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Lecture Notes in Computer Science : Explicit Expressions for the Steady State Behavior of Discrete Time Stochastic Networks - Hans Daduna

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Lecture Notes in Computer Science

Explicit Expressions for the Steady State Behavior of Discrete Time Stochastic Networks

By: Hans Daduna

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Paperback | 18 July 2001

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156 Pages

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Building on classical queueing theory mainly dealing with single node queueing systems, networks of queues, or stochastic networks has been a field of intensive research over the last three decades. Whereas the first breakthrough in queueing network theory was initiated by problems and work in operations research, the second breakthrough, as well as subsequent major work in the area, was closely related to computer science, particularly to performance analysis of complex systems in computer and communication science.
The text reports on recent research and development in the area. It is centered around explicit expressions for the steady behavior of discrete time queueing networks and gives a moderately positive answer to the question of whether there can be a product form calculus in discrete time. Originating from a course given by the author at Hamburg University, this book is ideally suited as a text for courses on discrete time stochastic networks.

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Introduction	p. 1
Introduction	p. 1
Symbols and Conventions	p. 6
State Dependent Bernoulli Servers	p. 9
Indistinguishable Customers	p. 9
Customers of Different Types	p. 18
Bernoulli Servers with Immediate Feedback	p. 20
Closed Cycles of State Dependent Bernoulli Servers with Different Customer Types	p. 23
Steady State Behaviour and Arrival Theorem	p. 24
Closed Cycles of Bernoulli Servers - The Multichain Case	p. 31
Delay Time Distribution for Customers in a Closed Cycle of State Independent Bernoulli Servers	p. 32
Computational Algorithms for Closed Cycles of State Independent Bernoulli Servers	p. 50
Open Tandems of State Dependent Bernoulli Servers with Different Customer Types	p. 53
The Principle of Adjusted Transfer Rates	p. 54
Steady State and Arrival Theorem	p. 57
Delay Time Distribution for Customers in an Open Tandem of State Independent Bernoulli Servers	p. 63
Re-entrant Lines	p. 67
Networks with Doubly Stochastic and Geometrical Servers	p. 73
Description of the Doubly Stochastic Server	p. 74
Description of the Geometrical Server	p. 83
Open Networks of Doubly Stochastic and Geometrical Nodes	p. 86
Stationary State for the Open Network with Doubly Stochastic and Geometrical Nodes	p. 90
Performance Measures for Open Networks	p. 92
Closed Networks of Doubly Stochastic and Geometrical Nodes	p. 95
Open Tandems of Doubly Stochastic Nodes with State Independent Arrival Streams, and Reversibility	p. 98
General Networks with Batch Movements and Batch Services	p. 105
The General Network Model	p. 106
Steady States	p. 108
Related Examples and Discussion of the Model	p. 111
WalrandÆs S-Queues and Networks	p. 117
Networks with Triggered Batch Movements	p. 118
Appendix	p. 121
Time Reversed Processes	p. 121
Symmetric Functions	p. 122
Bibliography	p. 125
Index	p. 137
Table of Contents provided by Publisher. All Rights Reserved.

Lecture Notes in Computer Science

Explicit Expressions for the Steady State Behavior of Discrete Time Stochastic Networks

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