it is important that spillback from primary bottlenecks to upstream links is modeled consistently. The main objective of this the second test case is therefore to check the role of merges and diverges (in addition to being potential primary bottlenecks), whether they cause the right amount of spillback to the right upstream links, creating the right amount of delay. To do so, an uninterrupted corridor with two merges and one diverge was modeled where the supply and demand components are adjusted to simulate desired conditions. Aspects verified in these test case scenarios include: positivity, continuity, capacity and flow maximization requirements of merge and diverge models. Besides, consistency of the ratio of turning movements (called turning fractions) is tested and since overtaking is not possible in the model, we check if we indeed observe FIFO (first-in first-out) at the link end. Another important aspect in a corridor network with diverge model, is checking the (in)consistency of the travel time and splitting rate at diverges with the OD matrix. If the diverge model cannot handle this situation, wrong traffic can arrive at the wrong destination.

The Achilles heel of urban network is how to model intersections where the majority of delays and capacity constraints occur. These delays have different components that affect the routing behavior on both under-saturated and over-saturated conditions. Therefore, it is crucial to capture these delays adequately to be able to estimate correct route volumes. To check the intersection delay, signalized intersection with different demand and supply properties are considered. The objectives of this test case is to check the capacity of turning flows, deterministic and stochastic delay components and FIFO consistency.

Last test case is devoted to Route Choice component. The Route Choice Model calculates the demand pattern in form of arc conditional probabilities for given performance pattern of travel costs and times. The main objectives of this test case are to explore different route choice definitions (deterministic, stochastic), convergence measure and transparency of intermediate results. To do so, different

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scenarios are conducted with stochastic route choice model. By running these scenarios, we verify the effect of routes cost on stochastic route choice. Finally, we check whether the model can find the equilibrium in the case where gridlock can occur during the iterations. This section illustrates the pros and cons using MSA (Method of Successive Averages) in the convergence criteria.

Besides testing DNL and RCM components, different aspects of the software are explored such as user-friendliness, visualization, retrieving the output data, ability of combining with external scripting language and so on.

Structure of the document

This report continues with series of test cases, which have following structure. The target of the test case and setup information are mentioned in Topic, Test ID and Network. In Relevance section, we explain why this aspect is important for the applicability, usability, correctness and stability of the model. The challenges that encounter the model are explained in the Motivation section. In this section, we elaborate the underlying reasons when the test cannot pass successfully or specific uncertainty/suspicious about the model which should be concerned. In addition, the theoretical background is highlighted in Motivation section. If current test case results affect other test cases or are affected by other test cases, Links to Other Tests section is used to address this relationship. In the Aim section, we list as specific as possible what we are testing; i.e. in the form of specific questions/challenges that the model can pass/fail; this may involve specification of experimental conditions in which the phenomenon of interest should occur. Other related information regarding the software, version used for this study, who has performed the tests also history of document revisions are mentioned in the relevant sections. In the Test Results section, results of each aim are shown and interpretation of the analyses related to particular aim is discussed. If anything was found which is relevant to the report but does not fit in the format mentioned above, it was added in Any Other Business section. In the New Questions Triggered section, we address the issue if any new question rises after analysis of the result that we were not aware before and they are worth analyzing. At the end, the conclusion of each aim is listed along with findings, challenges and shortcoming of the model in providing desirable result. The model passes the test if the result is fully consistent with the theory background and fulfill the theoretical expectations/analytical solution. In the case of minor deviation, the model will be partially passed and the related problem will be explained. If the model output is inconsistent to the theoretical expectations/analytical solution or the model cannot provide expected output or the model cannot perform desired task, model will be failed. During completion of this report, we have given the software developers opportunity to provide us with feedback according partially passed and failed tests and their suggestions, recommendations and explanations have been listed in the developers’ perspective section.

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Test ID 1

Topic Propagation mechanism

Test 1 Uninterrupted flow propagation model + output retrieval/visualization

Network

We consider a simple linear network of 5 km with section AB (1km located at x=3km) being a potential bottleneck (i.e. CAB≤COA= CBD). The bottleneck can be triggered either because:

AB is a stationary bottleneck and demand OD is too high over entire time domain,

AB is a stationary bottleneck and demand OD is too high only during some peak between t1 and t2,

Demand OD is constant, but AB is a temporary bottleneck only during an incident between t3 and t4.

Relevance A DTA is supposed to be sensitive to dynamic queue formation. It is important that queue formation and dissipation are modelled correctly, i.e. create the correct amount and severity of spillback upstream (spatial extent, speed/flow reduction) and flow reduction downstream, otherwise travel times over the congested corridor will be wrong and/or traffic conditions downstream are modelled with too much congestion. These aspects can all be tested with the elementary simple bottleneck in this test of which the correct queue formation and dissipation are well-known in traffic flow theory. This situation occurs frequently in any motorway network with peak load, where the bottleneck (here just modeled as a given capacity) can be caused by different reasons, including: lane reduction, merging/weaving traffic, discontinuity in road profile (tunnel, bridge,…), steep grade, spillback from an off-ramp, work zone, low speed limit,…

Motivation Dependent on the chosen traffic propagation model in the software, its parameters and time/space discretization, the prediction of occurrence, location, dynamics and severity of queues (delay) can differ substantially. Problems that may occur include:

wrong density (hence spatial extent) of queue upstream

inaccurate capacity modeling (numerical convergence problem)

(un)desired 2nd order effects like oscillatory congestion, (un)intended capacity drop or lack of control over these phenomena because of unclear impact of model parameters

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Illogical/undesired effects on outputs of time/space discretization (smoothing, numerical instability, calculation time increase, numerical diffusion (i.e. vehicles running at speeds higher than free flow, or vehicles never able to flow out of the network),…)

Spillback of queues into the origin (are these vehicles preserved? are resulting delays before entry accounted for in output statistics?)

Apart from congestion, also traffic in free flow can pose challenges. Problems that may occur include:

no or illogical speed reductions in dense, yet not saturated traffic (curved fundamental diagram)

numerical convergence problems

For applications of motorway control, the model should allow influencing traffic propagation on motorways:

speed limit influence

Variable speed limit: can it be modeled at all and is the impact correct? Can it be modeled as exogenous control time series or as endogenous response consistent with propagation?

Shoulder lane running: can it be modeled at all and is the impact correct?

detectors: definition of flow, speed,… at detector locations could differ from that in reality, so that comparison between modeled and real detector outputs is deceptive or even impossible

Even if all calculations are done correctly, the question is whether they are available for the user (and well-documented, so that one knows what exactly one is looking at), either directly through the graphical interface or indirectly for export and further analysis in other tools.

Links to other tests This test affecting results of other tests:

Test 2: merges & diverges in corridors – all conclusions from test 1 are directly relevant for this extension to full motorway corridors

Test 4: route choice – travel time component of route cost is directly derived from propagation

Test 4: convergence of DTA – limits/problems of numerical precision of propagation may affect convergence of DTA equilibrium

Other tests affecting this test:

none

Aims 1.1 Is free flow propagation satisfactorily modeled?

1.2 Fixed bottleneck activation & dissipation due to demand excess correctly modeled and visualized? (Capacity drop? if so, is it controllable? precision outflow? density upstream? influence model parameters (like anticipation, if any)? stability of queue?

1.3 Is spillback into origin adequately dealt with and reported (in numerical and graphical outputs)?

1.4 Can temporary bottlenecks be modeled and does queue dissipate correctly? (Dissipation from the head of queue? precision outflow values?)

1.5 How is a speed limit modeled? Does it impact capacity and if so, is this plausible?

1.6 Can VSL be modeled? If so, exogenous or endogenous? How plausible is the impact?

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1 Note that extensions to basic first order models exist that do consider capacity drop; such models have a ‘reversed lambda’-shaped fundamental diagram. To the best of our knowledge, there exists at this moment no commercial software implementing such extended first order theory.

1.7 Can shoulder lane running be modelled? How plausible is the impact?

1.8 Can detectors be modeled? Are the outputs consistent?

1.9 Can all required outputs be visualized? Any specific dynamic plots in the GUI like time series, xt of selected sub routes?

1.10 Can all required outputs be retrieved from database for analysis in external tool? Are all output specifications clear and unambiguous (do we know exactly what we get)?

1.11 How is route travel times aggregated from link variables? Impact of space/time discretization on this?

Software OmniTrans StreamLine

Version OmniTRANS 6.1.4.7667 / StreamLine

Operator Farzad Fakhraeiroudsari, Wei Huang

File location StreamLine\Test_ID_1_Simple_Bottleneck

Document history 1.0 14-12-14 Farzad Fakhraeiroudsari, Wei Huang, Chris Tampère

2.0 27-02-15 Farzad Fakhraeiroudsari, Chris Tampère

Remarks of VVC processed

Test results 1.1 Introduction to 1st and 2nd order models

Before describing the phenomena of propagation in StreamLine which is based on second order models, it is worth describing briefly the difference between first and second order models.

First order models have some advantages , like;

Reliability: Flow and density variables are always consistent in any point at any time within the physical limits of the network (Qmax Kmax )

Existence of the analytical solution: In simple benchmark cases it is possible to calculate exact solutions

Despite the advantages, the first order models have also some drawbacks, like;

transitional phases are not correctly modeled; e.g. deceleration at queue tail is modeled instantaneously

Speed is not considered as a variable; as a result, capacity drop1, instabilities and stop & go waves cannot be reproduced.

Second order models were developed to relax the problems with first order models, which means

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They present the transitional phenomena during variations in traffic flow (smooth transition/deceleration free flow – congestion)

They also taking into account the speed as a principal variable. That is unlike first order model, capacity drop and stops & goes traffic may occur in the results.

Although despite these advantages, second order models also have some drawbacks,

Complications: second order models are more complicated. Analytical solution cannot be found even in very simple cases. The numerical solution is highly dependent on the numerical scheme (and discretization) that is used. Commercial solvers usually have oversimplified numerical schemes, such that the behavior of the model is a result of the analytical properties of the underlying traffic flow model + of the artefacts introduced by the numerical scheme and discretization.

Difficult to control: there are many parameters (including numerical discretization parameters – in good numerical schemes this would not be the case!) that influence the speed variable and calibrating these parameters is difficult.

For more information please check (Slim Hammadi 2013) or other standard literature.

Short description of propagation model in StreamLine (according to the manual):

The macroscopic traffic propagation model StreamLine uses is called MaDAM. The model is based on the METANET model a 2nd order Cell Transmission Model (CTM) which is considered a more sensitive approach than link performance or exit functions as these do not capture the dynamics of propagating traffic along the link.

By contrast, in a link based model, the model uses the characteristics of a whole link to determine the speed, flow and density on that link. Since the length of cells is shorter than the length of a whole link, the results of a cell based model are more accurate than the results of a link based model. For more information please check OmniTRANS Manual.

As a first test case, we check the free flow propagation model (refer to Aims 1.1).

In this test case, two scenarios are considered: when the demand increased near capacity but still in free flow condition, and demand exceeding the capacity (queue at the origin).

1.1 Free flow propagation

1.1.1 Free flow propagation without queue at the origin

In this test case, network consists of three links with the same capacity which is more than demand profile. Supply and demand characteristics are shown in following Table 1 and Figure 1.

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2 Check the OmniTRANS file for more information

Supply Propert ies

Table 1: Network properties

Supply Type2 Capacity Length (km)

Free Flow

Speed

Speed at Cap

No. of Lane

Link 5 4000 7

(5+1+1) 120 90 2

Connector_90 1 4600 5 90 50 2

Connector_50 1 4600 5 50 35 2

Demand Properties

Figure 1: Demand pattern and maximum network capacity for free flow without queue at the origin

Since Streamline uses second order model, many parameters of traffic propagation influence the speed calculation, as well as other network parameters (like connector speed). In order to be familiarized with speed calculation in Madam (Metanet), it’s worth to understand the underlying terms (anticipation, relaxation and convection).

The formula to calculate the speed of each cell is formulated below.

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Relaxation term. This term describes how speed of a cell changes as vehicles adapt their speed according to the fundamental diagram (V).

Convection term. This term describes how speed of a cell changes because vehicles ‘carry’ along their speed into (inflow) and out of the cell (outflow).

Anticipation term. This term describes how speed of a cell changes as because drivers anticipate on concentration conditions downstream the road. It is a very important term, as it is the only term that looks forward (downstream) in the flow. It hence is the only mechanism for traffic perturbations to travel in upstream direction (shockwave propagation, spillback) and determines behavior at the queue tail. It is also responsible for looking ahead over the node of a diverge or merge and influences in this way spillback phenomena over nodes.

The three terms together determine the speed dynamics. As outflow of a cell is determined solely by the product of density and speed in the cell, and speed depends on many terms and parameters and is thus difficult to control, also the outflow towards the downstream cell is difficult to control (and e.g. to keep it exactly below a capacity constraint, or to obey exactly merging rates). This will be illustrated later on in the test results.

Tau (τ)

The tau parameter influences both the relaxation and anticipation terms in the speed formula. Tau must be higher than zero (to avoid negative terms and division by zero). When tau is increased by 100%, both the relaxation and anticipation terms decrease by 50%.

The default value in StreamLine is set to 20 seconds.

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Nue (ν)

The Nue parameter only influences the anticipation term. When Nue is doubled, the anticipation term also increases by 100%. By varying Nue, the influence of the anticipation term is determined. When Nue is set to 0 km2/h, anticipation is neglected in the speed calculation and no upstream kinematic or shock waves are modeled.

The default value in StreamLine is set to 35 km2/h.

Kappa (κ)

Kappa influences the anticipation term. The formula of the anticipation term shows that the influence of kappa on the speed depends on the density and the density changes on the link. When kappa increases, the anticipation term will be relatively smaller since the denominator in the formula increases faster.

The default value in StreamLine is set to 13 km/h.

Unfortunately, in OmniTRANS manual there is very little information about these parameters; most of the information above was gathered from different sources. One recommendation could be to give more details about these terms and their influences. We will show later how sensitive is the model according to the changes in these terms.

Another important factor that influences the speed on the links is connector’s speed. As we mentioned earlier, regarding the anticipation term, vehicles would anticipate the difference between the density on the current and the next link segment. Therefore by changing the speed (and hence: density) of the connectors we are expecting to see the gradual changes in speed of the link upstream of the connector. Also, launching vehicles with a given speed from a connector into the network influences the speeds in the first links through the convection mechanism. Obviously, the influence of connector speeds further into the network fades as the distance from the connector increases. Hence, it is limited to the (immediate) vicinity of connectors and may therefore be strong in small networks, but relatively small in larger networks.

In the following, we will examine different cases where anticipation parameter Nue (ν) and connector’s speed changes. Since our model is very simple we won’t go more into the details of changing all speed’s term parameters.

Free Flow with connector’s speed 90 km/h

As a first test case, we use mentioned network along with connector’s speed 90 km/h. Regarding the underlying knowledge of second order models, we expected to see the smoothed propagation of flow in the network. Since speed of the first link (120 km/h) is higher than the speed of origin connector (90km/h) we expected to see the speed in the first link gradually increase up to the free flow speed and free flow speed for the proceeding links. This can be seen in the Figure 2.

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Figure 2: Speed of the links when connectors speed are set to 90km/h

Link 1 and link 3 have relatively lower speed compare to link 2 since they both are connected to the origin and destination connector (at 90 km/h) respectively. Note that in the high demand period, where traffic is loaded to 88% of capacity, speeds are still between 110 and 115 km/h, whereas the speed_at_capacity parameter is set to 90 km/h and traffic enters the network from a connector at low speed (90 km/h) already. It is unclear how speeds can increase so high (close to free speed of an unloaded link whereas we are close to capacity), which seems inconsistent with the input parameters.

Free Flow with connector’s speed 50 km/h

By decreasing the connector’s speed to 50 km/h, we would let the flow enter the model with the lower speed (link 1) and anticipate to lower speed (link 3) than the previous test and we expected to see more difference between link 1 and 3 on the one hand, and link 2 on the other hand. This can be seen in the Figure 3. Again in link 2, which is least influenced by the connectors, speed reaches 115 km/h at 88% load, which seems illogically high.

