Multiaccess, Reservations & Queues

By: Dee Denteneer, J.S.H. van Leeuwaarden

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Hardcover | 19 August 2008

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264 Pages

Dimensions(cm)
24.13 x 15.88 x 1.91

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Reservation procedures constitute the core of many popular data transmission protocols. They consist of two steps: A request phase in which a station reserves the communication channel and a transmission phase in which the actual data transmission takes place. Such procedures are often applied in communication networks that are characterised by a shared communication channel with large round-trip times.

In this book, we propose queuing models for situations that require a reservation procedure and validate their applicability in the context of cable networks.

We offer various mathematical models to better understand the performance of these reservation procedures. The book covers four key performance models, and modifications to these: Contention trees, the repairman model, the bulk service queue, and tandem queues.

The relevance of this book is not limited to reservation procedures and cable networks, and performance analysts from a variety of areas may benefit, as all models have found application in other fields as well.

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Foreword	p. v
Prologue
Multiaccess in Cable Networks	p. 3
Multiaccess Communication	p. 3
Methods for Multiaccess	p. 5
Data Transfer in Cable Networks	p. 7
Performance Analysis of Cable Networks	p. 10
Outline	p. 13
Selected Bibliography	p. 18
Key Models	p. 19
Contention Trees	p. 19
The Repairman Model	p. 24
The Bulk Service Queue	p. 27
Tandem Queues with Shared Service Capacity	p. 31
Contention Trees
Basic Properties of Contention Trees	p. 37
Introduction	p. 37
Formal Tree Models	p. 39
Tree Statistics	p. 47
Proofs	p. 57
Conclusion	p. 66
Delay Models for Contention Trees in Closed Populations	p. 69
Introduction	p. 69
Access via Contention Trees	p. 73
Properties of the Basic Model	p. 75
ROS Discipline	p. 78
GROS Discipline	p. 83
GPROS Discipline	p. 84
Numerical Results	p. 87
Conclusion	p. 91
The Repairman Model with Gros	p. 93
Introduction	p. 93
Model Description	p. 95
Approach and Main Results	p. 99
Transfer Map	p. 102
Proofs of Theorems	p. 105
Conclusion	p. 111
Bulk Service
Methodology	p. 115
Historical Perspective	p. 115
Generating Function Technique	p. 119
Random Walk Theory	p. 125
Wiener-Hopf Technique	p. 128
Summary	p. 131
Periodic Scheduling	p. 143
Introduction	p. 143
Model Description	p. 144
Queue Length	p. 145
Packet Delay	p. 150
Numerical Results	p. 156
Conclusion	p. 158
Reservations with Transmission Delays	p. 161
Introduction	p. 161
The Delayed Bulk Service Queue	p. 164
Adaptive Scheduling Strategies	p. 171
Numerical Assessment	p. 174
Conclusion	p. 178
Shared Service Capacity
A Tandem Queue with Coupled Processors	p. 189
Introduction	p. 189
Model Description	p. 190
Analysis of the Kernel	p. 192
Boundary Value Problem I	p. 196
Boundary Value Problem II	p. 198
Performance Measures	p. 201
A Two-Station Network with Coupled Processors	p. 213
Introduction	p. 213
Model Description	p. 214
Performance Measures	p. 217
Preemptive Priority	p. 219
Boundary Value Problem	p. 221
Conclusion and Further Research	p. 225
Epilogue
Cable Networks Revisited	p. 229
Introduction	p. 229
Traffic Model	p. 230
Total Average Packet Delay	p. 232
Numerical Assessment	p. 234
Further Research	p. 237
References	p. 241
About the Authors	p. 253
Table of Contents provided by Ingram. All Rights Reserved.

Multiaccess, Reservations & Queues

At a Glance

Hardcover

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