Author	Prabhu, N. U. author
Title	Foundations of Queueing Theory [electronic resource] / by N. U. Prabhu
Imprint	Boston, MA : Springer US : Imprint: Springer, 1997
Connect to	http://dx.doi.org/10.1007/978-1-4615-6205-4
Descript	XIV, 206 p. online resource

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

1 Introduction -- 1.1 Description of a Queueing System -- 1.2 The Basic Model GI/G/S -- 1.3 Processes of Interest -- 1.4 The Nature of Congestion -- 1.5 Littleโs Formula L = ?W -- 1.6 Control of Queueing Systems -- 1.7 Historical Remarks -- 2 Markovian Queueing Systems -- 2.1 Introduction -- 2.2 The System M/M/1 -- 2.3 The System M/M/s -- 2.4 A Design Problem -- 2.5 M/M/s System with Finite Source -- 2.6 The Machine Interference Problem -- 2.7 The System M/M/s with Finite Capacity -- 2.8 Loss Systems -- 2.9 Social Versus Self-Optimization -- 2.10 The System M/M/s with Balking -- 2.11 The System M/M/s with Reneging -- 2.12 Problems for Solution -- 3 The Busy Period, Output and Queues in Series -- 3.1 Introduction -- 3.2 The Busy Period -- 3.3 The M/M/S System with Last Come, First Served -- 3.4 Comparison of FCFS and LCFS -- 3.5 Time-Reversibility of Markov Processes -- 3.6 The Output Process -- 3.7 The Multi-Server System in a Series -- 3.8 Problems for Solution -- 4 Erlangian Queueing Systems -- 4.1 Introduction -- 4.2 The System M/Ek/1 -- 4.3 The System Ek/M/1 -- 4.4 The System M/D/1 -- 4.5 Problems for Solution -- 5 Priority Systems -- 5.1 Description of a System with Priorities -- 5.2 Two Priority Classes with Pre-emptive Resume Discipline -- 5.3 Two Priority Classes with Head-of-Line Discipline -- 5.4 Summary of Results -- 5.5 Optimal Assignment of Priorities -- 5.6 Problems for Solution -- 6 Queueing Networks -- 6.1 Introduction -- 6.2 A Markovian Network of Queues -- 6.3 Closed Networks -- 6.4 Open Networks: The Product Formula -- 6.5 Jackson Networks -- 6.6 Examples of Closed Networks; Cyclic Queues -- 6.7 Examples of Open Networks -- 6.8 Problems for Solution -- 7 The System M/G/1; Priority Systems -- 7.1 Introduction -- 7.2 The Waiting Time in M/G/1 -- 7.3 The Sojourn Time and the Queue Length -- 7.4 The Service Interval -- 7.5 The M/G/1 System with Exceptional Service -- 7.6 The Busy Period in M/G/1 -- 7.7 Completion Times in Priority Systems -- 7.8 Low Priority Waiting Time -- 7.9 Problems for Solution -- 8 The System GI/G/1; Imbedded Markov Chains -- 8.1 Imbedded Markov Chains -- 8.2 The System GI/G/1 -- 8.3 The Wiener-Hopf Technique; Examples -- 8.4 Set-up Times; Server Vacations -- 8.5 The Queue Length and Waiting Time in GI/M/1 -- 8.6 The Queue Length in M/G/1 -- 8.7 Time Sharing Systems -- 8.8 The M/M/1 System with RR Discipline -- 8.9 Problems for Solution -- A Appendix -- A.1 The Poisson Process -- A.2 Renewal Theory -- A.3 The Birth-And-Death Process -- A.4 Markov Processes with a Countable State Space -- A.5 Markov Chains -- A.6 Two Theorems on Functional Equations -- A.7 Review Problems in Probability and Stochastic Processes -- B Bibliography

1. Business
2. Operations research
3. Decision making
4. Probabilities
5. Business and Management
6. Operation Research/Decision Theory
7. Probability Theory and Stochastic Processes