Figure 3: Speed of the links when connectors speed are set to 50km/h

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Free Flow with connector’s speed 90 km and different Nue parameters value

By increasing the anticipation factor Nue from 35 to 140, the difference between link 2 and link 1 should be smaller: the higher the value, the stronger the influence of anticipation relative to convection from the slower connector. This can be seen in the Figure 4.

Figure 4: Speed of the links when connectors speed are set to 90km/h and anticipation factor (Nue) is set to 140 km2/h

For the same reason, link 3 is now slower as it adjusts stronger to the destination connector with lower speed.

In Figure 5 we can see the flow propagation along with demand pattern (speed parameters have been reset to default values). This shows the transient phase from empty network to the full load and again empties the network.

Demand Properties

Figure 5: Flow propagation in free flow condition network

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Flow has been smoothed and enters the network gradually. This means forward waves are dispersed significantly because of the speed dynamics.

To summarize the first test case (free flow without queue at the origin), it seems free flow propagation, despite its theoretical simplicity, exhibits some problematic behavior:

speed of connectors has significant influence on propagation speed in the actual network, especially close to the connectors (less of an issue in larger networks)

even though free speed and speed_at_cap can be differentiated, simulated speed values seem to depend less on flows (close to capacity) than one may expect

The influence of parameters in the speed equation is not well documented and makes it difficult for the modeler to control propagation.

1.1.2 Free flow propagation with queue at the origin

In this test case, the demand is increased up to 4200 (more than capacity). The aim here is to test what happens when queue is already built up at the origin.

In this case we use the same network as case 1 except for the demand pattern which is configured in Figure 6.

Figure 6: Demand pattern and maximum network capacity for free flow with queue at the origin

As we see, in second time slice, demand is increased up to 4200 which is 200 veh/h more than links capacity.

Same as previous case, we checked both conditions when the speeds of connectors are varied from 50 km/h to 90 km/h, see Figure 7 and Figure 8.

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Figure 7: Speed pattern when connectors speed are set to 90 km/h

Figure 8: Speed pattern when connectors speed are set to 50 km/h

Both graphs shows the same pattern when speed on the first link drops dramatically caused by queuing vehicle at the origin. This is because of convection from the connector, in which the speed decreases over time as more queue is accumulated. However, one may wonder how realistic it is if the average speed of traffic over a 5km link downstream of a queue still has not increased above 60 km/h. We therefore doubt whether the default speed parameters are empirically correct. However, as they influence many more traffic flow phenomena, it is likely that optimal calibration for phenomena downstream of congestion would turn out to be suboptimal for other traffic flow phenomena (capacity drop, shock wave propagation, spillback over nodes) and vice versa. This raises the question: even if one spends maximal efforts in calibration of the speed dynamics, does there

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actually exist a single set of optimal parameters that yields acceptable validity for all relevant traffic flow phenomena simultaneously?

Speed on second link in both cases is identical and speed on link 3 in the case with connector’s speed at 50 km/h is reduced due to anticipation term.

Comparing the flow propagation figure and demand graph, the smoothing of flow propagation can be seen, see Figure 9

Figure 9: Flow propagation when queue is at the origin

From the figure above we can see that when queue is at the origin, the links won’t be used by their capacity. In this case the capacities of the links are 4000 but they don’t reach up to 4000. Apparently, the speed dynamics lead to a certain level of capacity drop. Although this may be qualitatively realistic (capacity drop is a confirmed empirical phenomenon), it is unclear how it can be quantitatively controlled in StreamLine.

Before moving to the next test cases, we do a final check to verify whether by disaggregating the longer link we will observe the same output results. To do so, the first link has been divided into 5 links with the same length of 1 km and same test cases have been done. Comparing the result of both cases, aggregated and disaggregated proves that the results of downstream links are satisfactorily consistent.

Figure 10 shows the correlation of density at the downstream link after disaggregation (in previous case we called that link as link number 2).

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Figure 10: Density correlation by disaggregating the link

Although by looking at the figure above we can see that aggregation and disaggregation of the link (fortunately!) doesn’t change the outcome of the proceeding links (and hence we would typically recommend parsimonious modeling with the least possible links), better understanding of the fundamental variables and visualization motivate us to use disaggregated links for several test in this report.

Therefore from now on, we use disaggregation for the sake of better understanding.

To conclude this test case, we can see that when there is insufficient capacity for all traffic to enter the network:

no traffic is lost, rather a queue forms at the origin as it is supposed to

however, downstream of this queue,

o speeds are unrealistically low over multiple kilometers

o The model exhibits capacity drop, which is qualitatively ok, but because its extent cannot be controlled, one should question the quantitative validity of this phenomenon in the model. In general, our attitude towards models is: every relevant phenomenon that affects the outputs needs to be controllable by setting independent parameters with understandable influence on that phenomenon. This is not the case for the speed dynamics.

1.2 In other to test bottleneck activation, discharge and dissipation, three scenarios have been defined. Fixed Bottleneck with constant high demand (1.2), Fixed bottleneck with peak high demand (1.3), and Temporary bottleneck with constant demand (1.4).

1.2 Stationary bottleneck and demand is too high over entire time domain

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The aim of this test is to check the activation, shock wave and discharge behavior of a fixed bottleneck. Please refer to point 1.2 at section Aims.

In this scenario we used the same network (see Table 2) as in the previous test case although the first link has been divided into several smaller links. This network consists of 9 links (two connectors) with the Free speed 120 (km/h), speed at capacity 90 (km/h) and saturation flow 2000 (veh/h/lane) and each link has two lanes. Exceptions are the bottleneck link 5 with 1500 veh/h/lane over 2 lanes and the connector with speed 90 (km/h) and 4600 (veh/h) capacity.

Supply Propert ies

Table 2: Network properties

Supply Type Capacity Length (km)

Free Flow

Speed

Speed at Cap

No. of Lane

Link 1:7 5 4000 1km 120 90 2

Link 5 (Bottleneck)

5 3000 1 120 90 2

Connector_90 1 4600 1 90 50 2

The departure pattern is shown in figure below. The simulation time contains four hours and is divided in four equal intervals. The demand on the network in the first three intervals are set to 3800 veh/h which is higher than the capacity of the bottleneck (3000 veh/h) and a congestion situation occurs. In the fourth time slice the demand on the network decreases to zero to empty the network which makes that the congestion in the network slowly disappears.

Demand Properties

Figure 11: Flow propagation with stationary bottleneck

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w (

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/h)

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Link 2

Link 3

Link 4

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Link 6

Link 7

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In the Figure 11 shows that when the fixed bottleneck is activated, the links after the bottleneck are used with their full capacity. This has contradiction with what has been observed in the previous case.

Links 6 and 7 are located downstream of the bottleneck. As can be seen, the capacity drop observed in the previous test does not occur in this case and outflow sets exactly at the bottleneck capacity of 3000 veh/h. Although this may seem evident, it is not what one would expect in a second order model as we discuss in the text box (capacity drop – or on the contrary overshoot – would actually be more consistent with the default 2nd order speed dynamics). We suspect that some heuristic rule in the software here overrules the speed dynamics; the contradiction with the previous test is likely because this rule is not active in the specific case when a bottleneck activates in the transition from connector to actual links. We consider such heuristic to be an improvement over default 2nd order propagation behavior which in this scenario seems to work quite well.

Figure 12 shows the progress of activation of the bottleneck and its discharge over time.

Time Flow (veh/h)

4 min

(7:10)

Intermezzo: 2nd order bottleneck discharge behavior

Let us analyze the outflow at the location of a bottleneck (transition node from higher to lower capacity). Outflow would only match exactly capacity (top of the fundamental diagram) and remain there stably, if density and speed of the bottleneck cell would remain exactly on the fundamental diagram (only then the relaxation term would be zero), AND the sum of anticipation and convection terms is zero. Otherwise the speed dynamics would increase or decrease speed, such that speed x density would no longer equal capacity. (NB: note that theoretically there is still another possibility: speed x density in bottleneck cell = capacity AND sum of three speed terms (each ≠ zero) equal to zero, which would even be more of a coincidence than the situation discussed below).

Sum of anticipation and convection terms would be zero only if both terms are zero OR if they would be exact opposites. Can this happen?

Both terms equal to zero will not occur, as this would require speeds and densities to be equal in successive cells, which is by definition of a queue head not the case. Both terms to be exact opposites would be an extreme coincidence: there is no reason why density and speed differences in both cells would make both terms opposites; moreover they are highly dependent on nue tau and kappa parameters which makes this even less likely.

Conclusion: in pure 2nd order dynamics, there is no reason why discharge of a bottleneck would remain constant and equal to capacity in the fundamental diagram. Rather one would expect higher or lower outflow that evolves over time, dependent on the fundamental diagrams of the

cells involved and on all the dynamic speed parameters.

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10 min (7:10)

20 min

(7:20)

40 min

(7:40)

100 min

(8:40)

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182 min (10:32)

Figure 12: Flow propagation with stationary bottleneck

Completely dissolved at T = 237 min (10:57).

Queue discharge in the beginning of simulation

Even though the bottleneck outflow seems to settle exactly at 3000 veh/h, a closer analysis reveals that in the beginning of the simulation, a temporary mild drop is present (of about 5%). Also, the trajectory of states and the final discharge rate of 3000, are certainly not exactly on the fundamental diagram. The next series of graphs shows how traffic state first reaches to 3000 veh/h approximately, after which density increases and speed decreases simultaneously, herewith keeping the flow near capacity (see Figure 13). Next, this state stabilizes at flow near capacity; it is unclear what determines the exact density at which this stabilization occurs.

Time Density (veh/km/lane)

4 min

(7:10)

10 min

(7:10)

20 min

(7:20)

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40 min

(7:40)

100 min

(8:40)

182 min (10:32)

Figure 13: Density pattern in stationary bottleneck with default parameters

The following graphs show the flow-density and speed-density diagram for the bottleneck link (link 5) and one link after that (see Figure 14, Figure 15).

Figure 14: Flow - Density (left) and Speed – Density (right) for link 5 (bottleneck)

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3500

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/h)

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Link 5_Flow vs Density

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140

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d (

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)

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Link 5_Speed vs Density

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Figure 15: Flow – Density (left) and Speed - Density (right) for link 6 (bottleneck downstream)

Influence of anticipation parameter (Nue)

If we put Nue equals to zero we would remove the anticipation term. We would expect traffic to propagate until it is inside the bottleneck link 5 (since it didn’t anticipate to it) and then the relaxation term would push speeds, and herewith flow, down (see Figure 16). Severe congestion would form inside the bottleneck with density diverging to infinity, as upstream traffic does not anticipate this queue and keeps on flowing in. We indeed observe the density increase inside the bottleneck. However, apparently another heuristic rule in the StreamLine software prevents excessive density by somehow reducing the inflow when a certain maximum density is reached. As a result, congestion spills back, finally into the origin. This can be seen in the Figure 17. One can conclude that the software here overrules the misspecification by the user (who should never have chosen such low Nue values in the first place!) in order to keep density within reasonable limits.

Time Density (veh/km/lane)

10 min

(7:10)

20 min

(7:20)

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500

1000

1500

2000

2500

3000

3500

0 5 10 15 20

Flo

w (

veh

/h)

Density (veh/km)

Link 6_Flow vs Density

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120

140

0 5 10 15 20

Spee

d (

km/h

)

Density (veh/km)

Link 6_Speed vs Density

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40 min

(7:40)

60 min

(8:00)

80 min

(8:20)

Figure 16: Density pattern in stationary bottleneck when anticipation parameter is zero

Figure 17: Flow - Density (left) and Speed – Density (right) for link 5 (bottleneck)

In the other test, Nue parameter, increased up to 140 which is its maximum value according to literature. In this case, we expected to see the mild congestion effects from links before the bottleneck and it will propagate much faster upstream because all vehicles respond very strong to the slightest density increase downstream (see Figure 18).

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3500

0 50 100 150 200

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/h)

Density (veh/km)

Link 5_Flow vs Density

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d (

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Link 5_Speed vs Density

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Time Density (veh/km/lane)

10 min

(7:10)

20 min

(7:20)

40 min

(7:40)

60 min

(8:00)

180 min

(9:30)

Figure 18: Density pattern in stationary bottleneck when anticipation parameter is zero

Figure 19 and Figure 20 show the fundamental diagrams of bottleneck and upstream link.

Figure 19: Flow - Density (left) and Speed – Density (right) for link 5 (bottleneck)

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3000

3500

0 5 10 15

Flo

w (

veh

/h)

Density (veh/km)

Link 5_Flow vs Density

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140

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Link 5_Speed vs Density

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Figure 20: Flow - Density (left) and Speed – Density (right) for link 4 (upstream link of bottleneck)

This case shows the sensitivity of the model on the speed anticipation parameters which has been already confirmed.

As conclusion for this test, we can see that:

in contrast to (and better than) what is expected from a default 2nd order model, StreamLine respects rather well capacity of fixed bottlenecks. Discharge of bottleneck initially exhibits some transient behavior that we were unable to explain (but which may not be that problematic in practice).

Behavior upstream of the bottleneck (shock wave) is extremely sensitive to the Nue parameter of the speed dynamics (which is logical as it is the only mechanism controlling upstream behavior) that hence needs to be calibrated carefully. The software however protects unrealistic high density values from occurring if the user misspecifies Nue.

1.3 1.3 Stationary bottleneck and demand is too high only during some peak between t1 and t2 The aim of this test is to check the activation and dissipation of fixed bottleneck under dynamic demand. Please refer to point 1.3 at section Aims.

In this scenario, the network and location of the bottleneck are like the previous test case (see Table 3) and time is again divided in four equal intervals of 3600 seconds (1 hour). In the first hour, the demand is set to 2000 veh/h, in the second hour, demand is increased to 3800 veh/h, then demand decreases again down to 2000 veh/h and in the last time segment there is no traffic departing. The demands are chosen in such a way that in the second hour, demand will be higher than capacity of the bottleneck and congestion will be formed.

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Link 4_Flow vs Density

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Link 4_Speed vs Density

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Supply Propert ies

Table 3: Network properties

Supply Type3 Capacity Length (km)

Free Flow

Speed

Speed at Cap

No. of Lane

Link 1:7 5 4000 1km 120 90 2

Link 5 (Fixed Bottleneck)

5 3000 1 120 90 2

Connector_90 1 4600 1 90 50 2

Demand Properties

Figure 21: Flow propagation with stationary bottleneck and peak demand

In Figure 21, the pattern of flow propagation in the network can be seen. Before peak demand, all links were used below their capacity and by the time that demand increase more than capacity of link 5, queue starts to form and spills back. Following figures show the numerical and graphical congestion formation and its spillback. As in the previous case, capacity discharge is remarkably well reproduced.

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1500

2000

2500

3000

3500

4000

7:00 7:30 8:00 8:30 9:00 9:30 10:0010:3011:0011:30

Flo

w (

veh

/h)

Link 1

Link 2

Link 3

Link 4

Link 5

Link 6

Link 7

Demand

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Time Flow (veh/h)

30 min

(7:30)

70 min

(8:10)

120 min

(8:30)

190 min

(9:10)

240 min (10:00)

Figure 22: Flow propagation in stationary bottleneck with peak demand

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Another interesting graph that shows the congestion’s effect is space time diagram (see Figure 23). Although this figure cannot be easily extracted from OmniTRANS, Matlab user interface make it easier to have an access to the database tables and filter required data.

Figure 23: Space – Time diagram when link 5 is stationary bottleneck with peak demand

As can be seen from the figure above, congestion starts shortly after peak demand reaches the bottleneck. Spillback (even into the origin) and dissipation look consistent with theoretical expectations.

As we showed in this test case, activation of a stationary bottleneck and resulting queue propagation are modelled adequately. Outputs can be analyzed numerically and graphically, and can be exported for additional analysis and visualization.

1.4 1.4 Temporary bottleneck during an incident between t3 and t4 when demand OD is constant The aim of this test is to see the ability of temporarily bottleneck modeling and its characteristics. (refer to Aims 1.4)

In this test, we consider the same supply part of previous network; although Link 5 is now a temporary bottleneck (see Table 4). The capacity of this link has been reduced from 4000 to 2000 veh/h for one hour. Meanwhile the demand profiles keeps sending 3000 veh/h for 3 hours. As a result we expect to see the congestion trigger shortly after temporary bottleneck formation, discharge during one hour at reduced capacity of 2000 veh/h and restore later to the original capacity of 4000 veh/h.

