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Page 28: 102.4365278 9, 7852:?7

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λ λ1 C...

λ λ1 C...

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fixed optical filters

Resolution MechanismBatcher/Banyan Contention

PortController 1

PortController N

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EO

EO

PortController 1

tunable

lasers

passive star

input queues

PortController N

OE

OE

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Page 29: 102.4365278 9, 7852:?7

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optical filters

tunable

lasers

fixed freq.

......

..

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Controller 1Output

Controller NOutput

TokenProcessor

TokenProcessor

passive star

Controller 1

Controller NInput

Input

TokenGenerator

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� ! � 6�� � + � �,+ & ��6 � &������ &����9& �"6 �

+ � +��9& ��6 � &������ &����9& �"6 $ &������ &���� P 2G) $ �K\

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Page 53: 102.4365278 9, 7852:?7

2 �

0

50

100

150

200

250

300

350

400

450

500

2 4 6 8 10 12 14 16

Arr

ival

Slo

ts

Process

Mean Interarrival TimeSquared Coeff. of Variation of Interarrival Time

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Page 54: 102.4365278 9, 7852:?7

2 2

(a) C = 4

(b) C = 6

(c) C = 8

1 1 2 3 3 4 4 5 8

1 1 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9

1 x x x x x x x x 2 3 4 5 6 7 8 9

2 5 6 6 7 7 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16

10 10 11 11 12 12 13 13 14 14 15 15 16 162

16151413121110

arrival slots

service slots & serviced input port

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Page 55: 102.4365278 9, 7852:?7

2&%

1e-011

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Inpu

t Por

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s

Buffer Size

C = 4C = 6C = 8

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��H�>?=�02hl`'><0JO8=�H(E85WH-jlOG,MOG, $ 5WH->?7GadOGHbab02.(H �@^�>?:?:Whb,F=(OGh �I,M�9H�HI0�7G02H�0J78:<;SH(EG,F>?7KHI,!.452�9H(><0J78=T8>?=(�!O8=(=I,MT�5Whb0u`2,2%GhdOGHC52:?=I0&H(EG,S,9tb,M�9H(=�02/�H(EG,"�4E8527GZJ>?7GZ&HI.45wv���ad5WHIHI,!.478=�T8OG,�HI0�H(EG,S.(,M52:?:<0'�!5WH(><0J702/"0JOGHIadOGH6ab02.(H(=B^�><H(E H(EG,�52T8T8><H(><0J7 02/$7G,!^ �4E852787G,M:?=NP =I,!,��c5Whd:<, 2G) �K\() ��7,L�><ZJOG.(, 2G) �,+'%UH(EG,HI.45wv��"52:?:<0'�!5WHI,MTHI0BH(E8>?=CjlOG,MOG,"TG,M�9.(,M52=I,M=�/1.(0J3 � + � 02/�H(E85WH�0Wtb,!.(,MTHI06>?7GadOGHFab02.(H �SHI0 ��� � 52=� >?78�9.(,M52=I,M="/1.(0J3 2xHI0 �l)��UE8>?="�4E8527GZ2,�>?7gH(EG,6HI.45wv��65W.(.4><`W52:�.45WHI,NPR/1.(0J3 5x3B,M527i7G02.43652:?>��!,MT0Wtb,!.(,MT�:<0J52Tx02/ +') � � %�HI0 +') �,+@%6ab,!.�5W.(.4><`W52:�=(:<02H9\C>?=U,M7G0JOGZJENHI0�0Wtp=I,!H�H(EG,&�4E8527GZ2,�>?7YH(EG,&=I,!.(`'>?�9,.45WHI,2)N�UEG,AF��+ `W52:?OG,M=$/102.A� 6 �x5W.(,:<,M=(=$H(E8527iH(E85WH&/102.A� 6 2�>?7 L�><ZJOG.(, 2G) ���T8OG,6HI0�H(EG,/R52�9H�H(E85WHUH(EG,��4E8527GZ2,&>?7YH(EG,�3B,M527N7G02.43652:?>��!,MT0Wtb,!.(,MT�:<0J52TiPR/1.(0J3 +') � $ ��HI0 +') + � $ 2ab,!.U5W.(.4><`W52:=(:<02H9\@>?=C7G02H�=(OGhd=IH(527KH(>?52:_,M7G0JOGZJE�HI0B0Wtp=I,!H�H(EG,"�4E8527GZ2,$>?7�H(EG,"=I,!.(`'>?�9,S.45WHI,2)D �=�� >?78�9.(,M52=I,M=CHI0 �l%EG0u^F,!`2,!.M%KH(EG,!.(,U>?=�7G0"�4E8527GZ2,�>?7&H(EG,�0Wtb,!.(,MTBHI.45wv��C/102.@,M><H(EG,!.@jlOG,MOG, �K52=�,9e'ab,M�9HI,MTp%JH(EG,�AF��+i.4>?=I,M=^�><H(EiH(EG,�TG,M�9.(,M52=I,>?7iH(EG,�7G02.43652:?>��!,MTk=I,!.(`'>?�9,6.45WHI,2)��UEG,�365weG>?3&O83 5Whd=I0J:?OGHI,�,!.(.(02.&02hd=I,!.(`2,MThb,!Ho^F,!,M7�H(EG,�5278:?5M;lH(>?�U.(,M=(O8:<H(=D5278T6H(EG,�3B,M527�=(>?3&O8:?5WHI,MT6.(,M=(O8:<H(=@/102.FjlOG,MOG, $ 02/�>?7GadOGH-ab02.(H ��^C52=� � � � � �,+ � � �lH(EG,S:<0J=(=D/102.C>?7GadOGHDjlOG,MOG, $ 02/�ab02.(H ���90JO8:?T�7G02HFhb,�,M=IH(>?365WHI,MT�/102.FH(EG,S=(523B,�.(,M52=I0J7

