Front Cover -- Stochastic Models in Queueing Theory -- Copyright Page -- Contents -- Preface -- Chapter 1. Stochastic Processes -- 1.1 Introduction -- 1.2 Markov Chains -- 1.3 Continuous-Time Markov Chains -- 1.4 Birth-and-Death Processes -- 1.5 Poisson Process -- 1.6 Randomization: Derived Markov Chains -- 1.7 Renewal Processes -- 1.8 Regenerative Processes -- 1.9 Markov Renewal Processes and Semi-Markov Processes -- Problems -- References and Further Reading -- Chapter 2. Queueing Systems: General Concepts -- 2.1 Introduction -- 2.2 Queueing Processes -- 2.3 Notation -- 2.4 Transient and Steady-State Behavior -- 2.5 Limitations of the Steady-State Distribution -- 2.6 Some General Relationships in Queueing Theory -- 2.7 Poisson Arrival Process and Its Characteristics -- References and Further Reading -- Chapter 3. Birth-and-Death Queueing Systems: Exponential Models -- 3.1 Introduction -- 3.2 The Simple M/M/1 Queue -- 3.3 System with Limited Waiting Space: The M/M/1/K Model -- 3.4 Birth-and-Death Processes: Exponential Models -- 3.5 The M/M/oo Model: Exponential Model with an Infinite Number of Servers -- 3.6 The Model M/M/c -- 3.7 The M/M/c/c System: Eriang Loss Model -- 3.8 Model with Finite Input Source -- 3.9 Transient Behavior -- 3.10 Transient-State Distribution of the M/M/c Model -- 3.11 Multichannel Queue with Ordered Entry -- Problems and Complements -- References and Further Reading -- Chapter 4. Non-Birth-and-DeathQueueingSystems: Markovian Models -- 4.1 Introduction -- 4.2 Bulk Queues -- 4.3 Queueing Models with Bulk (Batch) Service -- 4.4 M/M(a,b)/1: Transient-State Distribution -- 4.5 Two-Server Model: M/M(a,b)/2 -- 4.6 The M/M((l,b)/c Model -- Problems and Complements -- References and Further Reading -- Chapter 5. Network of Queues -- 5.1 Network of Markovian Queues -- 5.2 Channels in Series or Tandem Queues.

5.3 Jackson Network -- 5.4 Closed Markovian Network (Gordon and Newell Network) -- 5.5 Cyclic Queue -- 5.6 BCMP Networks -- 5.7 Concluding Remarks -- Problems and Complements -- References and Further Reading -- Chapter 6. Non-Markovian Queueing Systems -- 6.1 Introduction -- 6.2 Embedded-Markov-Chain Technique for the System with Poisson Input -- 6.3 TheM/6/1 Model: Pollaczek-Khinchin Formula -- 6.4 Busy Period -- 6.5 Queues with Finite Input Source: M/G/l//M System -- 6.6 System with Limited Waiting Space. M/G/l/K System -- 6.7 The M+/G/l Model with Bulk Arrival -- 6.8 The M/G(a,b)/l Model with General Bulk Service -- 6.9 The G/M/l Model -- 6.10 Multiserver Model -- 6.11 Queues with Markovian Arrival Process -- Problems and Complements -- References and Further Reading -- Chapter 7. Queues with General Arrival Time and Service-Time Distributions -- 7.1 The G/G/1 Queue with General Arrival Time and Service-Time Distributions -- 7.2 Mean and Variance of Waiting Time tV -- 7.3 Queues with Batch Arrivals G(X)/G/1 -- 7.4 The Output Process of a G /G / 1 System -- 7.5 Some Bounds for the G/ G / 1 System -- Problems and Complements -- References and Further Reading -- Chapter 8. Miscellaneous Topics -- 8.1 Heavy-Traffic Approximation for Waiting-Time Distribution -- 8.2 Brownian Motion Process -- 8.3 Queueing Systems with Vacations -- 8.4 Design and Control of Queues -- 8.5 Retrial Queueing System -- 8.6 Emergence of a New Trend in Teletraffic Theory -- Problems and Complements -- References and Further Reading -- Appendix -- Index.