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4 Please check the OmniTRANS file for more information

Supply Propert ies

Table 4: Network properties

Supply Type4 Capacity Length (km)

Free Flow

Speed

Speed at Cap

No. of Lane

Link 1:7 5 4000 1km 120 90 2

Link 5 (Temp Bottleneck)

5

2000

(7:30-8:30)

1 120 90 2

Connector_90 1 4600 1 90 50 2

Two options are available in order to make temporary bottleneck in OmniTRANS; Outflow limit control and Dynamic link attributes Adapter changes. The Outflow limit control only reduces the output, while the Dynamic link attributes Adapter changes the speed-flow curve. In the first case, the original curve is used, but after the calculation, the software simply checks the maximum allowed outflow. That is the speed won’t be on the fundamental diagram while using Outflow limit. Figure 24 illustrate the case that both options were tested.

Figure 24: Speed difference with capacity reduction alternatives

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-5 -4 -3 -2 -1 0 1 2 3 4 5Sp

ee

d D

iff

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tFlo

w -

Dyn

am

ic)

Density Diff (Outflow - Dynamic)

Speed Difference

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As it can be seen, with the same density, these options provide different speed values.

In this test, we chose Dynamic link attributes Adapter in order to be consistent with the aim of this test and the theory behind it

Demand Properties

Figure 25: Flow propagation with temporary bottleneck

As can be seen in Figure 25, by activating the temporary bottleneck, congestion forms with bottleneck discharge exactly equal to reduce capacity: no capacity drop is observed during the temporary blocking. However, when capacity is restored, outflow is lower than the original capacity of 4000 veh/h: again some sort of capacity drop is observed (to 3800 veh/h approximately). Even though we do not report them here, additional tests show that this capacity drop depends on the dynamic speed parameters, as can be expected from theory.

By looking at Figure 26, congestion formation and discharge, as well as dissipation of the queue when capacity is restored can be seen graphically.

Time Flow (veh/h)

29 min (7:29)

One min before temp

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/h)

Link 1

Link 2

Link 3

Link 4

Link 5

Link 6

Link 7

Demand

BottleneckCap

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45 min

(7:45)

89 min

(8:29)

One min before relax

105 min

(8:45)

180 min

(9:30)

Figure 26: Flow propagation in temporary bottleneck

Looking at the space time diagram below, Figure 27, also gives us better understanding of queue formation and dissipation when a temporary bottleneck activated. This plot is consistent with theoretical expectations.

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Figure 27: Space – Time diagram when link 5 is temporary bottleneck

As conclusion for this test, making temporary bottleneck is possible in two ways, filtering the outflow with changing the speed or change the link attributes while filtering the outflow. Both can be done easily and the output results are precise to what is expected. Capacity drop does not occur while temporary bottleneck is active. However, during dissipation after capacity has been restored, capacity drop is present, dependent on the dynamic speed parameters. Even though this is qualitatively correct, one must wonder about the usefulness of this feature as it is not controllable (or at least not independently from other dynamic propagation phenomena).

1.5 1.5 Speed limit modeling Not tested yet

1.6 1.6 Variable speed limit In all macroscopic dynamic traffic assignment models, the fundamental diagram plays a vital role as it defines the relationship between speed and density and is used in determining how fast the traffic can propagate across the transport network. In StreamLine, it is embedded in the framework in various forms (METANET, Van Aerde), but no matter what type is chosen it eventually comes down to a few properties that are used during simulation:

Speed

Capacity (saturation flow)

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Speed at capacity (critical speed)

The Dynamic Link Characteristics Adaptor control is able to adjust these properties on a per mode basis for a certain link at pre-specified times during the StreamLine simulation run. This allows the user to change the free speed or the capacity per lane or even the speed driven by users at capacity. This control is very generic and can therefore be used for a different number of real world situations such as:

Road works (capacity reduction)

Variable speed limits (speed adjustment)

Weather changes (capacity reduction, speed at capacity reduction)

For testing Variable Speed Limit (VSL), a small test case has been defined.

Supply profile

Table 5: Network properties

Supply Type Saturation

(veh/h/lane)

Length (km)

Free Flow

Speed

Speed at Cap

No. of Lane

Link 1:7 5 2000 1 120 90 1

Connector_90 1 4000 1 120 90 1

Link 5 (DTM) 5 2000 1 80

(9h-10h)

60 1

Demand Profi le

Table 6: Demand pattern

Demand 7:00-8:00 8:00-11:00 11:00-12:00

Flow(veh/h) 1000 2000 0

The following XT plots show the activation of Variable Speed Limit.

Keep in mind that in scenario without VSL, critical density is 22.22 veh/km and when speed is decreased from 120 to 80 as free flow speed and speed at capacity from 90 to 60 within 9-10h the critical density increased up to 33.33 veh/km. these changes can be seen in the following XT plots, see Figure 28 and Figure 29.

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Figure 28: Space – Time diagram when VSL is not activated

Figure 29: Space – Time diagram when VSL is activated

We conclude that StreamLine offers a quite flexible facility to implement time-varying supply characteristics in the form of time-varying fundamental diagrams, herewith enabling to model dynamic traffic control, dynamic behavior, VSL etc. The time-dependency should however be given exogenously; there is no adaptation to the simulation state, which could for instance change speed limits automatically as soon as in the DNL certain thresholds would be passed. The Ruby script language enables to create such adaptability as an exogenous loop as a consistency problem (i.e. iteratively define dynamic VSL as a function of DNL propagation, and DNL as a function of time-varying VSL until consistency).

1.7 1.7 Shoulder lane modeling Shoulder lane modeling can be done by Lane Adaptor attribute. The Lane Adaptor control is meant to dynamically change the number of lanes on a link during the StreamLine simulation run. Extra lanes can be added or existing lanes can be closed at user specified times.

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SL_MADAM and Lane Adaptor

The way that a change in lane configuration is modelled is dependent on the chosen propagation model. For SL_MADAM, a change in lane configuration has direct impact on the variables being tracked, i.e. density, speed and (out) flow. Here is what happens under the hood:

The number of lanes is updated according to the new situation

The density is updated based on the new number of lanes

o The new density is based on the difference in capacity between the original situation and the new situation. This difference is then applied to the current density (inversed).

o When the new number of lanes is less than before, it is possible that the density exceeds the maximum density set for a link. This however is a realistic situation; whenever a lane is removed while the link is congested it will lead to more cars than can actually fit on the link. In this situation there is no inflow possibly anymore until the density will drop below the maximum density again.

The outflow is recalculated

o As the flow is dependent on density, we have to update the outflow as well based on the new density.

The characteristics of the link are updated

o A change in the number of lanes can lead to a different way of calculating the speed. SL_MADAM takes merge effects and lane drops into account and changing the number of lanes on a link can have impact on these calculations. Therefore the link calculation characteristics have to be adjusted based on the new situation.

For testing the shoulder lane running, small test case has been defined.

Supply profile

Table 7: Network Properties

Supply Type Saturation

(veh/h/lane)

Length (km)

Free Flow

Speed

Speed at Cap

No. of Lane

Link 1:7 5 2000 1 120 90 1

Connector_90 1 4000 1 120 90 1

Link 5 (DTM) 5 1000 1 120 90

2(8-9h)

1 (otherwise)

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Demand Profi le

Table 8: Demand pattern

Demand 7:00-8:00 8:00-9:00 9:00-10:00 10:00-12:00

Flow(veh/h) 800 2000 800 0

With these settings there is a 1000 veh/h bottleneck in link 5 in absence of shoulder lane use. With activation of the shoulder lane, total capacity is in theory 2000 veh/h which should just be sufficient to accommodate demand. The results are shown in Figure 30 .

Time Density (veh/km)

7:30

Low Flow

o Density

o Flow

o Speed

Shoulder Lane will be activated during 8h-9h with one extra Lane. The capacity of Link 5 will be 2000 veh/h and demand also will be 2000 veh/h

8:30

High Flow

o Density

o Flow

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o Speed

Demand decreases to 800 and shoulder lane capacity remains at 1000

9:30

Low Flow

o Density

o Flow

o Speed

Figure 30: The effect of shoulder lane running

As can be seen from figures above, activation of shoulder lane can facilitate the traffic flow. Although it appears that increasing the lanes from 1 to 2 lanes in link 5 does not directly increase the saturation to 2000. As mentioned before, changing lanes leads to modified speed calculations and density difference; the impact of this on capacity is apparent in the results, but not very well understood by us. Although we agree qualitatively that shoulder lane running does not warrant full capacity, we prefer a modeling mechanism with more direct quantitative control over this phenomenon (e.g. give the user responsibility for defining the true additional capacity of the shoulder lane).

Following graphs show two scenarios;

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shoulder lane is not activated (we have temporary bottleneck due to having higher demand than link 5’s capacity)

shoulder lane is activated (trying to relax the bottleneck capacity by adding one extra lane)

Figure 31: Space – Time diagram without shoulder lane running

Figure 32: Space – Time diagram with shoulder lane running

The XT plot in the first row shows the first scenario (see Figure 31), when we have temporary bottleneck due to higher demand. Second row (see Figure 32), shows the second scenario when extra lane activated to accommodate the extra demand. Due to lane changing and diverge effects, capacity drops can be observed. Comparing these two scenarios, it’s clear that adding extra lane plays significant role although due to lane changes full capacity usage cannot be observed.

Figure 33 shows the travel time comparison between these scenarios.

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Figure 33: Travel time with (light blue line) and without (dark blue line) shoulder lane

Just like with VSL, Lane adaptor that is used in this case for shoulder lane test case should be defined exogenously, meaning that it’s not possible to trigger this control regarding defined attributes (such as when density exceed specific amount, shoulder lane can be activated).

Another alternative that can be used instead of lane adaptor is Dynamic Link Attributes adaptor. The later control gives different attributes for modifications, like free flow speed, speed at capacity and saturation flow within pre-defined time interval. Since this control has already been tested in previous cases (temporary bottleneck) we excluded it for further analysis.

1.8 1.8 Detector modeling Not tested due to lack of time.

1.9 1.9 Output visualization In order to get the graphs out of Omnitrans, the safest and best option is to get it externally from the database. Unfortunately there is no function to get a space-time diagram using OmniTRANS. It has to be made manually, e.g. using a script to collect the data and plot it using the OtChart class or using Matlab or other software to draw desired graphs.

In this case study, we collected the data from the database and used excel. Another option was to use OtChart but the quality was not satisfactory and required more time to understand the codes.

1.10 1.10 Retrieve output Most of output can be extracted from the database although specification clarification of the output may need to be developed. As an example it is not unambiguously clear what you see as load: is it inflow, outflow or average flow?

1.11 1.11 Travel times result Ran and Boyce (1996) suggested two travel cost concepts such as ‘ideal’ and ‘instantaneous’ route travel costs in dynamic assignments. The ‘ideal’ or ‘realistic’ (Predictive in StreamLine) route travel cost is the one that a traveler will experience whilst

0

10

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30

40

50

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70

7:30 8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00

Trav

el t

ime

(min

)

Choice Moment Departure time

Travel Time

Before Shoulde Lane Usage After Shoulde Lane Usage

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traversing the network. In other words, when we calculate a route travel cost, we take account of the fact that it takes some time to exit a link after entering it, and the network conditions may have changed by that time. Accordingly, the cost on the next link is calculated based on the condition at the time of entry to the link. On the other hand, when we calculate the ‘instantaneous’ or ‘naive’ (Reactive in StreamLine) travel cost, we assume that current network conditions will not change substantially unti l travelers arrive at their destinations. Therefore, the instantaneous travel cost is calculated by summing the travel cost on each of the links that form a route at the time of entry to the first link.

In StreamLine both options are available and can be selected. Although predictive travel time calculation cannot be used for the first iteration since it looks back to previous iteration to calculate the travel time. For this test, reactive travel time method is used. For more information please check the OmniTRANS manual.

Any other business

New questions triggered

Conclusions Conclusion from the test result on this aim

Passed/ failed/ unanswered/

partially failed (mark bold if critical)

Perspective offered by developers: are we aware of plans to improve this result e.g. in next releases? if so, when?

1.1 Propagation model was evaluated in two scenarios, where the network was in free flow condition and when queue was present in the origin.

In the case of free flow propagation:

Speed of connectors plays an important role and can influence speed propagation especially for the links connected to them. This can cause an issue in small networks and links near origins/destinations in large networks.

Even when the network was utilized near capacity, simulated speed showed little sensitivity to level of the flow.

The influence of the parameters in the speed equation is not well documented and makes it difficult

Partially Passed

Connectors speed

Speed term’s parameters calibration

Speed reduction near capacity usage

Unrealistic low speed when having queue at the origin

Capacity drop behavior

G-LTM propagation model is being implemented, which is a first order model with fundamentally different propagation. A test version was available for this project, but was just too immature (and not documented) to be used in this test.

It is as yet unclear which issues of current propagation in StreamLine (Madam model) this new model will solve, and whether it will exhibit new issues.

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for the modeler to control propagation.

Because of speed dynamics, flow smoothed and gradually entered the network.

In the case of having queue at the origin, :

No traffic is lost, rather a queue forms at the origin as it is supposed to.

however, downstream of this queue,

speeds are unrealistically low over multiple kilometers

The model exhibits capacity drop, which is qualitatively ok, but because its extent cannot be controlled, one should question the quantitative validity of this phenomenon in the model.

It seems, it’s very difficult to calibrate a single set of optimal parameters in speed terms that yields acceptable validity for all relevant traffic flow phenomena simultaneously.

1.2 The test with a stationary bottleneck at high demand OD over entire time domain revealed that:

StreamLine respects rather well capacity of fixed bottlenecks, in contrast to (and better than) what

Partially passed

Speed Term’s parameters calibration

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is expected from a default 2nd order model.

Upstream of the bottleneck is highly sensitive to Nue parameter of the speed dynamics (which is logical as it is the only mechanism controlling upstream behavior) that hence needs to be calibrated carefully.

By defining the maximum density, StreamLine protects unrealistic high density values from occurring if the user misspecifies Nue.

Fixed bottleneck activation & dissipation due to demand excess is thus modeled correctly however, calibration of speed term’s parameter is still questionable.

1.3 The test with temporary demand excess for a fixed bottleneck showed that activation of the bottleneck and queue propagation are modelled adequately. Outputs can be analyzed numerically and graphically, and can be exported for additional analysis and visualization.

Passed

1.4 Making temporary bottleneck can be done in two ways. We discussed the difference between those ways and showed how the queue formation and dissipation when a temporary bottleneck activated is consistent with the expectations.

The model does not exhibit any capacity drop during bottleneck activation. However, during

Partially Passed

uncontrollable capacity drop behavior

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dissipation after capacity has been restored, capacity drop is present, dependent on the dynamic speed parameters. Even though this is qualitatively correct, one must wonder about the usefulness of this feature as it is not controllable (or at least not independently from other dynamic propagation phenomena).

1.5 Not tested

1.6 StreamLine offers a quite flexible facility to implement time-varying supply characteristics herewith enabling to model dynamic traffic control like VSL. The time-dependency should be given exogenously; there is no adaptation to the simulation state.

The Ruby script language enables to create such adaptability as an exogenous loop as a consistency problem (i.e. iteratively define dynamic VSL as a function of DNL propagation, and DNL as a function of time-varying VSL until consistency).

Output of this method gave plausible results

Passed

VSL can be modeled exogenously or using Ruby script in a loop along with DNL.

1.8 Shoulder lane running can be modeled in StreamLine via Lane adaptor or Dynamic Link Attributes Adaptor. Both can be modeled exogenously, meaning that it’s not possible to trigger this control regarding defined attributes.

Passed partially

Same as previous vase, Shoulder lane running can be modeled exogenously

No exact control over impact on capacity

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Output of this method gave qualitatively plausible results: capacity is affected by temporarily adding lanes. However, there is no (or very difficult) control over the level of capacity reduction. A user-defined impact would be more desirable.