Page 56: 102.4365278 9, 7852:?7

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L�><ZJOG.(,�2G) � �@��7GadOGH@ab02.(HF�9,M:?:_:<0J=(=Da8.(02hd5Whd>?:?><Ho;A:<>?; 0F/102.��76=28& �9& ��52=C5�/RO878�9H(><0J7602/�hdO'tb,!.C=(>��!,/=

52=UH(E85WHU/102.�jlOG,MOG, �"02/->?7GadOGHCab02.(H � � )�UEG,AF��+ 5WH&0JOGHIadOGH$ab02.(H ��>?=�=(>?36>?:?5W.4:<;�5wtb,M�9HI,MT hl;fH(EG,�=(�4EG,MT8O8:<,6ad5W.4523B,!HI,!.4=�P =I,!,

L�><ZJOG.(,�2G) � $ \()S��7NH(EG,��!52=I,�^�EG,!.(, � 6 2G%b^F,�E85M`2,� 6 ��5278T ���10wP%$p\ 6 � $ %p3B,M5278>?7GZ�H(E85WH

52=$36527K;�52= � $ 5W.(.4><`W52:?=�365M;ghb,&a8.(,M=I,M7KHI,MTfHI0YH(E8>?=S0JOGHIadOGHSab02.(H"T8OG.4>?7GZ�5/1.4523B,�^�E8>?:<,&0J78:<;��365M;�hb,B=I,!.(`'>?�9,MTp) � 6 � $ /102.�� 6 �5278T � 6 ��^�><H(E �

��10uP%$p\�6 � $ 5278T �

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.(,M=Iab,M�9H(><`2,M:<;2)-�UEG,CTG.452365WH(>?�F�4E8527GZ2,�>?7 ���10uP%$p\�>?=cT8OG,FHI0SHo^F0$365��I02.��4E8527GZ2,M=�>?7�H(EG,�=(�4EG,MT8O8:<,�� =

=IHI.4O8�9H(OG.(,2)oL802."� 6 �l%�H(EG,�H(O878>?7GZ�H(>?3B,�/102.$5HI.45278=(36><HIHI,!.$�4E8527GZ2,M="/1.(0J3�2x=I,!.(`'>?�9,B=(:<02H(=SHI0 $=I,!.(`'>?�9,S=(:<02H(=C5278T�H(EG,S`W52:?OG,M=D02/�,.!#�C�4E8527GZ2,S/1.(0J3 $ =I,!.(`'>?�9,S=(:<02H(=FHI0 �S=I,!.(`'>?�9,S=(:<02H!)@�UEG,�,9tb,M�9H�02/H(EG,M=I,&ad5W.4523B,!HI,!.$�4E8527GZ2,M=�0J7�H(EG,�=(�4EG,MT8O8:<,&>?=�H(E85WHS5�=(><ZJ78>PO_�!527KH�523B0JO87KH�02/@H(EG,&hd5278TG^�>?TGH(Ex>?7H(EG, ���4E852787G,M:��!52=I,�>?=SO87lO8=I,MTgT8OG,�HI0YHI.45278=(36><HIHI,!.4="E85M`'>?7GZHI0YH(O87G,�HI0YH(EG,636527K;�/1.(,MjlOG,M78�!><,M=!)�UEG,B.(,M52TG,!.�>?="T8><.(,M�9HI,MTgHI0 � � ���D/102.�5Y�90J3Bad:<,!HI,�T8>?=(�!O8=(=(><0J7N02/CH(E8>?=SadEG,M7G0J3B,M785')B�UEG,�AF��+�/102.0JOGHIadOGH�ab02.(H �Bhb,ME85M`2,M=S=(>?36>?:?5W.4:<;�>?7 L�><ZJOG.(,�2G) ���l)��UEG,&365weG>?3&O83 5Whd=I0J:?OGHI,$,!.(.(02.�hb,!Ho^F,!,M7�H(EG,=(>?3&O8:?5WHI,MT65278T�527852:<;lH(>?��:<0J=(=@`W52:?OG,M=�/102.D0JOGHIadOGH@ab02.(H(= �U5278T��S^F,!.(, � � 2&% ���,+ � � 5278T � � � ���,+ � �2%.(,M=Iab,M�9H(><`2,M:<;2)

