The single server queue:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland Publ. Co.
1982
|
| Ausgabe: | Rev. ed. |
| Schriftenreihe: | North-Holland series in applied mathematics and mechanics
8. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 694 S. |
| ISBN: | 0444854525 |
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| 245 | 1 | 0 | |a The single server queue |c Jacob Willem Cohen* |
| 250 | |a Rev. ed. | ||
| 264 | 1 | |a Amsterdam |b North-Holland Publ. Co. |c 1982 | |
| 300 | |a XIV, 694 S. | ||
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| 650 | 4 | |a Queuing theory | |
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Datensatz im Suchindex
| _version_ | 1804116726791536640 |
|---|---|
| adam_text | CONTENTS
Part I. Stochastic Processes
1.1. Introduction 3
1.2. Markov Chains with a Discrete Time Parameter 6
1.2.1. Definition of the process 6
1.2.2. Classification of states 12
1.2.3. Ergodic properties of aperiodic irreducible Markov chains 18
1.2.4. Foster s criteria 21
1.2.5. Taboo probabilities 31
1.3. Markov Chains with a Continuous Time Parameter 34
1.3.1. Definition of the process 34
1.3.2. TheQ matrix 37
1.3.3. Types of states and ergodic properties 50
1.3.4. Foster s criteria 56
1.4. Birth and Death Processes 61
1.4.1. Introduction 61
1.4.2. The Poisson process 68
1.4.3. Death process with constant death rate 76
1.4.4. Birth and death process with constant birth and death rates .... 77
1.5. Derived Markov Chains 86
1.5.1. Introduction 86
1.5.2. Derived Poisson process 89
1.5.3. Derived death process 90
1.6. Renewal Theory and Regenerative Processes 95
1.6.1. Introduction 95
1.6.2. Renewal theorems 100
XI
XII CONTENTS
1.6.3. Past lifetime and residual lifetime 108
1.6.4. Regenerative processes 115
1.6.5. Some special renewal distributions 135
1.6.6. Fluctuation theory 141
Part II. The Single Server Queue
n.l. The Model 159
11.1.1. Introduction 159
11.1.2. Description of the model 162
11.1.3. Some general theorems and relations 167
H.2. The Queueing System M/Af/1 175
II.2.1. The number of customers in the system 175
U.2.2. The busy period 187
11.2.3. The waiting time 193
H.2.4. The departure process 195
11.3. The Queueing System G/M/l 203
II.3.1. Introduction 203
H.3.2. Description of the process for / « 204
H.3.3. The entrance and return time distributions 211
11.3.4. The transition probabilities 220
11.3.5. The busy period 225
11.3.6. The waiting time 229
11.3.7. The departure process 231
11.4. The Queueing System Af/G/1 234
11.4.1. Introduction 234
H.4.2. The imbedded Markov chain z« for » °° 236
11.4.3. Transition probabilities and first passage times 239
11.4.4. The busy period 249
11.4.5. The waiting time 253
H.4.6. The departure process 264
11.5. The Queueing System G/G/l 267
H.5.1. Introduction 267
11.5.2. Pollaczek s integral equation 271
11.5.3. The joint distribution of wn, dn, «re_i and bn 275
11.5.4. The actual waiting time 277
11.5.5. The busy period, the idle period and the busy cycle 283
11.5.6. The virtual waiting time and the idle time 290
11.5.7. The queue length 298
H.5.8. Integral representations 303
H.5.9. Truncated service time distribution, the system G/Ge/1 307
CONTENTS XIII
II.5.10. The queueing system GIKn/1 322
H.5.11. The queueing system ATm/G/1 329
H.6. Some Special Methods 332
II.6.1. Introduction 332
H.6.2. The method of the supplementary variable for the Af/G/1 queue. . 332
II.6.3. Lindley s integral equation 337
H.6.4. The method of collective marks 340
11.6.5. The phase method and its variants 341
H.6.6. The combinatorial method 349
II.6.7. Stochastic mean value theorems 363
Part III. Some Variants of the Single Server Queue
III.l. Introduction 377
IH.2. The Bulk Queue G/G/l 379
IH.2.1. The model 379
IH.2.2. Group arrivals, individual service for G/G/l 381
III.2.3. Group arrivals, individual service for M/G/l 385
HI.2.4. Group arrivals, batch service for Af/G/1 388
HI.2.5. The transportation problem 404
III.2.6. The bulk queue Af/G/1 with accessible batches 412
HI.2.7. The queue G/Af/1 with batch service 413
ni.2.8. The bulk queue G/Af/1 in inventory control 420
111.2.9. The G/G/l bulk queue with single arrivals and delayed service . . 424
III. 3. Priority Disciplines for a Single Server Queue 427
111.3.1. Introduction 427
111.3.2. Waiting time for last come, first served 430
111.3.3. Random service for Af/G/1 439
111.3.4. Random service for G/Af/1 443
IU.3.5. Completion times 446
III.3.6. Pre emptive resume priority for Af/G/1 with two priority levels. . 449