1.9 Interface and access to database is rather complete, even though not all the output can be visualized. For example route cost can be exported but it’s not possible to visualize it directly using OmniTRANS interface.

Other output can be visualized using OmniTRANS interface or OtChart codes.

Passed

Expect route cost, the rest can be visualized or exported

1.10 The output can be exported using Ruby scripts, Matlab interface, direct copy from database, making a report using OmniTRANS.

Partially passed

Output specification is not clearly documented (what does load mean; inflow, outflow or average flow?

The modeler is limited to use one programing language (Ruby)

1.11 Travel time can be calculated using reactive (instantaneous travel times) or predictive (trajectory based travel times). In this test, reactive method is applied since only one iteration was used.

Passed

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Test ID 2

Topic Propagation mechanism

Test 2 Uninterrupted corridor (merges and diverges)

Network

We consider this corridor with two on-ramps and one off-ramp. The capacities and demand levels will change depending on the exact scenario and what we want to test there. This network allows us to create the following scenarios:

simple merge with free outflow in C

simple merge with potential spillback of the outflow in A

simple diverge with free outflow in B

simple diverge with capacity constrained outflow in B

simple diverge with spillback constrained outflow in B

Relevance On motorways, backbone of almost any regional network, the main source of delay is congestion, the main source of congestion are discontinuities: merges and diverges (possibly combined into weaving sections). Merges and diverges are thus crucial as triggers of congestion. Moreover, the spatial extent of congestion (spillback) can cause delays to traffic that does not pass the cause of the congestion, but intended to leave the network upstream of the bottleneck, however after having suffered part of the bottleneck queue (blocked off-ramp phenomenon). Hence, it is important that spillback from primary bottlenecks to upstream links is modeled reliably. This is another role of merges and diverges (in addition to being potential primary bottlenecks): do they cause the right amount of spillback to the right upstream links, creating the right amount of delay?

Motivation In a corridor, different routes can be present (ie: one for each OD). Generally it is quite clear how link travel time (travel speed) is defined. However, the way in which link travel times are aggregated to route travel times (if provided at all in the outputs) may know degrees of freedom. This is comparable to the various travel time algorithms as discussed in (Himpe et al. 2012): piecewise constant speeds, piecewise

linear speeds,…

O1 B C D2

O2 O3D1

A

01A 02A AB BC BD1 O3C CD2

length 5 5 5 1 1 5 1

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Even though the process at merges and diverges may seem quite chaotic at times in reality, in a model there are certain requirements that merge and diverge models should meet in order to be consistent models. Here are some theoretical considerations for both models.

Merge

The theory of merging models states that a set of constraints needs to be fulfilled for any merge model (see Tampère et al., 2011; or earlier Daganzo, 1995):

- all flows should be positive at all times - continuity needs to be respected over the merge: the outflow should at all times be equal to the sum of the inflows - outflow should never exceed the capacity of the receiving link, neither the max receiving flow of the receiving link (which can be

lower than capacity eg in spillback conditions)

- neither of the inflows should exceed the capacity of the corresponding sending link - neither of the inflows should exceed the sending flow of the sending link (that is, the amount of traffic that was able to reach the

end of the sending link) - there exists a degree of freedom whenever the sum of inflows exceeds the receiving flow: there is then a constraint on the sum

of the inflows, but ambiguity remains about the separate values of the terms in the sum

- this degree of freedom needs to be additionally specified, taking into account the following: o realism: the real reason to specify the DoF is that it best reflects real behavior at merging points. In fact, the macro

assignment of outflow opportunities over the candidate incoming links is an aggregate of the underlying microscopic behavior. That is why for instance the number of lanes may be a good indicator of this assignment: if X outflow opportunities per time unit occur towards a 3-lane outgoing link, it is reasonable to believe that the sending link with 2 lanes will consume double of those opportunities compared to his 1-lane sending link competitor in the merge.

o invariance principle: the assignment of outflow opportunities over sending links should be invariant for substituting the sending flows of the incoming links with their corresponding capacities. Otherwise the model would give instable results (flip-flop). Eg a rule based on ‘demand’ (=sending flow) will not be invariant: constrained receiving flow is assigned over the sending links according to the sending flows; suppose this causes a queue to grow on both sending links. Now they would both send capacity towards the merge (discharge from queuing), which would yield a different assignment of receiving flow over the sending links. Cases can be constructed in which this new assignment makes one of the incoming queues dissolve, after which the process repeats in oscillation.

o flow maximization: each flow in the merge is limited by either the sending flow, or by the receiving flow (or exceptionally by both); no flow should be strictly lower than all of its constraints; in other words: all flows should be actively constrained by either merge demand (sending flow) or supply (receiving flow)

Diverge

For diverges, the following theoretical requirements hold:

- same positivity, continuity, capacity and flow maximization requirements as merge; - in the single sending link, traffic is combined that is bound for the various outflow links. The ratios of these turning movements

(called turning fractions) need to be respected in the solution of the model. Eg. if 1 out of 4 vehicles in the sending link want to turn left, and the left receiving link can only accommodate half of this turning flow, then also the outflow from the sending link towards the other outgoing links will be restricted to half of the sending flow. Note that this is the same as requiring FIFO (first-in first-out) at the link end, as if no overpassing is possible. Even though in

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reality overtaking is possible (eg when there are turning lanes), this should never be the case in the model (unless explicitly modelled eg by modeling turning lanes as two parallel but separated links – however one then gets a general n-in-m-out node rather than a simple diverge). The reason why FIFO should hold near the node is that otherwise FIFO could be violated on the OD-level: a vehicle leaving its origin later may overtake its predecessors at the non-FIFO node and arrive earlier in its destination; this conflicts with the typical equilibrium conditions, in that the predecessors can now arrive earlier at their destinations by leaving later – yielding an inconsistent model.

A final thing that can go wrong in a corridor network is that travel times and split rates at diverges can be inconsistent with the OD matrix. Indeed, traffic bound for a destination will after a certain travel time to a diverge turn towards the outgoing link that leads to their destination. Should they experience any delay between their origin and that diverge, then their contribution to the turning rate will come later. Some models do this correct by definition, because the data structures of flow on links are disaggregated by destination. Then the delayed flow ‘carries’ the information of the destination later towards the diverge and hence the split rate will be calculated later accordingly. Other models make separate flow/travel time and turning fraction calculations (in which all flow is treated as a single commodity, carrying no information on where it is going – this will be regulated by the turning fractions). Such models are only (approximately) consistent after convergence of the network loading. However, if convergence is not perfect, traffic could end up in the wrong destinations, so the OD table is not respected.

Links to other tests

This test affecting results of other tests:

Test 4: route choice – travel time component of route cost is directly derived from propagation

Test 4: convergence of DTA – limits/problems of numerical precision of propagation may affect convergence of DTA equilibrium

Other tests affecting this test:

Test 1 on propagation

Aims 2.1 Does a single merge with free outflow comply with all the theoretical requirements? Which distribution rule is used for constrained outflow (here at capacity); is it behaviorally plausible; is it numerically stable and precise?

2.2 Does a single merge with congested outflow (spillback from further downstream) comply with all theoretical requirements?

Which distribution rule is used?

2.3 Does a diverge always respect turning rates (and hence FIFO)?

2.4 Are turning rates at a diverge always consistent with the OD-table, even when (time dependent) delays occur between origin and the diverge?

2.5 Does the model provide route travel time outputs? If so, how are they aggregated from the link travel times or from link (cumulative) flows? Are there nu numerical artefacts in this procedure?

2.6 Can one analyze turning flows in the outputs, or only aggregate link flows?

2.7 Is it possible to define ramp metering control at on-ramps? If so, how is the metering rate defined (exogenously or endogenously)? Can the time step for control be chosen freely?

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Software OmniTrans StreamLine

Version OmniTRANS 6.1.4.7667 / StreamLine

Operator Farzad, Wei

File location StreamLine\Test_ID_2_Merges_Diverges

Document history

1.0 14-12-14 Farzad Fakhraeiroudsari, Wei Huang, Chris Tampère

2.0 27-02-15 Farzad Fakhraeiroudsari, Chris Tampère

Remarks VVC processed

Test results 2.1 Introduction

In order to perform dynamic traffic assignment properly, we need to consider some requirements such as causality, the FIFO discipline and satisfactory flow propagation when we model traffic inflows, outflows, and travel costs on a link. Moreover, the way of calculating route travel cost is not so straightforward as in the static case because travel cost can change over the time during which travelers traverse a route. Different scenarios were defined and tested in Test case 1 for the propagation model with StreamLine / Madam. In this test, merge and diverge models are analyzed under different criteria.

We consider here networks where the maximum number of links entering and/or leaving a node is 3. Thus, nodes can be classified into three types: “diverge” if only one link enters the cell but two leave it, “merge” if two links enter and one leaves, and “ordinary” if one enters and one leaves.

To perform all scenarios, one network is used with following supply properties. However, to achieve the goal of each scenario, capacities of specific links are adopted.

Supply Propert ies

Supply Type Capacity Length (km)

Free Flow Speed

Speed at Cap

No. of Lane

Highway Links 5 1000 0.3 120 90 1

On-Ramp Links 10 1000 0.3 80 30 1

Off-Ramp Links 10 1000 0.3 80 30 1

Connector 1 3000 1 80 30 1

Demand Properties

In this test, following demand pattern is considered although to achieve the goal of each scenario, demand flows are adapted.

O1D2 : Highway to Highway

O1D1: Highway to Off-Ramp

O2D2: First On-Ramp to Highway

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O3D2: Second On-ramp to Highway

2.1 Single merge model behavior where the receiving link’s capacity is the constraint The idea in this scenario is to test merging behavior, when congestion is due to capacity of the receiving link.

Test 2.1.1 The aim of this test is to check single merge behavior where the receiving link’s capacity is the constraint and both inflow of sending links exceed their reduced outflow capacity (while assuming capacity-proportionality).

Demand and adjusted supply properties

Demand profile and changes in supply capacity are mentioned in the following table which is available for three hours. For the first two hours, flow pattern is mentioned (first hour, first column and second hour second column) and for the third hour, no demand is used in order to empty the network.

This demand simulation time profile is consistent for all scenarios however some cases were needed to run for longer time. For those cases, adjusted demand profile will be mentioned.

Table 9: Demand profile and adjusted supply properties for test 2.1.1

D1 D2 D1 D2 Cap

O1 - 800 O1 -

800 ALL 1000

O3 - 100 O3 -

600

Expectations

Queue on BC and O3C, both sending 500 veh/h into C-D2 (assuming capacity-proportionality) or some other well-founded systematic rule for distributing outflow to competing incoming links

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Results

T= 15 min (7:15) free flow state

T=119 (8:59) last time step of demand feeding. Highest level of queue

Figure 34: Flow propagation in single merge for test 2.1.1, at time 7:15 (above) and last time step of demand feeding (below)

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Space – Time Plot

Figure 35: Space-Time plot for highway (left) and second on-ramp

By looking at Figure 34, it can be seen that at the merging point C, both incoming links have 1000 veh/h capacity while the out capacity is only 1000 veh/h. Therefore both BC and O3C will get 50% share reduction of their out capacity (500 veh/h each). This is indeed the case by looking at the outflow of those segments. We conclude in this case that indeed capacity proportional distribution rule is used; also it appears that in a merge where the receiving link’s capacity is the constraint, this constraint is strictly respected. All these findings are fully consistent with theoretical expectations/analytical solutions. Note that this may seem evident, but it certainly isn’t for a 2nd order propagation model (see explanation in Test 1 report). There must be in SL heuristic rules overruling the default 2nd order behavior, herewith improving substantially the theoretical consistency, controllability and validity of the merge bottleneck. Congestion pattern can be seen in Figure 35.

Test 2.1.2 The aim of this test is to check single merge behavior where the receiving link’s capacity is the constraint and only highway’s inflow exceed its constrained outflow capacity (while assuming capacity-proportionality).

Demand and adjusted supply properties

Table 10: Demand profile and adjusted supply properties for test 2.1.2

D1 D2 D1 D2 Cap

O1 - 800 O1 -

800 ALL 1000

O3 - 100 O3 -

400

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Expectations

We expect queue on BC only: as merging link CD2 has lower capacity than total demand sent into it, we expect congestion. Assuming capacity proportional distribution of available outflow over the competing incoming links, link O3C would receive 500, where its demand is only 400; we then expect no congestion on that link, and link BC consuming the remaining supply of 600 veh/h. Note that capacity proportionality is only one possible systematic and theoretically consistent distribution rule. Any alternative but theoretically consistent rule would be acceptable.

Results

T = 30 (7:30) Free Flow State

T=119 (8:59) congestion formed as it was expected

Figure 36: Flow propagation in single merge for test 2.1.2, at free flow stage (above) and last time step of demand feeding (below)

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Space – Time Plot

Figure 37: Space-Time plot for highway (left) and second on-ramp

These results are as consistent as the previous case: in this case the sending flow of the O3C (400 veh/h) is less than the reduced capacity (500 veh/h), therefore the rest of unused capacity is indeed utilized by the BC segment (see Figure 36). Therefore the expected outflow of BC segment would be 600 veh/h (500-400 + 500). The output indeed fulfills this behavior and the result is satisfactory with the expectations. Congestion pattern can be seen in Figure 37.

Test 2.1.3 The aim of this test is to check single merge behavior where the receiving link’s capacity is the constraint and only on-ramp’s inflow exceed its constrained outflow capacity (while assuming capacity-proportionality).

Demand and adjusted supply properties

Table 11: Demand profile and adjusted supply properties for test 2.1.3

D1 D2 D1 D2 Cap

O1 - 400 O1 -

400 ALL 1000

O3 - 100 O3 -

800

Expectations

Queue on O3C only; the reason is exactly the same as in the previous case, now it is BC that cannot consume its capacity proportional share

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Results

T = 30 (7:30) Free Flow state

T=119 (8:59) congestion formed as it was expected

Figure 38: Flow propagation in single merge for test 2.1.3, at free flow stage (above) and last time step of demand feeding (below)

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Space – Time Plot

Figure 39: Space-Time plot for highway (left) and second on-ramp

The same pattern would be expected to observe although this time on O3C segment. Looking at Figure 38, it is completely according to expectations. Congestion pattern can be seen in Figure 39.

Test 2.1.4 The aim of this test is to check single merge behavior where the receiving link’s capacity is the constraint and only highway’s inflow exceed its constrained outflow capacity (while assuming capacity-proportionality).

Demand and adjusted supply properties

Table 12: Demand profile and adjusted supply properties for test 2.1.4

D1 D2 D1 D2 Cap

O1 - 800 O1 -

800 ALL 1000

O3 - 100 O3 -

400 BC 2000

Expectations

Queue on both BC and O3C, but with twice the flow on BC than on O3C (because of capacity proportionality; however any other theoretically consistent distribution rule would be acceptable)

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Results

T = 30 (7:30) Free Flow state

T=119 (8:59) congestion formed as it was expected

Figure 40: Flow propagation in single merge for test 2.1.4, at free flow stage (above) and last time step of demand feeding (below)

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Space – Time Plot

Figure 41: Space-Time plot for highway (left) and second on-ramp

It can be seen from Figure 40 that at the merging point C, the incoming capacity of the BC segment is 2000 and O3C is 1000 with outflow capacity of 1000, therefore BC segment gets 2/3 and O3C gets 1/3 exit capacity. O3C sends 400 veh/h and due to entry capacity reduction, only 333.33 (=1000*1000/(1000+2000)) veh/h can leave the O3C segment. On the other hand BC segment could send 666.66 ((=1000*2000/(1000+2000)) veh/h The result is consistent with the output although with some rounding errors. Congestion pattern can be seen in Figure 41.

2.2 2.2 Single merge model behavior while having congestion spillback from downstream bottleneck

Test 2.2.1 The idea in this scenario is to test merging behavior in congestion, when congestion is now not due to capacity of the receiving link, but rather triggered by spillback from a more downstream bottleneck.

