Ebook: Foundations of Queueing Theory

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.

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The order and presentation of Foundations of Queueing Theory is drawn from Professor Prabhu's extensive experience as a researcher, teacher, expositor, and editor. The book deals with the foundations of queueing theory and is intended as an advanced text for courses on queueing theory, and as a professional reference to queueing research. The results of queueing theory are established within the context of the book's instructional framework. The central results of queueing theory are stated in the form of theorems for accessibility and reading ease.
Current research has shown the need to pay more attention to the basic concepts and techniques of queueing theory. These include the busy period, imbedded chains, regeneration points, Wiener-Hopf technique, time-reversibility, output, vector Markov processes, remaining workload and completion times. The use of these concepts and techniques considerably simplifies the analysis of models involving last come, first served queue discipline, priorities, networks, set-up times and server vacations. It is these conceptional techniques that form the foundations of queueing theory.

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The order and presentation of Foundations of Queueing Theory is drawn from Professor Prabhu's extensive experience as a researcher, teacher, expositor, and editor. The book deals with the foundations of queueing theory and is intended as an advanced text for courses on queueing theory, and as a professional reference to queueing research. The results of queueing theory are established within the context of the book's instructional framework. The central results of queueing theory are stated in the form of theorems for accessibility and reading ease.
Current research has shown the need to pay more attention to the basic concepts and techniques of queueing theory. These include the busy period, imbedded chains, regeneration points, Wiener-Hopf technique, time-reversibility, output, vector Markov processes, remaining workload and completion times. The use of these concepts and techniques considerably simplifies the analysis of models involving last come, first served queue discipline, priorities, networks, set-up times and server vacations. It is these conceptional techniques that form the foundations of queueing theory.
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-11
Markovian Queueing Systems....Pages 13-41
The Busy Period, Output and Queues in Series....Pages 43-57
Erlangian Queueing Systems....Pages 59-77
Priority Systems....Pages 79-96
Queueing Networks....Pages 97-122
The System M/G/1; Priority Systems....Pages 123-148
The System GI/G/1; Imbedded Markov Chains....Pages 149-179
Back Matter....Pages 181-206

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The order and presentation of Foundations of Queueing Theory is drawn from Professor Prabhu's extensive experience as a researcher, teacher, expositor, and editor. The book deals with the foundations of queueing theory and is intended as an advanced text for courses on queueing theory, and as a professional reference to queueing research. The results of queueing theory are established within the context of the book's instructional framework. The central results of queueing theory are stated in the form of theorems for accessibility and reading ease.
Current research has shown the need to pay more attention to the basic concepts and techniques of queueing theory. These include the busy period, imbedded chains, regeneration points, Wiener-Hopf technique, time-reversibility, output, vector Markov processes, remaining workload and completion times. The use of these concepts and techniques considerably simplifies the analysis of models involving last come, first served queue discipline, priorities, networks, set-up times and server vacations. It is these conceptional techniques that form the foundations of queueing theory.
Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-11
Markovian Queueing Systems....Pages 13-41
The Busy Period, Output and Queues in Series....Pages 43-57
Erlangian Queueing Systems....Pages 59-77
Priority Systems....Pages 79-96
Queueing Networks....Pages 97-122
The System M/G/1; Priority Systems....Pages 123-148
The System GI/G/1; Imbedded Markov Chains....Pages 149-179
Back Matter....Pages 181-206
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