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An Introduction to Queueing Systems : Network and Systems Management - Sanjay K. Bose

An Introduction to Queueing Systems

Network and Systems Management

Hardcover Published: 31st December 2001
ISBN: 9780306467349
Number Of Pages: 288

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Queueing is an aspect of modern life that we encounter at every step in our daily activities. Whether it happens at the checkout counter in the supermarket or in accessing the Internet, the basic phenomenon of queueing arises whenever a shared facility needs to be accessed for service by a ]arge number of jobs or customers. The study of queueing is important as it gravides both a theoretical background to the kind of service that we may expect from such a facility and the way in which the facility itself may be designed to provide some specified grade of service to its customers. Our study of queueing was basically motivated by its use in the study of communication systems and computer networks. The various computers, routers and switches in such a network may be modelled as individual queues. The whole system may itself be modelled as a queueing network providing the required service to the messages, packets or cells that need to be carried. Application of queueing theory provides the theoretical framework for the design and study of such networks. The purpose of this book is to support a course on queueing systems at the senior undergraduate or graduate Ievels. Such a course would then provide the theoretical background on which a subsequent course on the performance modeHing and analysis of computer networks may be based.

List of Figuresp. xv
Introductionp. 1
Queueing Model Parametersp. 2
A Simple Queueing Modelp. 3
Some Basic Queueing Modelsp. 7
A Summary of the Contentsp. 7
Basic Queueing Theory: Fundamentals of Analyzing Single Queuesp. 9
Markov Processes and Markov Chainsp. 9
Birth-Death Processesp. 15
Kendall's Notation for Queuesp. 20
Little's Resultp. 22
Equilibrium Solutions for M/M/-/- Queuesp. 23
Delay Analysis for FCFS M/M/1/[infinity] and M/M/m/[infinity] Queuesp. 34
Departure Process from a M/M/m/[infinity] Queuep. 38
Time Reversibility Property of Irreducible, Aperiodic Markov Chainsp. 40
The Method of Stages for Solving a M/-/1/[infinity] FCFS Queuep. 41
Queues with Bulk (or Batch) Arrivalsp. 45
Problemsp. 49
Analysis of the M/G/1 Queue in Equilibrium: Performance Analysis Using Residual Life and Imbedded Markov Chain Approachesp. 55
The Residual Life Approach for Analysing the M/G/1 Queuep. 57
The Imbedded Markov Chain Approach for Analysing the M/G/1 Queuep. 64
Distributions of Time Spent in System and the Waiting Time Prior to Service in a FCFS M/G/1 Queuep. 70
Busy Period Analysis of a M/G/1 Queuep. 72
Delay Analysis for a LCFS M/G/1 Queuep. 76
The M/D/1 Queuep. 79
Alternative Derivation for the Delays in a FCFS M/G/1 Queuep. 81
Problemsp. 86
Advanced Queueing Theory: Vacations, Bulk Arrivals and Priorities in a M/G/1 Queue and the Geo/G/1 Queuep. 89
M/G/1 Queue with Vacationsp. 90
M/G/1 Queue with Only One Vacation after Idlep. 97
M/G/1 Queue with Exceptional First Servicep. 98
M[superscript [X]/G/1 Queue - Single Server Queue with Batch Arrivalsp. 101
Single Server M/G/1 Priority Queuesp. 106
The Discrete Time Geo/G/1 and Geo[superscript [X]/G/1 Queuesp. 127
Problemsp. 140
Fundamentals of Queueing Networks: Open and Closed Networks with Product-Form Solutionsp. 143
Classification of Different Types of Queueing Networksp. 145
Probabilistic Routing in a Queueing Networkp. 148
Open Networks of M/M/m Type Queues and Jackson's Theoremp. 150
Extensions to Jackson's Theorem for Other Open Networksp. 161
Closed Queueing Networksp. 164
Convolution Algorithm for Finding the Normalisation Constant for a Closed Queueing Networkp. 172
Mean Value Analysis (MVA) Algorithm for a Closed Queueing Networkp. 174
Analysis of a Sample Closed Network Using Convolution and MVA Algorithmsp. 181
Norton's Theorem for Closed Queueing Networksp. 184
Problemsp. 189
Advanced Queueing Networks: Approximation Techniques for Open and Closed Queueing Networksp. 193
Mixed Queueing Networksp. 193
The GI/G/m Approximation for the Approximate Analysis of Open Queueing Networks (the QNA Technique)p. 198
Fork/Join Queues in Open and Closed Networks of Infinite Capacity Queuesp. 211
Models of Blocking in Open and Closed Networks of Finite Capacity Queuesp. 218
Approximate Analytical Methods for Solving Closed Networks of Finite Capacity Queuesp. 221
Approximate Analytical Methods for Solving Open Networks of Finite Capacity Queuesp. 234
The Generalised Exponential Distributionp. 254
Simulation Techniques for Queues and Queueing Networks: Basic Principles for the Design of Queueing Simulatorsp. 257
Simulation Model of a Real World Systemp. 258
Discrete Event Simulationp. 263
Collecting and Processing Simulator Outputs for Queuesp. 268
Estimation of Confidence Intervals and Confidence Levelsp. 271
Transient Behaviour and the Warm-up Intervalp. 274
Data Collection in Steady State Conditionsp. 275
Generating Random Numbersp. 280
Referencesp. 283
Indexp. 285
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780306467349
ISBN-10: 0306467348
Series: Network and Systems Management
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 288
Published: 31st December 2001
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 3.18
Weight (kg): 1.36