HI.3.7. Pre emptive repeat priority for Af/G/1 with two priority levels . . 453
III.3.8. Non break in priority for Af/G/1 with two and three priority levels . 454
IH.3.9. General pre emptive resume priority for Af/G/1 462
111.3.10. General non break in priority for Af/G/1 464
ni.3.11. Non break in random priorities for Af/G/1 470
HI.3.12. Comparison of variances for various service disciplines for Af/G/1 . 475
III.4. Uniformly Bounded Actual Waiting Time 478
IH.4.1. Introduction 478
HI.4.2. The time dependent solution 479
IH.4.3. The stationary distribution 487
XIV CONTENTS
IH.4.4. Entrance times and return times 491
IU.4.5. Application to the system M/G/l 495
111.4.6. Application to the system G/M/l 501
111.4.7. Application to the system M/M/l 505
111.5. The Finite Dam; Uniformly Bounded Virtual Waiting Time 507
IU.5.1. Introduction 507
111.5.2. The time dependent solution 509
111.5.3. The stationary distributions 518
HI.5.4. Entrance times and return times 524
HI.5.5. The finite dam model M/G/l 530
IH.5.6. The finite dam model G/M/l 541
111.5.7. Application to the system Af/M/1 545
111.5.8. The distribution ofcrossings of a level K for the infinite dam M/G/l. 546
111.5.9. The integro differential equation for the finite dam Af/G/1 ... 552
111.5.10. The dam M/G/l with non constant release 555
111.5.11. The dam G/G/1 with non instantaneous input 559
111.6. The M/G/l Queueing System with Finite Waiting Room 563
HI.6.1. Introduction 563
IH.6.2. The integral equation and its solution 564
III.6.3. Stationary distributions 570
ni.6.4. Entrance times and return times 578
HI.6.5. Return times of a state K within a busy cycle for the M/G/l queue
with infinite waiting room 587
111.7. Limit Theorems for Single Server Queues 595
HI.7.1. Introduction 595
111.7.2. Heavy traffic theory 596
111.7.3. The relaxation time 600
111.7.4. Limit theorems for the M/G/l queueing system 614
111.7.5. Limit theorems for the G/M/l queueing system 627
111.7.6. Behaviour of vt for/ °o if a 631
Part IV. Some Recent Developments
IV.1. Introduction 637
IV.2. A Survey of Recent Research 638
IV.2.1. Analysis of queueing processes 638
IV.2.2. Computer models and queueing networks 644
IV.2.3 Optimization and control 647
Appendix 650
Notes on Literature 657
References 667
References Supplement 676
Author Index 683
Index of Notations 686
Subject Index 689
|
| any_adam_object | 1 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.8/2 |
| dewey-sort | 3519.8 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Rev. ed. |
| format | Book |
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| isbn | 0444854525 |
| language | English |
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| spelling | Cohen, Jacob Willem 1923-2000 Verfasser (DE-588)118871927 aut The single server queue Jacob Willem Cohen* Rev. ed. Amsterdam North-Holland Publ. Co. 1982 XIV, 694 S. txt rdacontent n rdamedia nc rdacarrier North-Holland series in applied mathematics and mechanics 8. Files d'attente, Théorie des Queuing theory Einbediener-Wartesystem (DE-588)4151229-7 gnd rswk-swf Warteschlange (DE-588)4189150-8 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Einbediener-Wartesystem (DE-588)4151229-7 s 1\p DE-604 Warteschlange (DE-588)4189150-8 s 2\p DE-604 North-Holland series in applied mathematics and mechanics 8. (DE-604)BV001900898 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001490928&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohen, Jacob Willem 1923-2000 The single server queue North-Holland series in applied mathematics and mechanics Files d'attente, Théorie des Queuing theory Einbediener-Wartesystem (DE-588)4151229-7 gnd Warteschlange (DE-588)4189150-8 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| subject_GND | (DE-588)4151229-7 (DE-588)4189150-8 (DE-588)4255044-0 |
| title | The single server queue |
| title_auth | The single server queue |
| title_exact_search | The single server queue |
| title_full | The single server queue Jacob Willem Cohen* |
| title_fullStr | The single server queue Jacob Willem Cohen* |
| title_full_unstemmed | The single server queue Jacob Willem Cohen* |
| title_short | The single server queue |
| title_sort | the single server queue |
| topic | Files d'attente, Théorie des Queuing theory Einbediener-Wartesystem (DE-588)4151229-7 gnd Warteschlange (DE-588)4189150-8 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| topic_facet | Files d'attente, Théorie des Queuing theory Einbediener-Wartesystem Warteschlange Warteschlangentheorie |
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