Analysis of Queueing Networks with Blocking

By: Simonetta Balsamo, Vittoria de Nitto Persone, Raif Onvural

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Hardcover | 30 November 2000

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276 Pages

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23.39 x 15.6 x 1.75

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Queueing network models have been widely applied as a powerful tool for modelling, performance evaluation, and prediction of discrete flow systems, such as computer systems, communication networks, production lines, and manufacturing systems. Queueing network models with finite capacity queues and blocking have been introduced and applied as even more realistic models of systems with finite capacity resources and with population constraints. In recent years, research in this field has grown rapidly. Analysis of Queueing Networks with Blocking introduces queueing network models with finite capacity and various types of blocking mechanisms. It gives a comprehensive definition of the analytical model underlying these blocking queueing networks. It surveys exact and approximate analytical solution methods and algorithms and their relevant properties. It also presents various application examples of queueing networks to model computer systems and communication networks.
This book is organized in three parts. Part I introduces queueing networks with blocking and various application examples. Part II deals with exact and approximate analysis of queueing networks with blocking and the condition under which the various techniques can be applied. Part III presents a review of various properties of networks with blocking, describing several equivalence properties both between networks with and without blocking and between different blocking types. Approximate solution methods for the buffer allocation problem are presented.

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Algebra Computing & I.T.Computer Networking & Communications Business & Management Operational Research Computer Science Probability & Statistics Optimisation

Game Theory Information Technology General Issue Computer Programming & Software Development Computer Hardware Network Hardware

Preface	p. ix
Queueing Network Models With Blocking and Applications
Introduction	p. 3
Commonly used probability distributions	p. 4
Analysis of a single queue	p. 6
Queueing networks	p. 8
Product form solutions and BCMP theorem	p. 9
Numerical solutions	p. 12
Simulation	p. 12
Approximate solutions	p. 13
Performance metrics	p. 13
Queueing networks with finite capacity queues	p. 15
Bibliographical notes and references	p. 16
Books on queueing theory and queueing systems	p. 16
Surveys, tutorials and books on queueing networks with blocking	p. 17
Publications on queueing networks	p. 17
Queueing networks with blocking	p. 25
Single class networks	p. 25
Blocking mechanisms	p. 28
Blocking and state dependent routing	p. 35
Multiclass queueing networks with finite capacity queues	p. 35
Performance indices	p. 37
Bibliographical notes	p. 43
References	p. 45
Application examples of queueing networks with blocking	p. 51
References	p. 59
Analysis of Queueing Networks With Blocking
Exact analysis of Markovian networks	p. 63
The Markov process as the network model	p. 63
Repetitive Service Blocking - Random Destination	p. 65
Repetitive Service Blocking - Fixed Destination	p. 67
Blocking After Service	p. 68
Blocking Before Service - Server Occupied	p. 73
Blocking Before Service - Server Not Occupied	p. 77
Blocking Before Service - Overall	p. 78
A simple example	p. 80
Stop and Recirculate Blocking	p. 83
Heterogeneous networks	p. 86
Queue length distribution and average performance indices	p. 89
Arrival time distribution	p. 95
Cycle time distribution	p. 97
Bibliographical notes	p. 99
References	p. 101
Exact analysis of special networks	p. 103
Product form networks	p. 103
Product form solution of the joint queue length distribution	p. 104
Algorithms for product form networks	p. 110
Convolution algorithm	p. 111
Performance indices	p. 120
Symmetrical networks	p. 123
Solution reduction technique	p. 125
Performance indices	p. 129
Arrival theorem	p. 134
Bibliographical notes	p. 136
References	p. 138
Approximate and bound analysis	p. 143
Introduction	p. 143
Approximate analysis of closed networks	p. 145
Approximate methods for cyclic networks	p. 147
Approximate methods for arbitrary topology networks	p. 154
Approximate analysis of open networks	p. 158
Approximate methods for tandem networks	p. 158
Approximate methods for acyclic and arbitrary topology networks	p. 163
Bound analysis	p. 168
Bibliographical notes	p. 170
References	p. 172
Properties of Networks With Blocking
Equivalence, insensitivity and monotonicity properties	p. 179
Equivalence properties: state distribution and average performance indices	p. 180
Special equivalences	p. 181
Equivalences between networks with and without blocking	p. 183
Equivalences between different blocking types	p. 184
Equivalence properties: passage time distribution	p. 195
Equivalence properties: fork/join networks	p. 196
Insensitivity	p. 201
Monotonicity	p. 202
Performance comparison of blocking symmetrical networks	p. 203
Bibliographical notes	p. 211
References	p. 213
Buffer allocation in queueing networks with finite capacities	p. 217
Buffer allocation problem	p. 218
An approximation algorithm for open networks with blocking	p. 220
Dynamic programming approach	p. 222
Forward problem	p. 222
Backward problem	p. 224
Algorithm	p. 225
An extension	p. 225
Forward problem	p. 227
Backward problem	p. 227
Algorithm	p. 228
Validation	p. 229
Bibliographical notes	p. 232
References	p. 233
References	p. 235
Table of Symbols	p. 249
Index	p. 251
Table of Contents provided by Syndetics. All Rights Reserved.

Analysis of Queueing Networks with Blocking

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