Elsevier S & T

Stochastic Models in Queueing Theory

Medhi, Jyotiprasad

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Table of contents
  • Cover
  • Contentsvii
  • Prefacexv
  • Chapter 1. Stochastic Processes1
  • 1.1 Introduction1
  • 1.2 Markov Chains2
  • 1.3 Continuous-Time Markov Chains14
  • 1.4 Birth-and-Death Processes23
  • 1.5 Poisson Process25
  • 1.6 Randomization: Derived Markov Chains32
  • 1.7 Renewal Processes35
  • 1.8 Regenerative Processes37
  • 1.9 Markov Renewal Processes and Semi-Markov Processes39
  • Problems41
  • References and Further Reading46
  • Chapter 2. Queueing Systems: General Concepts47
  • 2.1 Introduction47
  • 2.2 Queueing Processes50
  • 2.3 Notation51
  • 2.4 Transient and Steady-State Behavior52
  • 2.5 Limitations of the Steady-State Distribution53
  • 2.6 Some General Relationships in Queueing Theory54
  • 2.7 Poisson Arrival Process and Its Characteristics59
  • References and Further Reading62
  • Chapter 3. Birth-and-Death Queueing Systems: Exponential Models65
  • 3.1 Introduction65
  • 3.2 The Simple M/M/1 Queue65
  • 3.3 System with Limited Waiting Space: The M/M/1/K Model77
  • 3.4 Birth-and-Death Processes: Exponential Models81
  • 3.5 The M/M/oo Model: Exponential Model with an Infinite Number of Servers83
  • 3.6 The Model M/M/c84
  • 3.7 The M/M/c/c System: Eriang Loss Model95
  • 3.8 Model with Finite Input Source101
  • 3.9 Transient Behavior110
  • 3.10 Transient-State Distribution of the M/M/c Model127
  • 3.11 Multichannel Queue with Ordered Entry138
  • Problems and Complements145
  • References and Further Reading159
  • Chapter 4. Non-Birth-and-Death QueueingSystems: Markovian Models165
  • 4.1 Introduction165
  • 4.2 Bulk Queues174
  • 4.3 Queueing Models with Bulk (Batch) Service185
  • 4.4 M/M(a,b)/1: Transient-State Distribution196
  • 4.5 Two-Server Model: M/M(a,b)/2202
  • 4.6 The M/M((l,b)/c Model205
  • Problems and Complements210
  • References and Further Reading217
  • Chapter 5. Network of Queues221
  • 5.1 Network of Markovian Queues221
  • 5.2 Channels in Series or Tandem Queues222
  • 5.3 Jackson Network226
  • 5.4 Closed Markovian Network (Gordon and Newell Network)233
  • 5.5 Cyclic Queue236
  • 5.6 BCMP Networks238
  • 5.7 Concluding Remarks240
  • Problems and Complements242
  • References and Further Reading249
  • Chapter 6. Non-Markovian Queueing Systems255
  • 6.1 Introduction255
  • 6.2 Embedded-Markov-Chain Technique for the System with Poisson Input256
  • 6.3 TheM/6/1 Model: Pollaczek-Khinchin Formula259
  • 6.4 Busy Period276
  • 6.5 Queues with Finite Input Source: M/G/l//M System289
  • 6.6 System with Limited Waiting Space. M/G/l/K System292
  • 6.7 The M+/G/l Model with Bulk Arrival295
  • 6.8 The M/G(a,b)/l Model with General Bulk Service304
  • 6.9 The G/M/l Model306
  • 6.10 Multiserver Model314
  • 6.11 Queues with Markovian Arrival Process324
  • Problems and Complements326
  • References and Further Reading334
  • Chapter 7. Queues with General Arrival Time and Service-Time Distributions339
  • 7.1 The G/G/1 Queue with General Arrival Time and Service-Time Distributions339
  • 7.2 Mean and Variance of Waiting Time tV348
  • 7.3 Queues with Batch Arrivals G(X)/G/1356
  • 7.4 The Output Process of a G /G / 1 System358
  • 7.5 Some Bounds for the G/ G / 1 System360
  • Problems and Complements368
  • References and Further Reading371
  • Chapter 8. Miscellaneous Topics375
  • 8.1 Heavy-Traffic Approximation for Waiting-Time Distribution375
  • 8.2 Brownian Motion Process383
  • 8.3 Queueing Systems with Vacations398
  • 8.4 Design and Control of Queues423
  • 8.5 Retrial Queueing System427
  • 8.6 Emergence of a New Trend in Teletraffic Theory441
  • Problems and Complements455
  • References and Further Reading461
  • Appendix469
  • Index477
Book details
  • Vendor Elsevier S & T
  • SKU 9780124874626
  • ISBN-13 9780080541815
  • Author Medhi, Jyotiprasad
  • Edition 2nd
  • Category Mathematics
  • Subject General

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Description eBook delivery & access Reviews
This is a graduate level textbook that covers the fundamental topics in queuing theory. The book has a broad coverage of methods to calculate important probabilities, and gives attention to proving the general theorems. It includes many recent topics, such as server-vacation models, diffusion approximations and optimal operating policies, and more about bulk-arrival and bull-service models than other general texts.

* Current, clear and comprehensive coverage
* A wealth of interesting and relevant examples and exercises to reinforce concepts
* Reference lists provided after each chapter for further investigation