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Page 57: 102.4365278 9, 7852:?7

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Page 58: 102.4365278 9, 7852:?7

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1e-030

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oss

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Page 59: 102.4365278 9, 7852:?7

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Page 60: 102.4365278 9, 7852:?7

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Page 61: 102.4365278 9, 7852:?7

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λ λ1 C...

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input queues

lasers

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inputpassive star

port 1

output

output

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λ(1)

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,M3�hb,MT8TG,MTi5WH&5W.(.4><`W52:�=(:<02H$hb0JO878T85W.4><,M=!)��UEG,B02.4TG,!.�02/C,!`2,M7KH(=&>?=�52=$/10J:?:<0u^�=!)��UEG,6=I,!.(`'>?�9,NP > ) ,2)<%HI.45278=(36>?=(=(><0J7b\-�90J3Bad:<,!H(><0J702/-5��9,M:?:b0'�!�!OG.4=�5WHU527Y>?78=IH(527KH �(O8=IHChb,!/102.(,SH(EG,",M78T�02/-5B=I,!.(`'>?�9,"=(:<02H!) �7�5W.(.4><`W52:'365M;�0'�!�!OG.�5WH@527�>?78=IH(527KH �(O8=IHchb,!/102.(,FH(EG,C,M78T&02/_527B5W.(.4><`W52:l=(:<02H!%2hdOGH-5W/1HI,!.�H(EG,�=I,!.(`'>?�9,�90J3Bad:<,!H(><0J76>?78=IH(527KH�02/p5$=I,!.(`'>?�9,U=(:<02H@^�EG0J=I,�,M78T6>?=@52:?><ZJ7G,MT�^�><H(E�H(EG,U,M78TB02/p52765W.(.4><`W52:G=(:<02H!)��UEG,$ Lo��� �F+�TG,M=(�9.4><hd>?7GZ�H(EG,�5W.(.4><`W52:pa8.(0'�9,M=(=�HI0�H(EG,&jlOG,MOG,�365W[2,M=�56=IH(5WHI,&HI.45278=(><H(><0J7x>?363B,MT8>?5WHI,M:<;5W/1HI,!.BH(EG,5W.(.4><`W52:F>?78=IH(527KH!)DL�>?7852:?:<;2%-H(EG,��5W.([20u` �4E852>?7 >?=�02hd=I,!.(`2,MT 5WH�H(EG,�hb0JO878T85W.(;g02/�,M52�4E5W.(.4><`W52:�=(:<02H!% ����( ����H(EG,&=IH(5WHI,�HI.45278=(><H(><0J7Nhl;YH(EG, $ Lo��� �F+-)��UEG,�02.4TG,!.�02/@H(EG,M=I,&,!`2,M7KH(=">?=�=(EG0u^�7>?7 L�><ZJOG.(,�%l) �'PRhp\()

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a

(a)

Frame

λc

(b)

observation instant

transition instant

service completioninstant

2-MMBP statearrival instant

x-1 x x+1

x x+1

ik

L�><ZJOG.(, %l) � �FP 5l\GMl,!.(`'>?�9,@ab,!.4><0'TS02/8>?7GadOGHbab02.(H��d/102.�`'><.(H(O852:2.(,M�9,M><`2,!. �d%25278T�PRhp\_TG,!H(52>?:K=(EG0u^�>?7GZUH(EG,.(,M:?5WH(><0J78=(E8><aN523B0J7GZ=I,!.(`'>?�9,��90J3Bad:<,!H(><0J7p%b5W.(.4><`W52: % $ Lo��� �F+ =IH(5WHI,�HI.45278=(><H(><0J7p%_5278TN02hd=I,!.(`W5WH(><0J7>?78=IH(527KH(=�^�><H(E8>?756=I,!.(`'>?�9,$5278TY527N5W.(.4><`W52:p=(:<02H