Demand and adjusted supply properties

Table 13: Demand profile and adjusted supply properties for test 2.2.1

D1 D2 D1 D2 Cap

O1 - 500 O1 -

500 ALL 1000

O2 - 400 O2 -

400

O3 - 100 O3 -

500

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Expectations

Congestion with a reduced flow of 500 veh/h spills back from bottleneck C onto merge A. Thanks to the same merging principles as tested before, we expect this reduced outflow to be distributed over O1A and O2A according to capacity proportions. In this case, this should be queue on both O1A and O2A (first on ramp) segments, each with 250 veh/h flow.

Results

T = 30 (7:30) Free Flow state

T=119 (8:59) end of congestion phase

Figure 42: Flow propagation in single merge with congestion triggered by spillback from downstream bottleneck for test 2.2.1, at free

flow stage (above) and last time step of demand feeding (below)

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Figure 43: Sending flow at merging point A (left) and C (right)

Figure 44: Space-Time plot for highway (top left), first on-ramp (top right) and second on-ramp (bottom )

Activation of bottleneck C happens according to expectations, as already shown in the previous cases (see Figure 42 and Figure 43). However, because of the higher order dynamics, the flow in the queue remains higher than 500 veh/h much longer (in the snapshot plotted: about 730 veh/h). Under this outflow constraint, we would expect 365 veh/h sent by both competing incoming links (because they have equal capacity. This is only approximately respected, although this may also be an impression, as we are not sure whether the plotted flow values are inflow, outflow or some average. Congestion pattern can be seen in Figure 44.

Test 2.2.2 The idea in this scenario is, just like the previous test, to test merging behavior in congestion, when congestion is now not due to capacity of the receiving link, but rather triggered by spillback from a more downstream bottleneck. The difference with the previous test is a different ratio of sending links’ capacities.

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Table 14: Demand profile and adjusted supply properties for test 2.2.2

D1 D2 D1 D2 Cap

O1 - 500 O1 -

500 ALL 1000

O2 - 400 O2 -

400 O1A 5000

O3 - 100 O3 -

500

Expectations

Same expectations as before. However as now capacity of O1A is much higher, it should receive a higher share (5/6) of the outflow constraint than O2A that gets 1/6 of the constraint. Again any other theoretically consistent distribution rule is acceptable.

Results

T = 30 (7:30) Free Flow state

T=119 (8:59) end of congestion phase

Figure 45: Flow propagation in single merge with congestion triggered by spillback from downstream bottleneck for test 2.2.2, at free

flow stage (above) and last time step of demand feeding (below)

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Space – Time Plot

Figure 46: Space-Time plot for highway (top left), first on-ramp (top right) and second on-ramp (bottom )

This case has the combination of all previous cases which is capacity reduction due to merging point C with the same share for the incoming links (BC and O3C) and spillback at point A with 1/6 capacity reduction for segment O2A and 5/6 reduction for segment O1A (see Figure 45). The expected outflow here would be 416.66 veh/h for O1A (500*5/6) and the remaining out capacity for O2A which is 83.33 (500-416.66). Even though it is not clearly visible in the plots (scenario should have run somewhat longer before demand dropped so that congestion would spill back further upstream), we verified that the capacity proportions are not respected; rather an approximate 50-50 distribution occurred. It appears that when the outflow of a merge is constrained by spillback (rather than capacity of the receiving link), capacity proportionality is not respected. Congestion pattern can be seen in Figure 46.

2.3 2.3 Single diverge model behavior where the receiving link’s capacity is the constraint and while having congestion spillback from downstream bottleneck

Test 2.3.1 The idea in this scenario is to test simple diverge model behavior in free flow condition.

Demand and adjusted supply properties

For this scenario, simulation was run for two hours; the first hour demand pattern is as following table and second hour was used to empty the network.

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Table 15: Demand profile and adjusted supply properties for test 2.3.1

D1 D2 D1 D2 Cap

O1 400 40

0

O1 -

- ALL 1000

O2 - - O2 -

- BD1/BC 500

O3 - - O3 -

- O3C/CD2 500

Expectations

Free flow in all segments; exactly 400 vehicles arrive in both destinations

Results

Figure 47: Flow propagation in simple diverge at free flow stage for test 2.3.1

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Space – Time Plot

Figure 48: Space-Time plot for highway (left) and off-ramp (right)

Result is satisfactory and fully consistent with the expectations (see Figure 47). Congestion pattern can be seen in Figure 48.

Test 2.3.2

The idea in this scenario is to test diverge model behavior where capacity of one of the receiving links is the constraint.

Demand and adjusted supply properties

Same as previous case, two hour simulation is used with one hour to empty the network.

Table 16: Demand profile and adjusted supply properties for test 2.3.2

D1 D2 D1 D2 Cap

O1 400 400 O1 -

- ALL 1000

O2 - - O2 -

- BD1 200

O3 - - O3 -

- O3C/BC/CD2 500

Expectations

Because of the FIFO principle that needs to be respected in diverge, we expect queue on AB, sending 200 to BD1 and 200 to BC.

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Results

T = 6 (7:06) loading the network, before getting congested

T=59 (7:59) end of feeding demand and highest level of queue and congestion’s spill back

Figure 49: Flow propagation in single diverge for test 2.3.2, at free flow stage (above) and last time step of demand feeding (below)

Space – Time Plot

Figure 50: Space-Time plot for highway (left) and off-ramp (right)

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In this case we are testing the behavior of diverging node when one of the outgoing links has a capacity constraint. In this case BD1 has 200 capacity constraint. As this constraint restricts 50% of vehicles arriving at B, the total outflow at B can be 200/50% veh/h, i.e. 400 veh/h. Hence, also 200 flow towards the unconstrained outgoing link BC. Eventually, 400 vehicles arrive in each destination. The behavior of StreamLine is fully consistent with these expectations. Congestion pattern can be seen in Figure 50.

Test 2.3.3 The idea in this scenario is to test diverge model behavior in congestion, when congestion is now not due to capacity of the receiving link, but rather triggered by spillback from a more downstream bottleneck.

Demand and adjusted supply properties

In this test one hour demand was not enough to get the expected result due to dynamic speed terms. Therefore simulation time was increased to 4 hours with 3 hours demand pattern as following table and one hour to empty the network.

Table 17: Demand profile and adjusted supply properties for test 2.3.3

D1 D2 D1 D2 Cap

O1 400 400 O1 -

- ALL 1000

O2 - - O2 -

- CD2 200

O3 - - O3 -

- O3C/ BC / BD1 500

Expectations

As a bottleneck activates at the end of link C limiting the flow to 200 veh/h, the outflow constraint on diverge B is caused by spillback. We expect the queue on AB to send 200 to BC and because of FIFO also 200 to BD1

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Result

T=59 (7:59) after one hour simulation

T=08:30

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T=09:37

Figure 51: Flow propagation in single diverge with congestion triggered by spillback from downstream bottleneck for test 2.3.3 after one hour simulation (above) and end of demand profile (below)

Looking at Figure 51 shows that due to capacity reduction at CD2, outflow is reduced to 200 veh/h. Consequently the congestion spills back with initially higher flow then gradually reduced to 200 at diverging node B. Looking at any time before 9:37 where diverge outflow is reduced to 200, total outflow of B is higher than 200 veh/h. The sum of outflow in BC and BD1 is to some extend close to the flows comes out of link AB and the share of flow on both BC and BD1 is close to 50%. It seems FIFO is respected but longer simulation time is needed to reach a stable result.

2.4 2.4 Consistency of turning rates at a diverge node

In this case we verify whether the turning rates at the diverge are always consistent with the OD-table, even when (time dependent)

delays occur between origin and the diverge.

Test 2.4.1

Demand and adjusted supply properties

In this test three hours simulation is used that two hours demand have following pattern and the third hour is used to empty the network.

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Table 18: Demand profile and adjusted supply properties for test 2.4.1

D1 D2 D1 D2 Cap

O1 100 300 O1

300 150 ALL 1000

O2 300 100 O2

100 250 BD1 300

O3 - - O3

- -

Expectations

Exactly 400*T vehicles should arrive at the each destination

Results

T = 59 (7:59) end of loading the first hour demand pattern.

T=119 (8:59) end loading the second hour demand pattern.

Figure 52: flow propagation with different demand pattern for test 2.4.1

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Figure 53: Cumulative of the flow arriving at each destination

In Figure 52 the propagation of flow over the time is shown. Looking at each destination, it can be seen that 300 veh/h arrive at each destination due to capacity reduction at BD1. This pattern is consistent until end of simulation. Since the aim of this test is to check whether correct amount of vehicles arriving at each destination while delays occur, cumulative of the arrival was produced. Cumulative vehicles at connectors to destination D1 and D2 are shown in Figure 53. It is strange that in the beginning of the simulation where there is no flow, outflow cumulative values are not zero and starting from some high values. Other than that, the plot confirms that indeed the expected 800 veh of total demand arrive at the destinations.

2.5 2.5 Route travel time outputs Route Travel time is available as an output of the StreamLine. There are two options to get the travel time in Streamline either from link’s cumulative or travel time calculator. However there is no clear information which method is used to calculate the route travel time and there is no option available to change between these options. Therefore route cost/travel time calculation is not clearly mentioned in the manual.

As already mentioned in Test Case 1, two methods are available to calculate travel costs, reactive (instantaneous) and predictive (realistic). For more information please refer OmniTRANS manual or Test case 1.

2.6 2.6 Turning flows output Turning flows at each intersection can be visualized or exported from the database if junction type is defined. In our case, no junction type was defined therefore no turning flow was available.

2.7 2.7 Ramp metering control on on-ramp Ramp metering was not tested due to lack of time but according to the StreamLine manual, “Ramp Metering control is a very versatile control. It acts as a local traffic light that reacts upon information collected from sensors placed on the adjacent motorway. A ramp meter control is composed of two sensors, an actuator and an activator as shown in the figure below.

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Figure 54: Ramp metering scheme in StreamLine

The sensors collect data from the motorway, the actuator applies the ramp metering result to the on ramp, while the activator makes sure that the actuator is switched on and off at the appropriate times based on the sensor data. Depending on the chosen ramp metering strategy, the interactions between the various components can vary and different results can be produced. A Ramp Metering control is simply connected to a link being on an on-ramp. The software will place the sensors automatically.” For more information please check OmniTRANS manual.

Any other business

New questions triggered

Conclusions

Conclusion from the test result on this aim Passed/ failed/ unanswered/

partially failed (mark bold if critical)

Perspective offered by developers: are we aware of plans to improve this result e.g. in next releases? If

so, when?

2.1 In the first test, single merge model behavior was analyzed. It appears that in a merge where the receiving link’s capacity is the constraint, this constraint is strictly respected and the findings are consistent with theoretical expectations/analytical solutions.

Passed

2.2 In this test, single merge model behavior was analyzed when the outflow of a merge is constrained by spillback (rather than capacity of the receiving link). The result shows that in this situation the capacity proportionality is not respected.

Partially passed

when the outflow of a merge is constrained by spillback, capacity proportionality is not respected

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2.3 In the this test, diverge model behavior was analyzed. Same finding was observed in diverge model.

When capacity of the receiving link is the constraint, result is satisfactory and fully consistent with the expectations

When the outflow of a diverge is constrained by spillback from bottleneck downstream, capacity proportionality is not respected.

Partially passed

when the outflow of a diverge is constrained by spillback, capacity proportionality is not respected

2.4 In this test we verified whether the turning rates at the diverge are always consistent with the OD-table, even when (time dependent) delays occur between origin and the diverge. This was indeed the case in our test.

In the beginning of simulation we see some cumulative outflow where there is no inflow.

Passed

cumulative vehicles for centroids are not available

strange behavior in inflow/outflow cumulative can be seen in the beginning of simulation

2.5 Route Travel time is available as an output of the StreamLine although it’s not clear how it’s calculated. Information about the travel time calculation is not sufficient in the document.

Passed

Although documentation needs to be developed

2.6 The results of turning flow are not available for this test case since junction type is not defined.

NA

2.7 Ramp metering was not tested due to lack of time but according to the StreamLine manual, it’s possible to have ramp metering endogenously.

This was not tested

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Test ID 3

Topic Intersections

Test 3 Signalized intersection

Network

We consider a single signalized intersection. The capacities and demand levels will change depending on the exact scenario and what we want to test there. This network allows us to create the following scenarios:

Intersections delays at B with flow below saturation

Intersections delays at B with flow at saturation

Intersections delays at B interacting with spillback

Relevance The majority of delays in urban networks are a result of vehicle interacting at intersections. Also at flow rates below saturation, delay is important and it will influence routing behavior. It is crucial for models to capture these delays adequately to be able to estimate correct route volumes. Otherwise these routes are too attractive and hence too competitive compared to motorways.

Motivation Delays at intersections are caused by three distinct mechanisms; a traffic model that misses either of them, inevitably underestimates delay in certain conditions:

primary control delay: because flow is interrupted by red phases, some vehicles must stop while others may pass undelayed; this can be modeled explicitly with alternating full capacity and blocking (yielding rapidly varying output that needs to be averaged for most analyses to average travel time) or implicitly where average delay is calculated and imposed on all flow

O1A AD1 AB BD2 O2B BD4 BO4 BC CD3 CO3

length 1 1 1 1 1 1 1 1 1 1

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arriving at the intersection (yielding a smoother travel time evolution). Actually, the precise value of delay is not only a function of the control characteristics (green and cycle time); also the arrival distribution matters. In general, the more stochastic the arrivals, the higher the delays (unless traffic arrives in platoons and green time is synchronized/coordinated with the arrival: green wave). Stochastic arrivals cannot be reproduced by explicit signal models; with implicit models coordination is difficult to reproduce.

delay due to conflicts: in the same green phase, multiple movements may be allowed. Obviously, non-conflicting movements go together, but also partial conflicts may be allowed, like left turn during green for opposing straight movement or left turn during opposing right turn. Depending on the priority rule, the minor of the conflicting movements may incur additional delay. Such internal conflicts are difficult to model macroscopically and may even lead to non-unique model results. Also, some algorithms trying to model internal conflicts by considering the intersection plane as a mini network of links, may lead to oscillatory solutions.

spillback delays: when an outgoing link is congested, movements towards it are delayed; this mechanism is comparable to that on motorway diverges and merges. However, the directions in which the queue will or will not spill back are much more difficult to determine.

An additional complexity with intersections is the existence of turning lanes or combined turns. They influence among other FIFO behavior and the capacity of a turn movement.

Links to other tests This test affecting results of other tests:

Test 4: route choice – travel time component of route cost is directly derived from delays at intersections

Test 4: convergence of DTA – limits/problems of intersection behavior may affect convergence of DTA equilibrium

Other tests affecting this test:

Test 2

Aims 3.1 Does a single turn movement comply with all the theoretical requirements? What is the effect of under saturated flow on delay?

What is the effect of saturated flow on delay?

How is spillback handled?

3.2 Do diverging turn movements with free outflow comply with all the theoretical requirements?

Do diverging turn movements with congested outflow (spillback from further downstream) comply with all theoretical requirements?

What is the impact of designated/mixed turning lanes for left, straight and right turning movement?

Does the intersection always (under saturation / saturation / spillback) respect turning rates (and hence FIFO)?

3.3 Do merging turn movements with free outflow comply with all the theoretical requirements? Which distribution rule is used for constrained outflow; is it behaviorally plausible; is it numerically stable and precise?

3.4 Are U-turns possible?

What about grid lock?

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3.5 Does congested crossing flow affect throughput?

Is left turning flow delayed by the volume of the flow it needs to cross?

If so what happens in a symmetrical setup?

3.6 Is it possible to set green times according to traffic volumes (actuated control)?

Software OmniTrans StreamLine

Version OmniTRANS 6.1.4.7667 / StreamLine

Operator Farzad, Wei

File location StreamLine\Test_ID_3_Signalized_Intersection

Document history 1.0 17-12-14 Farzad Fakhraeiroudsari, Wei Huang, Chris Tampère

2.0 27-02-15 Farzad Fakhraeiroudsari, Chris Tampère

Remarks VVC processed

Test results 3.1 Introduction

The modelling of junction delays leads to improved assignment results, especially in urban areas, and permits analyzing various different junction measures at network level.

