Foundations of Queueing Theory

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • N. U. Prabhu

   Pages 1-11

3. Markovian Queueing Systems

   • N. U. Prabhu

   Pages 13-41

4. The Busy Period, Output and Queues in Series

   • N. U. Prabhu

   Pages 43-57

5. Erlangian Queueing Systems

   • N. U. Prabhu

   Pages 59-77

6. Priority Systems

   • N. U. Prabhu

   Pages 79-96

7. Queueing Networks

   • N. U. Prabhu

   Pages 97-122

8. The System M/G/1; Priority Systems

   • N. U. Prabhu

   Pages 123-148

9. The System GI/G/1; Imbedded Markov Chains

   • N. U. Prabhu

   Pages 149-179

10. Back Matter

    Pages 181-206

    PDF

3. 2 The Busy Period 43 3. 3 The M 1M IS System with Last Come, First Served 50 3. 4 Comparison of FCFS and LCFS 51 3. 5 Time-Reversibility of Markov Processes 52 The Output Process 54 3. 6 3. 7 The Multi-Server System in a Series 55 Problems for Solution 3. 8 56 4 ERLANGIAN QUEUEING SYSTEMS 59 4. 1 Introduction 59 4. 2 The System M I E/c/1 60 4. 3 The System E/cl Mil 67 4. 4 The System MIDI1 72 4. 5 Problems for Solution 74 PRIORITY SYSTEMS 79 5 5. 1 Description of a System with Priorities 79 Two Priority Classes with Pre-emptive Resume Discipline 5. 2 82 5. 3 Two Priority Classes with Head-of-Line Discipline 87 5. 4 Summary of Results 91 5. 5 Optimal Assignment of Priorities 91 5. 6 Problems for Solution 93 6 QUEUEING NETWORKS 97 6. 1 Introduction 97 6. 2 A Markovian Network of Queues 98 6. 3 Closed Networks 103 Open Networks: The Product Formula 104 6. 4 6. 5 Jackson Networks 111 6. 6 Examples of Closed Networks; Cyclic Queues 112 6. 7 Examples of Open Networks 114 6. 8 Problems for Solution 118 7 THE SYSTEM M/G/I; PRIORITY SYSTEMS 123 7. 1 Introduction 123 Contents ix 7. 2 The Waiting Time in MIGI1 124 7. 3 The Sojourn Time and the Queue Length 129 7. 4 The Service Interval 132 7.

• Markov chain
• Markov process
• queueing theory

` ... presented in a clear and attractive fashion. The book can be warmly recommended to graduate students and teachers of applied mathematics and operations research.'
OR News, 7 (1999)

• Cornell University, Ithaca, USA

  N. U. Prabhu

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