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�UEG,�HI.45278=(><H(><0J76a8.(02hd5Whd>?:?><H(><,M=�0JOGHF02/�=IH(5WHI,BP%$'&)(4&�'\@5W.(,SZJ><`2,M7�>?7��c5Whd:<,1%l) �W)D �=Fhb,!/102.(,2%H(EG,U7G,9e'H�=IH(5WHI,�5W/1HI,!.�P%$'&)(4&�'\c52:<^C5M;'=�E852=@527B5W.(.4><`W52:'=(:<02H�7lO83�hb,!.-,MjlO852:'HI0 $ � �W)-��7�H(EG, Od.4=IH-.(0u^02/c�c5Whd:<, %l) ��^F,"52=(=(O83B,�H(E85WH�H(EG, $ Lo��� �F+�365W[2,M=U5&HI.45278=(><H(><0J7�/1.(0J3s=IH(5WHI, ��HI0B=IH(5WHI, � � PR/1.(0J3P 2G) $ \(%8H(E8>?=D,!`2,M7KHUE852=�5&a8.(02hd5Whd>?:?><Ho; � � ��� � �! 02/�0'�!�!OG.(.4>?7GZ'\(%'5278T�H(E85WH�7G0B�9,M:?:_5W.(.4><`2,M=CHI0�H(E8>?=FjlOG,MOG,T8OG.4>?7GZNH(EG,Y�!OG.(.(,M7KHB=(:<02HxPR/1.(0J3 P 2G) $ \&5278T P %l) �w\(%CH(E8>?=&0'�!�!OG.4=�^�><H(E a8.(02hd5Whd>?:?><Ho; � $ � � � �! � ��� �! \()M'>?78�9,�5WHC3B0J=IH � ! P%$ � �w\��9,M:?:?=D5W.(,�=I,!.(`'>?�9,MT�T8OG.4>?7GZ$5W.(.4><`W52:8=(:<02H $ � �W%'5278T�=(>?78�9,�7G0&�9,M:?:d5W.(.4><`2,M=!%H(EG,�jlOG,MOG,�:<,M7GZ2H(E�5WHDH(EG,�,M78T602/pH(EG,S=(:<02HD>?=D,MjlO852:8HI0�365we �"+ &)( $ � ! P%$ � �w\��J)���76H(EG,S=I,M�90J78T�.(0u^02/D�c5Whd:<, %l) �&^F,B52=(=(O83B,�H(E85WHSH(EG, $ Lo��� �F+ 365W[2,M="5�HI.45278=(><H(><0J7x/1.(0J3 =IH(5WHI, ��HI0=IH(5WHI, � � 5278T5�9,M:?:c5W.(.4><`2,M=�HI0H(EG,BjlOG,MOG,2)$�UE8>?=�5W.(.4><`'>?7GZ��9,M:?:c�!52787G02HShb,�=I,!.(`'>?�9,MTgT8OG.4>?7GZ6H(E8>?=�=(:<02H!%p5278TgE852=

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P%$'&)(4&�'\ P%$�� � &365we �"+ &)( $ � ! P%$ � �w\�� &� � \ � � ��� � �! P � $ � � � �! � ��� �! \

P%$'&)(4&�'\ P%$ � � &(36>?7 � = � !�� �! &� � &365we �"+ &)( $ � ! P%$ � �w\�� � � �2\

� � ��� � �! � � � �! � ��� �!

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� ! P%$p\ 6

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= � !�� �!

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Physical receiverscorresponding tovirtual receiver "k"

.

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passive star

.

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1

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input queues corresponding

receiver "k"to virtual

λ(1)

λ(Ν)

λ

λ

L�><ZJOG.(,�%l) 2 �/>SOG,MOG,M>?7GZB=(OGhGLo7G,!Ho^F02.([�/102.�`'><.(H(O852:_.(,M�9,M><`2,!.�������

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>?7GadOGHCjlOG,MOG,M=U>?=�['7G0u^�7p)��f,&�!527YH(EG,M7xTG, O_7G,$5xP%� � �w\ LoT8>?3B,M78=(><0J7852:p��5W.([20u`x�4E852>?7p%G^�EG,!.(,