The Junction Model module provides an additional layer of abstraction to the Propagation Model module to facilitate the modelling of both unsignalized and signalized junction within a DTA model.

XStream utilizes static junction theory which has been adapted to match a dynamic situation to determine the general delay and exit capacity on each turn during DNL. At the signalized intersection, Xstream calculates the capacity by lane group. In the case of signalized junction, Xstream creates signal groups based on the layout of the junction. This means that for each branch one to three signal groups are defined, depending the definition of the lanes on this branch. Depends on the junction type, mean delay is calculated regarding uniform, incremental and geometry delays, and although in the case of signalized intersection only incremental delay is taken into account. For more information, please check the manual of OmniTRANS or Junction Modeling in OmniTRANS document.

In order to check signalized intersection’s performance in StreamLine, a series of tests was prepared. The supply structure of these tests is the following table. These properties are identical for all tests unless any changes would be mentioned.

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Supply Propert ies

Table 19: Supply characteristics of the signalized intersection toy network

Supply Type5 Capacity Length (km) Free Flow Speed Speed at Cap No. of Lane

Links 10 1000 1 60 35 1

Connectors 1 1000 1 60 35 1

The intersection’s signal attributes are mentioned in the following table and same as supply properties, these values will be used for this report unless any changes would be mentioned.

Intersection Propert ies

Table 20: Intersection’s properties

Cycle Time Green Time Turn Saturation No. of

Lange Group

120 60 1000 1

As it’s already mentioned in the beginning of this report, a single signalized intersection is considered for this test. Each branch of this intersection, depending on the scenario, can be used as an origin or/and a destination. Figure 55 shows the layout of toy network for this test.

Figure 55: Network layout for signalized intersection

5 Check the OmniTRANS file for more information

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As can be seen in Figure 55, there are four origins – destinations with one signalized junction at node B and depending on the scenario, flow would propagate along the network.

This test compares the delays for a signalized intersection controlled in fixed-time and operated in a range of conditions extending from under-saturated to highly saturated and where congestion spills back from downstream bottleneck. Therefore, this test was divided into three sub sections, under saturated, over saturated and with spill back from downstream.

3.1 Single turn movement

3.1.1 Single turn movement with under-saturation flow

In the first test, behavior of the intersection is analyzed where intersection is utilized at under saturated condition. Each link has 1000 veh/h capacity while at the intersection only 50% green time is allocated to them. Therefore exit capacity of the intersection is reduced to 500 veh/h. In order to check the behavior of the intersection, 5 hours simulation time interval is used where demand increased from 25% to 98% level of saturation. The amount of demand per time interval is mentioned on the Table 21.

Demand Properties

Table 21: Demand profile for test 3.1.1

Time Demand/O1 – D3 Saturation %

7-8 125 25%

8-9 350 70%

9-10 425 85%

10-11 490 98%

11-12 0 empty

Expectations

This test loads only one turn without conflicting traffic until capacity. We expect increasing travel time (delay) when demand is increasing from 25% saturation till 98% (especially in near-saturation, i.e. from 80% and up). No congestion should occur.

Results

Figure 56 shows the flow propagation for each time interval. As can be seen when demand increases from 125 veh/h until 350 veh/h, no speed reduction is observed. This makes sense since intersection’s capacity is higher than 350 veh/h (turn capacity is 1000 veh/h and green time is 50% of cycle time). However, as soon as demand level is increased to 425 veh/h (85%

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saturation), speed drops significantly at the upstream link of intersection and downstream link of intersection shows only 350 veh/h as outflow. The same behavior can be seen while increasing demand up to 490 veh/h (98% saturation).

Time Demand Values: Flow(veh/h) / Colors: Speed (min4, max60)

7:30 125

8:30 350

9:30 425

10:30 490

11:00 0

11:30 0

Figure 56: Flow propagation for single intersection at under-saturated condition for test 3.1.1

Why 350 veh/h exit capacity at the junction instead of 500 veh/h?

Since the links capacity is 1000 veh/h, turn saturation flow should be set to 1000 veh/h otherwise capacity reduction due to signal setting will not be considered. By default (defined in the junctions.def, a file in the program folder) turns for a signalized junction is set at 1800 for right/through traffic and 1700 for left turns.

In this scenario, there is a potential partial conflict because of the opposing flow (including the left turn) has green simultaneously. Irrespective of whether this conflicting turn actually carries flow, StreamLine reduces turn capacity by a default (and quite arbitrary!) 300 veh/h. So, when set at 1000, the actual capacity used is 700. Having 50% green, means a flow of 350.

In this test case, our initial expectations went wrong due to this unexpected capacity reduction. Still, as we can see in the Figure 57, travel time of O1D3 is indeed increasing where demand is increasing from 125 veh/h to 350 veh/h (until 9h). By sending more flow, queue will be formed and cause travel time to be increased rapidly.

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Figure 57: Travel cost (min) for O1D3 in test 3.1.1

Looking at Figure 57, it can be seen that the delay is calculated implicitly where averaged and imposed on all flow arriving at the intersection.

As conclusion, we can confirm the fact that delays at the under-saturated condition increased while demand is increasing. This figure also verified the goal of next scenario where intersection is utilized at over-saturated condition.

3.1.2 Single turn movement with over-saturation flow

The aim of this test is to check the intersection’s behavior where intersection performs at over-saturated condition.

Demand Properties

To verify the behavior of signalized intersection at over-saturation condition, 600 veh/h flows is assigned to the network for one hour and second two hours are used to empty the network.

Time Demand/O1 – D3 Saturation %

7-8 600 120%

8-10 0 Empty the network

Expectations

With this test, we check the turn behavior of a single turn without conflicting traffic when it is saturated. We expect queue formation at B and propagation towards A.

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Travel Cost test 3.1.1

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Results

Figure 58 shows the flow propagation for each time interval. As it was expected, queue was formed correctly at the intersection and propagated backwards to A. Since the exit capacity of the intersection is reduced to 350 veh/h instead of 500 veh/h, more severe congestion was formed and travel cost would increase more extremely than we expected.

Time Values: Flow(veh/h) Colors: Speed (min4, max60)

7:10

7:20

7:31

7:40

7:59

8:01

8:30

Figure 58: Flow propagation for single intersection at under-saturated condition for test 3.1.2

Figure 59 shows the turn cost and flow for this test. By combining Figure 58 and Figure 59, it can be seen that from the beginning of the simulation the turn cost increases as long as the link AB (upstream of intersection) is not fully filled with the congestion. At 7:31 link AB is fully congested (look at Figure 58) and its entry capacity is reduced to 350 veh/h. Therefore turn cost on this time interval stays constant (see Figure 59). At 8, the network doesn’t receive any demand although there is still flow in the queue waiting and link AB is still fully saturated. This continues until 8:30 were outflow rate of link AB is reduced (see Figure 58) which results to reduce turn cost (see Figure 59). Turn cost is the generalized cost for executing the turn. The cost value represents the calculated average delay for a turning movement in minutes.

There are two abnormal behaviors in the Figure 59. One is the fluctuation of turn cost around 7:20 and the other is having turn cost higher than free flow cost after 9 while the network is empty. These issues don’t seem very crucial however.

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Figure 59: Turn cost and flow for test 3.1.2

Route costs

Route cost of this test is given in Figure 60. As it was expected, travel cost increases until the time that intersection is fully congested (8:30) and it reduces while entry flow of the congestion gets less that the capacity (after 8:30).

Figure 60: Travel route cost of test 3.1.2

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As conclusion for this test, it’s clear that saturated flow has significant influence on delay. This fulfills the expectation and results are fully consistent with the theoretical background (with the exception of reduced capacity already mentioned in the previous test).

3.1.3 Single turn movement with spillback from downstream bottleneck

The aim of this test is to check the intersection’s behavior where congestion from downstream bottleneck spills back into the intersection.

Demand Properties

Simulation time for this test is set to four hours: two hours with 350 veh/h demand and two more hours to empty the network. To have the congestion spill back into the intersection, capacity of downstream link of intersection is reduced to 200 veh/h. Table 22 shows the specification of the network.

Table 22: Demand and supply modification for test 3.1.3

Time Demand/O1 – D3 Bottleneck Cap

7-9 350 200

9-11 0 -

Expectations

In this test we verify turn delay of a single turn without conflicting traffic, when congestion spills back from the receiving link. We expect under-saturated delay to be overruled by queue formation due to spillback over the junction.

Results

Looking at Figure 61 shows the space-time diagram for segment O1D3. As can be seen from left figure, bottleneck at link 4 reduces the speed of upstream link 3 and after one hour where link 3 is fully congested, congestion spills back into the intersection. Right figure also shows the density of this network and as can be seen, link 3 gets to its highest jam density (180 veh/km)6.

6 Looking at Figure 61, we can observe very strange high density (almost 180 veh/km/lane) for link 3 (upstream of bottleneck). It’s not clear why the density of link 3 increased so significantly while all speed term parameters were already set to default values. This behavior has contradiction to what we had already observed in Test Case 1, propagation uninterrupted, scenario 1.2 (stationary bottleneck with constant high demand), where demand is constant and higher than bottleneck’s capacity. At that test, density of upstream of the bottleneck increased up to 40% of jam density but in this case, density increased up to jam density. Therefore additional test was preformed to

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Figure 61: Space – Time diagram for test 3.1.3, left figure is speed and right is density

Looking at Figure 62, turn flow and turn cost can be seen. Until 8:15 upstream link of intersection B sends 350 veh/h and as result, turn cost increases and stays constant. After 8:16, downstream link of intersection gets fully congested and queue spills back into the intersection. Therefore turn flow stays at 200 veh/h (which is the bottleneck’s capacity) and turn cost increases. Although same as previous test, it’s not clear why turn costs fluctuated when queue spills back to it.

check this behavior. This additional test was named as ”High_Dense_Up_Bottleneck” in Test Case 1 variant file. The result was very surprising that the model responds differently where the same supply characteristic is used but with %.50 reduction of the capacity and demand. Recall the test case 1, where all links had 2 lanes with 2000 capacity each, bottleneck capacity of 1500 and demand was 3800 veh/h. There no severe density was observed at the upstream of the bottleneck. Now by changing lane’s capacity to 1000 and bottleneck to 750 with 2000 demand, all of a sudden density of upstream of the bottleneck (link 3 here) increased up to jam density. This is indeed very strange behavior and should be verified by the developer.

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Figure 62: Turn cost and flow for test 3.1.3

As it was expected, travel time increased significantly when congestion spills back into the intersection (although this is obviously mainly due to normal congestion formation, not delay created by the node). This can be seen in Figure 63.

Figure 63: Route travel time for test 3.1.3

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As conclusion for this test, it’s clear that spillback from downstream bottleneck creates significant delay in the network. The intersection acts as a normal node for passing on congestion upstream. This fulfills the expectation and results are fully consistent with the theoretical background.

3.2 3.2 Diverging turn movement In order to check the diverge turn movement, lanes can be defined as shared turns lanes or designated turn lanes. In the following scenarios, shared turn lane is used to first verify whether its behavior is basically a combination of what was observed in 3.1, and diverge behavior of Test case 2, scenario 2.3 for uninterrupted corridor. In a second series of tests, diverge intersection should be tested while having designated turning lanes. However, such tests were not performed (yet?).

3.2.1 Diverging turn movement with under-saturation flow

The aim of this test is the same as test 3.1.1 however here the demand propagates from origin 1 to 3 destinations. Therefore the same analysis and expectations that was done for single movement, here is valid for diverge movement. Only one combined approach lane is modeled (no turning lanes). One big difference between this test and previous one is that, capacity reduction for intersection B has been relaxed (that is: we compensated for it by setting 300 higher turn capacity) and we can verify results with our expectations.

For running these tests, the same signal setting and supply properties have been applied as test 3.1.

Demand Properties

In this test, behavior of the diverging movement of a signalized intersection is analyzed where intersection is utilized at under saturated condition. In order to check the behavior of the intersection, 5 hours simulation time interval is used where demand increased from 25% to 98% level of saturation. The amount of demand per time interval is mentioned in Table 23.

Table 23: Demand profile for test 3.2.1

Time O1-D3 O1-D2 O1-D4 Sum Expectations

7-8 95 15 15 125 Small Delay

8-9 300 25 25 350 Small Delay

9-10 300 25 100 425 Delay

10-11 400 45 45 490 Heavy delay

11-12 0 0 0 0

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Expectations

We expect increasing travel time (delay) when demand is increasing from 25% saturation till 98%, especially from 80% and up. No congestion should occur (based on our experience from test 3.1.1, capacity reduction of intersection is fixed for this test).

Results

As it was expected, no congestion occurs and travel time increases while under-saturated flow increases. Figure 64 shows how turn cost is linearly increased while demand is increasing. This figure shows the straight movement although the same pattern can be seen for the other direction. This is reasonable where there is only a shared lane.

Figure 64: Turn cost and flow for test 3.2.1

Route travel time for O1D3 can be seen at Figure 65 with solid line where the peak at 11:45 should not occur and may be an artefact because of emptying the network. This is a well-known issue when travel times are derived from cumulative flows and these cumulative flows turn flat (at the end of demand period). Since the last time period no demand is assigned, calculating travel time from cumulative is problematic. To avoid this issue, only few fraction of demand can be used for the last time interval to empty the network (in this test 10 vehicle is used). By doing so, travel time calculation would show realistic results (see the dash line). The same pattern is also observed for the other ODs sine one combined approach lane is used.

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Figure 65: Route travel time for test 3.2.1

The output indeed fulfills this behavior and the result is partially consistent with the expectations. The increase in delay with saturation level is apparently quite linear. This suggests that only deterministic (uniform) primary delay is modeled, and no extra delay due to stochastic arrivals, in which case a sharp increase for saturations above 80% would be observed. When emptying the network, an unrealistic peak in travel time was observed.

3.2.2 Diverging turn movement with over-saturation flow

The aim of this test is to check the intersection’s behavior where intersection performs at over-saturated condition.

Demand Properties

In this test, behavior of the diverging movement of a signalized intersection is analyzed where intersection is utilized at over saturated condition. In order to check the behavior of the intersection, 2 hours simulation time interval is used where demand is 600 veh/h and intersection’s capacity is reduced to 500 veh/h due to 50% share of green time. The demand profile is mentioned in Table 24.

Table 24: Demand profile for test 3.1.2

Time O1-D3 O1-D2 O1-D4 Sum Expectations

7-8 400 100 100 600 Queue at B

8-9 0 0 0 0 -

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Expectation

With this test, we check the turn behavior of a diverging turn without conflicting traffic when it is saturated. We expect queue formation at B and propagation towards A.

Result

Since demand is higher than intersection’s capacity, there would be queue at the intersection. This can be seen in the space-time diagram of O1D3 segment in Figure 66.

Figure 66: Space – time plot for O1D3 in test 3.2.2, the left figure is speed and right one is density

The left figure shows the speed and as can be seen, due to capacity reduction at intersection, speed of upstream link (here link 2) has been decreased. This also has minor effect on link 1. Right figure shows the density XT plot. It’s visible that the density of link 2 has been increased up to 100 veh/km.

Having this congestion pattern, we also expect to have higher travel cost until 8:15 where congestion ends.

Route travel cost for O1D3 is shown Figure 67 and as it was expected, travel cost has been increased to its peak until 8:15 and then reduced to free flow travel time since there is no demand.

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Figure 67: Route travel cost for test 3.2.2

The output indeed fulfills this behavior and the result is fully consistent with the expectations from test 3.2.2.

3.2.3 Diverging turn movement with spillback from downstream bottleneck

The aim of this test is to check the intersection’s behavior where congestion from downstream bottleneck spillback into the intersection.

Demand Properties

Simulation time for this test is set to five hours which three hours with 350 veh/h demand and two more hours to empty the network. To have the congestion spillback into the intersection, capacity of downstream link of intersection is reduced to 200 veh/h. Table 25 shows the specification of the network.

Table 25: Demand and supply modification for test 3.1.3

Time Demand/O1 – D3 Bottleneck Cap

7-10 350 200

10-12 0 -

Expectations :

In this test we verify turn delay of a diverging turn without conflicting traffic, when congestion spills back from the receiving link. We expect under-saturated delay to be overruled by queue formation due to spillback over the junction.

