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Walk-In Clinic

SimulationTeam 14:

Archit AgnihotriJawed Karim

Salman Asif

Umer Iqbal

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Introduction

Medical attention and health care are two vital factors that influence ones life. The

amount of time one spends waiting to see a doctor is at times boundless.

The objective of our project is to analyze the waiting and service time at a clinic for

a patient, in an attempt to find the optimal number of doctors working at different

times during the day.

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Reception

Waiting Lounge

Doctor 3Doctor 2

Departure

Entrance

Doctor 1

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Data - VariablesEvent Counter System State Output

Arrival timeNumber of

arrivals

Patients at

Reception

Cost per

patient

Departure timeNumber ofdepartures

Patients inWaiting lounge

Number ofdoctors

Patients beingServed

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Assumptions Maximum capacity of the sitting area is K i.e. there cannot be more than K number of

patients waiting at any one time

Maximum number of doctors is N (corresponding to the total number of doctors offices)

We assume that patients have made no appointments with the doctor. Patients are served

on a first come, first serve basis.

Patients arrive one at a time i.e. no groups of sick people

One queue, multiserver system

Patients arrive independent of each other

The service time of all doctors is independent and identically distributed

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Summary of waiting timeMean 19.57

Var 571.19

Median 12.77

First Quartile 2.79

Third Quartile 23.55

Fourth Quartile 97.72

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Summary of service time

Mean 12.72

Var 85.16

Median 13.1

First Quartile 3.56

Third Quartile 20.43

Fourth Quartile 30.94

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Validation

Waiting times and Service Times follow exponential distribution.

Kolmogorov-Smirnov (K-S) test statistic

Sample means and variances using these values would not be adequate

Reliance on plots to determine the distribution

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Waiting time plot

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0

20

40

60

80

100

120

Wating time

Wa ting time

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Service time plot

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0

5

10

15

20

25

30

35

S ervic e Time

S ervice Time

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Simulation In order to improve the estimate of the average

waiting and service times, we simulated two

thousand data points

> mean(simulated.wait)

[1] 22.14312

> mean(simulated.serv)

[1] 12.57606

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Preliminary Conclusion

Average waiting time follows an exponential distribution with mean

(19.57) Minutes

Average service time follows an exponential distribution with mean

(12.72) - Minutes

Simulated mean for the waiting time - 22.14

Simulated mean for the service time - 12.57

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Recommendations

Collect more data points to avoid sampling errors and improve accuracy

Visit walk-in clinics across the country in order to collect data which is unbiased