6MM004Advanced Techniques in Operational Research Queuing TheoryWord格式文档下载.docx
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6MM004Advanced Techniques in Operational Research Queuing TheoryWord格式文档下载.docx
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Context–withinthefirststagethereisawaitingandservicetimewhereasinthesecondstagethereisjustacollectiontime(waitingandservicetimecombined).Thisisbecausetheservicetimewouldhardlyvarycustomertocustomer.Afterpayingforyouritems,withinthefirststage,youjointhecollectionqueue,withinthesecondstage.Inthecollectionqueueyouwaituntilyouarecalledtocollectyouritems,meaningthatcustomerwaitingtimewouldvarybuttheservicetimewouldhardlychangeasitemsarejusthandedover.
Poissondistribution–whenperformingourGPSSsimulationweareassumingaPoissondistribution,asthearrivalofcustomersdidnotoccuruniformly.ThismeanswecanrecyclethePoissondistributionforbothstages.
ObservedData
Thetablebelowshowsdetailsofthedatawegatheredontheday.
Thefirstcolumn,Customer,showstheorderofcustomerastheyjointhequeue,withatotalof50customersobserved.
Thesecondcolumn,Queue(In/Out),showsthetimeatwhichcustomersjoinedthequeueandleftQueueforTill.
Thethirdcolumn,Till(In/Out),showsthetimeatwhichcustomersjoinedTillandleftTilltocollecttheirproducts.
Thefourthcolumn,Collection(In/Out),showsthetimeatwhichcustomersjoinedandleftCollection.
Customer
Queue
Till
Collection
In
Out
1A
69
109
256
1B
70
285
575
1C
143
234
271
456
1D
312
313
684
1E
380
435
511
756
1F
411
595
916
1G
635
643
734
988
1H
707
772
1073
1I
726
843
1029
1J
733
781
835
1054
1K
735
894
1072
1L
841
876
1M
878
886
923
1N
947
956
1080
1182
1O
1184
1197
1334
1552
1P
1215
1245
1355
1533
1Q
1246
1367
2046
1R
1273
1390
1507
1S
1278
1403
1589
1T
1350
1453
1627
1U
1456
1652
1V
1418
1518
1W
1553
1554
1603
1739
1X
1799
1809
2766
1Y
1864
2034
2106
2305
1Z
2072
2185
2523
2A
2078
2352
3031
2B
2137
2463
2512
2C
2138
2570
2818
2151
2616
2706
2254
2649
2941
2304
2693
2850
2306
2806
2992
2309
2812
3184
2I
2624
2846
3167
2J
2656
2871
3417
2K
2928
3222
2L
2729
3241
3460
2M
2890
2972
3298
2N
2902
2985
3494
2O
2916
3057
3324
2P
3111
3216
3352
3599
2Q
3238
3279
2R
3303
3317
3677
3737
2S
3458
3539
3566
3711
2T
3550
3655
3743
2U
3846
3860
3909
3974
2V
3883
3964
4050
2W
3910
4022
4192
2X
4040
4090
4328
4481
Thesecondtableshowsmoredetailsofthedatawegatheredontheday.
Thefirstcolumn,Customer,showstheorderofcustomerastheyjointhequeue.
Thesecondcolumn,Arrivals,showsthetimeatwhichanewcustomerjoinedtheQueue,afterthepreviouscustomer.
Thethirdcolumn,WaitingTime,showsthewaitingtimeforeachcustomerintheQueueuntiljoiningtheTill
Thefourthcolumn,ServiceTime,showsthetotalservicetimeeachcustomerspentattheTill.
Thefifthcolumn,CollectionTime,showsacombinedtime,waitingandservice,eachcustomerspentatCollection.
Arrivals
WaitingTime
ServiceTime
CollectionTime
40
147
39
176
290
73
91
37
185
169
1
262
68
55
76
245
31
100
84
321
224
8
254
72
27
38
301
19
46
71
186
7
48
54
219
2
59
178
106
33
9
124
102
237
13
137
218
30
110
88
679
82
35
117
5
89
36
63
174
17
53
196
51
65
135
49
136
246
10
957
170
199
208
34
79
338
6
107
167
215
111
325
248
419
90
103
362
292
50
345
44
157
387
113
3
457
372
315
182
32
156
546
190
294
142
370
161
326
12
509
14
267
195
105
247
127
360
60
155
81
145
92
16
296
26
86
58
130
238
153
HandSimulation
Havingobservedthequeuingsystemandrecordedthedata,wecreatedahandsimulationofhowthetwo-stagequeuingsystemactuallyworkedinpractice
Time
Stage1
Stage2
Notes
Size
Start
End
StartA
EndA
StartB
EndB
-
1AENTERSQUEUE
1ALEAVESQUEUE
1AENTERSTILLA
1BENTERSQUEUE
1ALEAVESTILLA
1AENTERSCOLLECTION
1BLEAVESQUEUE
1BENTERSTILLA
1CENTERSQUEUE
1CLEAVESQUEUE
1CENTERSTILLB
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