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Results

Looking at Figure 68 shows the space-time diagram for segment O1D3. As can be seen from left figure bottleneck at link 4 reduces the speed of upstream link 3 and when link 3 is fully congested, congestion spills back into the intersection. Right figure shows the density for this segment.

Figure 68: Space – time diagram for O1D3 for test 3.2.3, left shows speed, right shows density

The same behavior of test 3.1.3 can be seen by looking at the turn cost and turn flow (see Figure 69). Although since all turns shared the lane, we cannot see how spillback affects traffic towards other turns. To do so, lane groups should be defined with their own signal setting although as mentioned earlier, we haven’t manage to perform this test.

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Figure 69: Turn flow and cost for route O1D3 in test 3.2.3

The output result is consistent with the expectations from test 3.1.3 however the same strange speed reduction happened and link 3 (upstream of the bottleneck) as in test 3.1.3.

3.3

These tests were not done

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3.2 3.2.1.1.1 125 15 1000 1000 0.5 0.5 same result as in 3.1.1.1 for delay of O1D3

3.2.1.1.2 125 15 1000 1000 0.5 right turn on red more delay because of merging

3.2.1.2.1 350 25 1000 1000 0.5 0.5 same result as in 3.1.1.2 for delay of O1D3

3.2.1.2.2 350 25 1000 1000 0.5 right turn on red more delay because of merging

3.2.1.3.1 425 25 1000 1000 0.5 0.5 same result as in 3.1.1.3 for delay of O1D3

3.2.1.3.2 425 25 1000 1000 0.5 right turn on red more delay because of merging

3.2.1.4.1 490 45 1000 1000 0.5 0.5 same result as in 3.1.1.4 for delay of O1D3

3.2.1.4.2 490 45 1000 1000 0.5 right turn on red more delay because of merging

3.2.2.1 600 100 1000 1000 0.5 0.5 same result as in 3.1.2 for delay of O1D3

3.2.2.2 600 100 1000 1000 0.5 right turn on red more delay because of merging

3.2.3.1 350 25 1000 200 0.5 0.5 increased queue formation because of additional demand

3.2.3.2 350 25 1000 200 0.5 right turn on red ?

3.2.4.1 125 15 15 1000 1000 0.5 0.5 (together with O4 to C) same result as in 3.1.1.1 for delay of O1D3

3.2.4.2 350 25 25 1000 1000 0.5 0.5 (together with O4 to C) same result as in 3.1.1.2 for delay of O1D3

3.2.4.3 425 25 100 1000 1000 0.5 0.5 (together with O4 to C) same result as in 3.1.1.3 for delay of O1D3

3.2.4.4 490 45 45 1000 1000 0.5 0.5 (together with O4 to C) same result as in 3.1.1.4 for delay of O1D3

3.2.5 600 100 100 1000 1000 0.5 0.5 (together with O4 to C) same result as in 3.1.2 for delay of O1D3

3.2.6 350 25 25 1000 200 0.5 0.5 (together with O4 to C) increased queue formation because of additional demand

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3.4

These tests were not done

3.5

These tests were not done

3.6 Same as test 3.1 but with actuated signal control

These tests were not done

Another Business

New questions triggered

Conclusions Conclusion from the test result on this aim Passed/ failed/ unanswered/

partially failed (mark bold if critical)

Perspective offerd by developers: are we aware of plans to improve this result e.g. in next releases? if so, when?

3.1 In the test 3.1.1 and 3.2.1, signalized intersection’s behavior was analyzed where intersection is utilized at under saturated condition. Due to unforeseen capacity reduction of interstation at test 3.1.1, the results were not fully compatible with the expectations. However this issue was solved in test 3.2.1,

The result of test 3.1.1 and 3.2.1 is partially consistent with the expectations. Delay is linearly increased with saturation level which means that only deterministic

Passed Partially

There is no clear documentation about capacity reduction of intersection. This should be mentioned at least in the junction manual

Travel time increased while emptying the network and as suggestion, very small fraction

Demand Capacity Green split at B Expected

test ID O1D1 O1D3 O3D3 All links A to C U-turns Result

3.4.1 125 1000 1000 0.5 U-turn at B is allowed same result as in 3.1.1.1 for delay of O1D1

3.4.2 50 350 125 1000 200 0.5 U-turn at B is only allowed comming from C Grid lock

U-turn at C is only allowed comming from B

Demand Capacity Green split at B Expected

test ID O1D3 O1D4 O4D2 O3D1 O3D2 All links except BD2 except AD1 A to C C to A Result

3.5.1 125 400 1000 200 0.5 0.5 Additional delays to flow O1D3 compared to 3.1.1.1

3.5.2.1 225 125 125 1000 0.5 0.5 Additional delays to flow O1D3 compared to 3.1.1.2

3.5.2.2 225 125 425 1000 0.5 0.5 Even larger additional delays to flow O1D3 compared to 3.5.2.1

3.5.2.3 225 125 350 1000 200 0.5 0.5 Flow coming from A is obstructed by congestion moving upstream from A

3.5.3 225 125 225 125 1000 0.5 0.5 Possible existance of multiple solution

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primary delay is modeled, and no extra delay due to stochastic arrivals.

In the test 3.1.2 and 3.2.2, intersection’s behavior where intersection performs at over-saturated condition was tested. The same issue with capacity reduction happened at test 3.1.2.

In both cases, queue at the intersection formed and spilled back to the upstream link as it was expected.

In the test 3.1.3 and 3.2.3 intersection’s behavior where congestion from downstream bottleneck spilled back into the intersection was analyzed. The same issue with capacity reduction happened at test 3.1.3.

The result of these tests, had contradiction with what we had already observed in test case 1, scenario 1.2. Density of the upstream link of the bottleneck has been increased significantly up to jam density. This behavior was not seen in Test Case 1, scenario 1.2. for more information please check footnote 2.

can be used to avoid this sharp peak travel time.

Strange extreme speed reduction or increase density was observed in test 3.1.3 and 3.2.3 which has contradiction with Test Case 1, scenario 1.2.

Intersection’s delay is calculated only based on incremental delays and only deterministic arrival is considered not stochastic arrivals.

3.2 In test 3.2, diverge turn movement was considered with one combine approach lane and designated turn lanes. In this report, only the share lane approach was tested where the reason was firstly to confirm the expectations from test 3.1 by relaxing the turn capacity reduction also to verify the behavior of intersection with diverge model behavior as in Test Case 2.

The expectations were confirmed within different scenarios as capacity reduction relaxed although the same concerns as 3.1 were pointed out. These concerns are already mentioned in 3.1

Passed Partially

3.3 Not tested

3.4 Not tested

3.5 Not tested

3.6 Not tested

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Test ID 4

Topic Route Choice

Test 4 Route Choice

Network For this test case different networks were used therefore specification of each network will be presented for each test.

Relevance The relevance of adequately modeling route choice is evident: this is why the DTA model was built. In most cases, the principle of route choice user equilibrium is used. We elaborate further on why (very) accurate calculation of the equilibrium is important. The choice for user equilibrium modeling is not evident:

There is no empirical evidence that the real route choice pattern is user equilibrated – rather on the contrary. Amongst others, the main reason for this is that some of the cost components influencing route cost cannot be (accurately) known at the moment when route choice decisions need to be made, for instance the occurrence of an accident could not be foreseen, neither is it repetitive over days so that one could learn. This is the reason why some attempts exist to model non-equilibrium route choice. TRE for instance offers an option for real-time re-routing. However a warning must be given here: whereas there may already exist multiple definitions of UE (see below), non-equilibrium can be defined in an infinite number of ways. Any particular choice relies heavily on a set of assumptions and parameters that are very difficult to validate. One must therefore be aware of the potential of ‘fake’ accuracy/validity of any non-equilibrium modeling.

Multiple definitions of UE can be used. The most important difference is probably that between deterministic and stochastic UE. The terms refer to the assumption that either all users have the same and perfect perception of route costs (deterministic), or there may be heterogeneity and/or imperfect perception of route costs (stochastic – note that ‘heterogeneous’ would be a better term, as the heterogeneous equilibrium can be deterministically determined, in contrast to for instance microsimulation models that rely on random generators and hence can truly be called ‘stochastic’). It may depend on the application if deterministic (DUE) or stochastic (SUE) is needed; hence software preferably supports both.

Motivation UE definition

In addition to the mere distinction DUE/SUE, the exact definition of UE can only be given if one specifies the cost function (both UE types) and the heterogeneity (SUE only).

cost function: empirical evidence supports the intuition that distance and time cost partly explain route choice. In addition, attributes like familiarity with the route, road category, perceived danger, scenic attractiveness, number of stops, ecology,… may be important. However rarely there is sufficient empirical data to validate their impact. More important may be toll, either in the form of toll gates at discrete locations or as per-km road pricing. Certain applications of DTA models require attributes to be flexible, for instance when analyzing rat-running and counter-measures for it (e.g. by GPS-navigation that discourages certain routes).

heterogeneity: the stochastic distribution of error term of the cost function determines to a large extent definition of SUE. Especially correlation structure between alternatives is important. In route choice, logit and probit models are quite common, as well as logit variants allowing to approximate effect of correlations through overlap factors. Which flexibility do the softwares offer?

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Moreover, for SUE in principle all route alternatives in a network need to be considered, which is impractical because of combinatorial problems. A heuristic is therefore needed to determine which routes will be considered. There is the choice to do this once before iterations to UE start, or to start with a small set and update (usually expand) the route set after every iteration (or after any nth iteration). The former has the advantage of speed (no shortest path calculations during iterations), but one needs to explicitly enumerate routes (memory in large OD tables and networks!) and needs to anticipate where congestion will occur and hence more route alternatives are needed. Some solutions to this problem are Monte Carlo sampling or starting with a route set from a static assignment on the network. The latter choice (route set updating) has the advantage that more route alternatives are selected only when it is needed (because of congestion pushing traffic to other routes), hence a more consistent route set is theoretically expected. Furthermore routes can be explicitly or implicitly ‘stored’. Explicit means that the links belonging to each route are identified and stored. Implicit means that by repeated shortest path calculations, diverge and merge points of different routes are identified and split fractions over these alternatives are updated. This requires in theory less memory and more calculation.

UE convergence

UE has converged if the dynamic loads and the dynamic costs they cause are exactly consistent with the route choices that determine those dynamic loads.

For DUE, this means that costs of all used routes for a departure at a certain time, are equal and less or equal to the cost of non-used routes. In DTA algorithms, full consistency is never achieved, as all values are calculated numerically (machine precision limits) and are a result of an iterative consistency algorithm that is halted when ‘sufficient’ numerical precision (or a maximum calculation budget) has been reached. A decent convergence measure (also called gap function) is therefore crucial to warrant quality of the UE. It typically measures in absolute or relative terms the aggregate, (often flow-weighted) cost differences between used paths in the network. Ideally, such costs differences are zero in UE, so the theoretical lower bound of such gap function is zero.

For SUE, this means that the route split fractions predicted by the route choice model based on the dynamic costs in the network, are exactly those that, when loaded onto the network, create those same dynamic costs. For the same reasons as for UE, a decent convergence measure or gap function is crucial. It is however different from the gap function in DUE, as in SUE the cost of used routes should not be equal (the flow-weighted differences being larger as variance of error increases). Therefore, the gap function will typically measure difference between successive iterations. Mind however that the gap function is defined over the route set that is considered: if the route set is wrong, then even seemingly good gap function values may hide the fact that the network has not reached equilibrium (and neither will it converge with more iterations!).

For practical reasons, it is of course important that UE converges as fast as possible, as the number of iterations needed largely affects computation time. However, the importance of accuracy of equilibrium is rarely acknowledged. It may seem that <1% gaps may be sufficient, however this is not true! Actually, for comparing scenarios, it is important to have highly precise convergence. Convergence of 1% means that if you run another iteration on the same scenario, flows (hence: costs) may change by ~1%. In other words: any difference of 1% or smaller should not be considered difference due to scenario variables, rather it is numerical noise. Suppose now that one compares two scenarios, e.g. toll has been introduced. On routes affected by toll, less traffic would be found. It is pushed away to other routes where a flow increase would be observed. However maybe not so much as one may think, as traffic that flowed there may be pushed towards yet other alternatives and so on. In other words: the primary effect of a measure is redistributed everywhere in the network and may be found as relatively small changes on a surprisingly large amount of links. However, if on half of those links, the effect does not surpass the noise level, we are not able to observe it! Hence, a large fraction of the effect of the scenario may not be

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observable in a model with inadequate convergence. That is what has driven static assignment software to try and reach machine precision (~10^-15) in equilibrium!

Unfortunately, in state-of-the-art DTA such precision levels cannot be achieved (yet?). This is therefore an important test on DTA software. Finally, it is important to realize that, even though DUE may be more elegant in terms of route sets and lack of theoretical consistency problems with error correlation structures, it has the drawback that – compared to SUE – it converges much slower in standard (and in DTA still most used) iterative schemes like MSA (method of successive averages). DUE in MSA typically tends to decrease the gap over a few iterations, to then suddenly overshoot equilibrium such that the gap increases sharply again: it zig-zags towards equilibrium.

Access to (partial) route cost results

Given the importance and difficulty of converging to dynamic UE, it is of high importance to have insight into the equilibration that is produced by DTA software: one should not just trust the overall statistics! We therefore value high easy access to route trees, selected link analyses, route cost information (total impedance ànd the separate cost attributes), partial route cost information (eg between diverge and merge points, a so-called PAS), not only for used routes but also of possible alternative routes or PAS.

This is not only important to verify convergence to UE. It may also be very informative to analyze or manipulate the assignment, e.g. to find optimization directions if one is dissatisfied with the current traffic patterns in the network (e.g. rat running) and is interested in ways to change chosen routes.

Note that implicit route enumeration may be interesting for memory usage and calculation speed; on the other hand it may be problematic to produce route-related output.

Time discretization intervals

A DTA requires discretization of time in various sub-modules. For instance, OD demand is given in time slices, route choice decisions are fixed during route choice intervals and supply simulation may require yet other (usually smaller) time steps. In some DTA (rather DNL) algorithms that propagate aggregate or single-commodity traffic flows without distinguishing routes, origin or destination information in the propagation phase, yet another time interval may be used to update turn fractions at diverge nodes.

When all these time intervals are chosen independently from each other, numerical inconsistencies are inevitable. Such numerical imprecision may have similar detrimental consequences on UE precision, hence on comparison between scenarios, as non-convergence of UE.

Note finally that time discretization of traffic phenomena that are in principle continuously evolving (e.g. queue growing gradually, leading to constantly evolving travel times), necessitates the choice for a ‘representative’ fixed value of time-varying costs over an interval. This may be the cost at some reference time within the interval (beginning, end, middle point,…) or some kind of average value over that interval. The choice of such representative cost may affect convergence, even existence of equilibrium.

Links to other tests Other tests affecting this test:

Test 1 on propagation

Test 2 on Uninterrupted corridor (merges and diverges)

Test 3 on Signalized intersection

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Aims 4.1 Several networks and scenarios were used therefore the aim of each scenario is presented on its own section.

Software OmniTrans StreamLine

Version OmniTRANS 6.1.4.7667 / StreamLine

Operator Farzad Fakhraeiroudsari, Wei Huang

File location StreamLine\Test_ID_4_RouteChoice_Overlap

Document history 01 19-12-14 Farzad Fakhraeiroudsari, Wei Huang, Chris Tampère

02 27-02-15 Farzad Fakhraeiroudsari, Chris Tampère

Remarks VVC processed

Test results 4.1 4.1 Stochastic Route Choice The framework of StreamLine:

1. The generation of routes. For each OD pair the most plausible routes are selected before equilibrium iterations start. StreamLine uses these routes during the whole simulation.

2. The calculation of the route costs of the route alternatives.

Determining the cost can be done in two ways: reactive (instantaneous travel times) or predictive (trajectory based travel times).

Reactive route cost: In the reactive approach, the current situation on the network is used to determine the route costs, also called instantaneous travel time. The travel times are estimated by the average speeds on the links at that moment in time.