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� � � � 6 � &������ &)� >?78T8>?�!5WHI,M=6H(EG,g7lO83�hb,!.�02/��9,M:?:?=�5WH�H(EG, � � 0JOGHIadOGH�jlOG,MOG, P � 6+ &�� &������ &)= � ����� �� \()

�UEG,6HI.45278=(><H(><0J78=S0JOGH$02/U=IH(5WHI,�P%$'&�0 &������ & � \��!527ihb,��90J3BadOGHI,MTiZJ><`2,M7iH(EG,�=(�4EG,MT8O8:<,65278TiH(EG,jlOG,MOG,$:<,M7GZ2H(ExT8>?=IHI.4><hdOGH(><0J7�02/-H(EG,�>?7GadOGHCab02.(H(=!)@V�0u^F,!`2,!.M%_/102.U.(,M52:?>?=IH(>?�"=I^�><H(�4ExT8>?3B,M78=(><0J78=!%lH(E8>?=3B,!H(EG0'TY^�>?:?:b:<,M52TxHI0�56=IH(5WHI,�=Iad52�9,$,9e'ad:<0J=(><0J7Y=(>?78�9,$H(EG,$HI02H(52:�7lO83�hb,!.U02/�=IH(5WHI,M=�>?=C02/-H(EG,$02.4TG,!.02/�� � � �� �'0 = � ����� �� )

� SESE6:F��G9<RT5 78X �[UGX UGX 9<;G] � ;G5��768�89 �AF0J78=(>?TG,!.U56`'><.(H(O852:p.(,M�9,M><`2,!. ������ ) M'>?78�9,"H(E8>?=U`'><.(H(O852:b.(,M�9,M><`2,!.�.(,M�9,M><`2,M=�HI.45wv��$,9eG�!:?O'L

=(><`2,M:<;�/1.(0J3 H(EG,C� >?7GadOGH�jlOG,MOG,M=$PR,9eG52�9H(:<;��$jlOG,MOG,�5WHU,M52�4E�>?7GadOGHCab02.(H9\F�902.(.(,M=Iab0J78T8>?7GZ&HI0�H(E8>?=`'><.(H(O852:p.(,M�9,M><`2,!.M%dH(EG,&=I^�><H(�4EN365M;Yhb,�TG,M�90J3Bab0J=I,MTxhl;Y`'><.(H(O852:b.(,M�9,M><`2,!.S>?7x02.4TG,!.�HI0�527852:<; �!,�H(EG,0JOGHIadOGH�=(>?TG,2)��UE8>?=�TG,M�90J3Bab0J=(><H(><0J7N>?=�=(EG0u^�7�>?7�L�><ZJOG.(, %l) 2G)S��7��90J78=(>?TG,!.4>?7GZ6`'><.(H(O852:�.(,M�9,M><`2,!. �d%><H�>?=�>?3Bad:?>?�!><H�>?7xT8>?=(�!O8=(=(>?7GZ6>?7GadOGHCab02.(H��FH(E85WH�0J78:<;H(EG,&jlOG,MOG,��02/�H(EG,&>?7GadOGH�ab02.(H�>?=U.(,M:<,!`2,M7KH��H(EG,!.(,!/102.(,$H(E8>?=�=Iab,M�!>PO_�!5WH(><0J7Y>?=U7G02H�,9e'ad:?>?�!><H(:<;�TG,M7G02HI,MTN>?7H(EG,"/10J:?:<0u^�>?7GZBT8>?=(�!O8=(=(><0J7p)

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Page 87: 102.4365278 9, 7852:?7

���

(a)

a i+1,caic

Frame

λc

(b)

observation instant

arrival instantinstant at which

x+1

x+1

xx-1

x

batch departure occurs

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Page 89: 102.4365278 9, 7852:?7

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Page 90: 102.4365278 9, 7852:?7

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λc

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observation instant

instant at whichdeparture ends

x+1

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Buffer Size [segments]

Process 1 (analysis)Process 1 (simulation)

Process 2 (analysis)Process 2 (simulation)

Process 3 (analysis)Process 3 (simulation)

Process 4 (analysis)Process 4 (simulation)

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put P

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Buffer Size [segments]

Process 1 (analysis)Process 1 (simulation)

Process 2 (analysis)Process 2 (simulation)

Process 3 (analysis)Process 3 (simulation)

Process 4 (analysis)Process 4 (simulation)

L�><ZJOG.(,&A�) 2 �C#SOGHIadOGHC+-02.(HU+�52�([2,!HS��0J=(=�+D.(02hd5Whd>?:?><Ho; :�0�/102.5� 6 