Stochastic models in queueing theory

0124874622......Page 1
Copyright Page......Page 5
Contents......Page 8
Preface ......Page 16
1.1 Introduction......Page 20
1.2 Markov Chains......Page 21
1.3 Continuous-Time Markov Chains......Page 33
1.4 Birth-and-Death Processes......Page 42
1.5 Poisson Process......Page 44
1.6 Randomization: Derived Markov Chains......Page 51
1.7 Renewal Processes......Page 54
1.8 Regenerative Processes......Page 56
1.9 Markov Renewal Processes and Semi-Markov Processes......Page 58
Problems......Page 60
References and Further Reading......Page 65
2.1 Introduction......Page 66
2.2 Queueing Processes......Page 69
2.3 Notation......Page 70
2.4 Transient and Steady-State Behavior......Page 71
2.5 Limitations of the Steady-State Distribution......Page 72
2.6 Some General Relationships in Queueing Theory......Page 73
2.7 Poisson Arrival Process and Its Characteristics......Page 78
References and Further Reading......Page 81
3.2 The Simple M/M/1 Queue......Page 84
3.3 System with Limited Waiting Space: The M/M/1/K Model......Page 96
3.4 Birth-and-Death Processes: Exponential Models......Page 100
3.5 The M/M/oo Model: Exponential Model with an Infinite Number of Servers......Page 102
3.6 The Model M/M/c......Page 103
3.7 The M/M/c/c System: Eriang Loss Model......Page 114
3.8 Model with Finite Input Source......Page 120
3.9 Transient Behavior......Page 129
3.10 Transient-State Distribution of the M/M/c Model......Page 146
3.11 Multichannel Queue with Ordered Entry......Page 157
Problems and Complements......Page 164
References and Further Reading......Page 178
4.1 Introduction......Page 184
4.2 Bulk Queues......Page 193
4.3 Queueing Models with Bulk (Batch) Service......Page 204
4.4 M/M(a,b)/1: Transient-State Distribution......Page 215
4.5 Two-Server Model: M/M(a,b)/2......Page 221
4.6 The M/M((l,b)/c Model......Page 224
Problems and Complements......Page 229
References and Further Reading......Page 236
5.1 Network of Markovian Queues......Page 240
5.2 Channels in Series or Tandem Queues......Page 241
5.3 Jackson Network......Page 245
5.4 Closed Markovian Network (Gordon and Newell Network)......Page 252
5.5 Cyclic Queue......Page 255
5.6 BCMP Networks......Page 257
5.7 Concluding Remarks......Page 259
Problems and Complements......Page 261
References and Further Reading......Page 268
6.1 Introduction......Page 274
6.2 Embedded-Markov-Chain Technique for the System with Poisson Input......Page 275
6.3 TheM/6/1 Model: Pollaczek-Khinchin Formula......Page 278
6.4 Busy Period......Page 295
6.5 Queues with Finite Input Source: M/G/l//M System......Page 308
6.6 System with Limited Waiting Space. M/G/l/K System......Page 311
6.7 The M+/G/l Model with Bulk Arrival......Page 314
6.8 The M/G(a,b)/l Model with General Bulk Service......Page 323
6.9 The G/M/l Model......Page 325
6.10 Multiserver Model......Page 333
6.11 Queues with Markovian Arrival Process......Page 343
Problems and Complements......Page 345
References and Further Reading......Page 353
7.1 The G/G/1 Queue with General Arrival Time and Service-Time Distributions......Page 358
7.2 Mean and Variance of Waiting Time tV......Page 367
7.3 Queues with Batch Arrivals G(X)/G/1......Page 375
7.4 The Output Process of a G /G / 1 System......Page 377
7.5 Some Bounds for the G/ G / 1 System......Page 379
Problems and Complements......Page 387
References and Further Reading......Page 390
8.1 Heavy-Traffic Approximation for Waiting-Time Distribution......Page 394
8.2 Brownian Motion Process......Page 402
8.3 Queueing Systems with Vacations......Page 417
8.4 Design and Control of Queues......Page 442
8.5 Retrial Queueing System......Page 446
8.6 Emergence of a New Trend in Teletraffic Theory......Page 460
Problems and Complements......Page 474
References and Further Reading......Page 480
Appendix......Page 488
Index......Page 496