Predictive route cost: Based on travel costs in the previous iteration, StreamLine predicts approximately what the travel time of a route will be (only consistent when iterations are not too different). In the very first iteration, as no travel costs of a previous iteration exists, reactive route cost is used.

3. The calculation of the route fractions. StreamLine compares the route costs of the route alternatives that are calculated in step 2.

When the route costs are determined at every route choice moment, the demand is divided among the route alternatives, regarding different methods:

Uniform, AON

MNL, PCL (Pair Combinational Logit)

Then MSA method is used to average the route fractions using current iteration and the fractions in the previous iterations.

4. The propagation model. MaDAM is used to propagate the demand in the network (refer to case study 1, propagation)

5. The calculation of the route costs, based on the new speeds, flows and densities.

6. Convergence criteria check, that can be maximum number of iteration or route costs difference between each iteration.

In these tests, only stochastic route choice was performed.

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4.1.1 Same travel cost

For this test a simple network is considered where two routes are available and both routes have the same cost. Three hours demand is assigned to the network where vehicles traveling from zone A to B. In the first two hours 1000 veh/h are sent into the network where all links’ capacities are set to 2000 veh/h. The last hour is used to empty the network. The aim here is to verify the behavior of route choice model when both alternatives are equally important.

Supply properties

Assumption and initial inputs values

Simulation time 3 Hours Route Choice Method MSA

Demand Profile [1000,1000,0] Initial Route Choice MNL

Default No. of Iteration 50 Pre-trip route choice MNL

Duality Gap threshold 0.01 Route choice moments: 10 min

Route Generator MONTECARLO

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7 In this figure, as for similar figures in the remainder of this document, the route fractions sum up to 60% rather than 100%. This was an error in our postprocessing for generating the figures. Vertical axis should thus be scaled by a factor 100/60.

Expectation

This is a very simple test case where both routes have the same cost. It’s expected to have 50% share of demand using both routes (not because of deterministic UE – we use SUE here - rather because of symmetry).

Output summery results

Equilibrated Yes

Stopping criteria Duality Gap

No. of Iteration 3

Max Delta Value 0

Result

Looking at the output we can confirm that the result is consistent with the expectations (see Figure 70).

Figure 707: Travel cost (left) and route fractions (right) for test 4.1.1

Travel times have indeed been equilibrated (on top of each other in the figure). Both routes have equal route fraction.

This test produced accurate results.

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4.1.2 Route with cost a bit higher than the other one (under saturated)

In this section, we will illustrate the stochastic route choice model behavior when one route is a little bit more expensive than the other alternative. In this test, two routes are available where one route costs some extra second more. Three hours demand is assigned to the network which 1000 veh/h for the first hour and 2000 veh/h for the second hour while the capacity of all links are 2000 veh/h. The aim here is to test the sensitivity of the stochastic route choice model (by comparison to the previous case).

Supply properties

Assumption and initial inputs v alues

Simulation time 3 Hours Route Choice Method MSA

Demand Profile [1000,2000,0] Initial Route Choice MNL

Default No. of Iteration 50 Pre-trip route choice MNL

Duality Gap threshold 0.01 Route choice moments: 10 min

Route Generator MONTECARLO

Expectation

The expected outcome is that the faster route is used more, herewith partially (not fully) reducing the travel time difference. The result should only marginally differ from that in the previous test.

Output summery results

Equilibrated Yes

Stopping criteria Duality Gap

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No. of Iteration 7

Max Delta Value 0.008

SimTime (s) 100

Originally we ran this test and found strange behavior. At the merge, for some reason, speeds in the slower route drop extremely, herewith pushing most traffic to the faster route. It appeared that this may have something to do with the speed dynamics term: anticipation to density difference before and after the merge. Since the lower route carries hardly any flow and flow rather comes over the northern route into the merge, there is a large density difference between the last segment of the lower (empty) route and the receiving link of the merge (carrying all flow, coming from the upper route). This is (mis)interpreted as a queue tail, leading to a sharp deceleration response. The low speed resulting from this, confirms the route choice over the north, hence also the density difference and hence the low speed: we are trapped in a wrong solution (see Figure 71).

Figure 71: Abnormal speed reduction by having short downstream link

After some trial and error, we found that by making the receiving link longer, this effect did not occur. It is not completely clear why not. Anyhow, in this case, the expected moderate shift of traffic to the faster upper route is indeed observed (see Figure 72).

Figure 72: Travel cost (left) and route fractions (right) for test 4.1.2

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4.1.3 Over saturation with travel cost difference

The aim of this case is to check route choice behavior when there is a queue building up in one route. In this test, two routes are available to connect the demand from zone A to B. The upper route is 40% cheaper plus the first segment (Link 1) has more capacity than the other parts. This test has 3 hours simulation where for the first hour, travel demand reaches the upper and lower link’s capacity and in the second hour 50% more demand with be fed into the network. At this time, only first segment of upper route (link 1) can accommodate extra demand meanwhile the queue is building up at the downstream link causing travel cost to become higher for the vehicle on this route. Therefore rerouting to the lower route is necessary to reach equilibrium.

Assumption and initial inputs values

Simulation time 3 Hours Route Choice Method MSA

Demand Profile [1000,1500,0] Initial Route Choice MNL

Default No. of Iteration 100 Pre-trip route choice MNL

Duality Gap threshold 0.001 Route choice moments: 10 min

Route Generator MONTECARLO

Expectation

Upper route is cheaper and as result most of the users would choose that route until the point that demand is higher than the capacity. We are expecting to see upper route attracts the demand in first hour and for the second hour still upper route should be more attractive until formation the queue. By that point people starts to shift their route to lower one.

Output summery results

Equilibrated Yes

Stopping criteria Duality Gap

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No. of Iteration 11

Sim time (s) 165

Travel Cost and Route Fractions

As it was expected, both routes are used over the simulation time. In the first hour since upper route is cheaper, more flow assigned to it and as demand in the second hour increases, more flow shifts to lower route causing to have higher travel time in both routes. Travel time of these routes and their fraction is given in Figure 73. We don’t observe the saturation on the upper route as was expected. It appeared that this is not because of some problem in the model. Rather we had designed the scenario for deterministic route choice, where the upper route would indeed saturate. For stochastic route choice, already some fraction chose the lower route, herewith keeping demand on the upper route below saturation. We should thus have used higher demand levels to observe the desired behavior (though only realized this after our license had expired).

Figure 73: Travel cost (left) and route fractions (right) for test 4.1.3

Choosing t ime interval to calculate the travel time

SamplePercentage is used to determine the (travel time) cost of a route in a time interval. A specific moment can be chosen in the interval representing the mean cost. This property specifies the moment in the collection Interval which is chosen. When this property is set to 1, the end time of the interval is chosen, when set to 0 the begin time is chosen. Collection Interval defines the time interval in seconds at which a mean of the cumulative in and outflows are stored to base the (travel time) cost calculation on. In these entire tests collection interval is set to 60 s.

To check the behavior of this parameter on route choice same network as previous case with the same supply and demand characteristics is used. Previous figures are produced when sample percentage was set to 0.5, means the median of collection Interval time (30s) is used to compute the travel time.

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By putting the sample percentage to zero, the beginning of collection interval is used to calculate the route cost (see Figure 74).

Figure 74: Travel cost (left) and route fractions (right) when beginning of collection interval is used to calculate the route cost

While using the last vehicle to calculate the travel cost (sample percentage to 1) then the results are completely different (using predictive travel time gives negative travel time so for sample ==1 the reactive travel time calculation is used) (see Figure 75)

Figure 75: Travel cost (left) and route fractions (right) when end of collection interval is used to calculate the route cost

One should note that, when SamplePercentahe is set to 1, assignment cannot be run with predictive route cost calculation. It gives negative travel time!. These results are not consistent with our expectations and what theory states about this: when taking the first vehicle, oscillations occur over successive intervals; equilibrium is supposed to be most stable when the last vehicle is taken. For more information please check (Heydecker, Benjamin 1999).

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Stopping Criteria

StreamLine stops the simulation when a stop criterion is reached. StreamLine applies two stop criteria: the duality gap and the maximum number of iterations.

Duality Gap

The duality gap is the extent to which the route costs in the network change in comparison with the previous iteration. The user can set the duality gap threshold for convergence.

For each OD pair and each route choice moment, the costs of a specific route are compared with the route with the minimum cost of that OD pair and multiplied with the flow on that route. The values of all OD pairs in the network are summed and are divided by the sum of the minimum cost of an OD pair times the total demand on that OD pair, for all OD pairs and route choice moments.

Where dg is duality gap, q is the flow, c is cost, r is route, rcm, is route choice moment, od is OD pair and 𝑐𝑚𝑖𝑛 is minimum route cost.

After each iteration, for each route choice moment, the maximum duality gap is compared with the maximum duality gap of the corresponding route choice moment in the previous iteration. When the largest difference of duality gaps (dgmax) is lower than the threshold, which is set by the user, the simulation will stop.

In a deterministic user equilibrium, the costs of all used paths (i.e., with positive path flow) between an OD pair must be equal, hence upon convergence this duality gap will be equal to zero. However, in the case of stochastic user equilibrium, costs for all paths will not be the same; hence, this duality gap will never go to zero, although it will stabilize at a certain (unknown) positive value. StreamLine uses duality gap function for both stochastic and deterministic route choice and clearly this cannot be a good measure in the case of SUE where the gap function will not go to zero. Whereas looking at the difference of flow or cost of two successive iterations can be used instead (Cascetta 2009).

According to DAT.Mobility help desk latest update (which was gathered after license expiration and finalizing the report), new modification will be applied to the duality gap calculation in the case of stochastic route choice. Improved calculation of the duality gap will be done by introducing additional term to the route cost which compensate the stochastic component.

As mentioned before when route fractions calculated stochastically, all used routes won’t have the same cost at the equilibrium and there would be a cost difference at the numerator of Duality gap formula. This positive value will be compensated as following;

For each OD pair the “minimum adjusted routecost" is calculated as:

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Where rs is the origin destination pairs, p is the paths, f is flow and c is routecost. This can be interpreted as, this is the value travelers perceive the route costs and they will diverge to the route with the minimal cost plus the spread times the natural logarithm of the flow, instead of just the minimal cost.

Then, adjusted route cost of all routes of the same od pair is compared like what has been already done in duality gap.

Where d is demand. Note that when the spread is equal to zero, we calculate the regular Duality Gap again, and when the spread is high, the route cost has less influence. This calculation is only applied when the Boolean stochasticDualityGap is set “True”.

This improved duality gap calculation is indeed a good measure but in our test series this information and adjustment were not available and what has been already discussed was with regular duality gap function.

4.2 Deterministic Route Choice

Not Tested

Any other business

New questions triggered

Conclusions Conclusion from the test result on this aim Passed/ failed/ unanswered/

partially failed (mark bold if critical)

Perspective offered by developers: are we aware of plans to improve this result e.g. in next releases? if so, when?

4.1 In this test study, stochastic user equilibrium was investigated in StreamLine and to which extent this equilibrium changes due to parameter changes in StreamLine.

StreamLine has the ability to provide both stochastic and deterministic route choice. Although in this test only SUE was considered.

Partially Passed

Choosing last vehicle for cost calculation provides result inconsistent with what can be expected

It’s not possible to combine predictive cost calculation and samplePercentage set to 1

There was an error in our coding that calculates the route fraction wrongly. By relaxing that error, the fraction would be correct.

DAT.Mobility help desk corresponded to the new modification that is applied to

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Simple test cases were considered with one OD pair and two route alternatives where both routes had the same travel time, one route was slightly cheaper and when one alternative was cheaper but had lower capacity than total demand. The overall results were partially satisfactory and consistent with expectations. Although there are some remarks that needs to be considered:

When there is a large density difference between an ingoing and the outgoing link at a merge node, it is possible that the speed on the link upstream the merge node decrease unrealistically. This speed drop might be caused by the anticipation term in the speed formula of MaDAM. This situation is likely to happen where the receiving link has a short length, like at the on-ramps on highways.

The length of a route choice interval influences the accuracy of the results. The shorter a route choice interval, the more realistic the development of the route costs will be, but there are more iterations needed before the route costs are converged.

SamplePercentage is used to determine the (travel time) cost of a route in a time interval. Different values were used to consider first, median and last vehicle to calculate the travel time. However, the results were inconsistent with the expectations and theory background. Up to this stage, no extra feedback was given from help desk to confirm or reject the results and why model performs inconsistently.

In Test Case 1, uninterrupted propagation, we showed the influence and importance of speed parameters and it is clear that the

Documentation regarding different methods for route choice is poor

Unrealistic speed drops on expensive route can be observe by having short receiving link in merges

No distinction was provided in the manual for how duality gap is measured while using SUE or DUE

the duality gap calculation in the case of stochastic route choice. However, this information was received after finalizing the report and software license expiry.

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parameters tau, kappa and nue do influence the equilibrium and theoretically it is possible that the effects are different when a larger and more complex network is used.

Once more, documentation about different methods in route choice (AON, Uniform, MNL, PCL) and their formula and parameters is poor.

Determining the cost can be done in two ways: reactive (instantaneous travel times) or predictive (trajectory based travel times) although it’s not clear why choosing last vehicle as a reference for travel cost calculation cannot be combined with predictive cost calculation.

Route travel time and route fractions are two output of SL that can be exported and visualized.

In general, it’s possible to store, export and visualize the intermediate results easily.

It’s possible to change some parameters of route choice in the beginning of simulation not directly within intermediate iterations although the definitions of these parameters are documented not well. For example, the definition, formula and general background is missing and many of the explanation in this document are either gathered from different sources or from help desk directly.

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Conclusion

In this report, a series of benchmark cases was analyzed with StreamLine model of DAT.Mobility. In the beginning of the report, the main advantages and drawbacks of using second order models were discussed which later confirmed by different test cases. It seems the model has been improved compare to the default 2nd order propagation model where some heuristic rules in the software overrules the speed dynamics in the case of capacity drop. Besides, it has shown that how speed terms parameters can influence the results. Therefore, it is possible that the effects are uncontrollable when a larger and more complex network is used.

Modeling of the intersection delays and turn capacity seems to be limited where only incremental delays are taken into account. As a result, delay on arterials may be underestimated, herewith rendering them in the simulation too interesting rerouting alternatives for congested motorways, compared to the reality where more delays may be expected for the same flow levels. StreamLine reduces turn capacity by a default (and quite arbitrary!) in the case of conflicting movement which should be taken into account while defining intersections.

Accessing to the database is easy and straightforward and gives possibility to use Ruby language to export any simulation output. In general, OmniTRANS provides strong visualization tools that almost any output and intermediate iteration results can be visualized. The results of path trees, route costs and their components can be extracted although the route cost cannot be visualized directly using OmniTRANS interface and extra post processing is needed.

Overall, except some theoretical issues (speed drops near merge nodes, predictively travel time calculation and etc.), the results of the tests were in line with theoretical expectations, moreover, improvements to the user interface and enrichments to the documents and tutorial are expected. One should note that using second order models besides providing realistic transitional phases like smooth transition/deceleration from/to free flow - congestion or modeling capacity drops, they are very complicated and difficult to control. Therefore, there is always a tradeoff for the user to select second order modes, between the added value and their capability and difficulties. StreamLine shows to be a powerful tool for predicting rerouting effects in networks due to operational or tactical traffic measures.

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Reference

Cascetta, E., 2009. Transportation Systems Analysis: Models and Applications, Springer Science & Business Media.

Heydecker, Benjamin, and N.V., 1999. Calculation of Dynamic Traffic Equilibrium Assignments. In TRANSPORTATION PLANNING METHODS. PROCEEDINGS OF SEMINAR F, EUROPEAN TRANSPORT CONFERENCE. CAMBRIDGE, UK.

Himpe, W., Tampère, C.M.J. & Moelans, B., 2012. A Parsimonous Method For Off-Line Freeway Travel Time Estimation From Sectional Speed Detectors. Journal of Intelligent Transportation Systems: Technology, Planning, and Operations, submitted.

Slim Hammadi, M.K., 2013. Advanced Mobility and Transport Engineering, John Wiley & Sons, Ltd.

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