Queueing Theory with Applications to Packet Telecommunication

342 Pages·2005·6.97 MB·english

by  Daigle J.N.

QUEUEING THEORY WITH
APPLICATIONS TO PACKET
TELECOMMUNICATION
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QUEUEING THEORY WITH
APPLICATIONS TO PACKET
TELECOMMUNICATION
JOHN N. DAIGLE
Prof. of Electrical Engineering
The University of Mississippi
University, MS 38677
Springer
eBookISBN: 0-387-22859-4
Print ISBN: 0-387-22857-8
©2005 Springer Science + Business Media, Inc.
Print ©2005Springer Science + Business Media, Inc.
Boston
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NOTE TO INSTRUCTORS
A complete solution manual has been prepared for use by those interested in
using this book as the primary text in a course or for independent study. Inter-
ested persons should please contact the publisher or the author at
http://www.olemiss.edu/~wcdaigle/QueueingText to obtain an electronic copy
of the solution manual as well as other support materials, such as computer
programs that implement many of the computational procedures described in
this book.
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Contents
List of Figures xi
List of Tables xv
Preface xvii
Acknowledgments xxiii
1. TERMINOLOGY AND EXAMPLES 1
1.1 The Terminology of Queueing Systems 2
1.2 Examples of Application to System Design 9
1.2.1 Cellular Telephony 9
1.2.2 Multiplexing Packets 11
1.2.3 CDMA-Based Cellular Data 14
1.3 Summary 17
2. REVIEW OF RANDOM PROCESSES 19
2.1 Statistical Experiments and Probability 20
2.1.1 Statistical Experiments 20
2.1.2 Conditioning Experiments 22
2.2 Random Variables 27
2.3 Exponential Distribution 33
2.4 Poisson Process 39
2.5 Markov Chains 45
3. ELEMENTARY CTMC-BASED QUEUEING MODELS 57
3.1 M/M/1 Queueing System 58
3.1.1 Time-Dependent M/M/1 Occupancy Distribution 58
3.1.2 Stochastic EquilibriumM/M/1 Distributions 60
3.1.3 Busy Period for M/M/1 Queueing System 76
viii QUEUEING THEORY FOR TELECOMMUNICATIONS
3.2 Dynamical Equations for General Birth-DeathProcess 81
3.3 Time-Dependent Probabilities for Finite-State Systems 83
3.3.1 Classical Approach 84
3.3.2 Jensen’s Method 88
3.4 Balance Equations Approach for Systems in Equilibrium 91
3.5 Probability Generating Function Approach 98
3.6 SupplementaryProblems 101
4. ADVANCEDCTMC-BASED QUEUEING MODELS 107
4.1 Networks 108
4.1.1 Feedforward Networks: Fixed Routing 109
4.1.2 Arbitrary Open Networks 110
4.1.3 Closed Networks of Single Servers 111
4.2 Phase-Dependent Arrivals and Service 122
4.2.1 Probability Generating Function Approach 124
4.2.2 Matrix Geometric Method 138
4.2.3 Rate Matrix Computation via Eigenanalysis 143
4.2.4 Generalized State-Space Methods 146
4.3 Phase-Type Distributions 152
4.4 Supplementary Problems 156
5. THE BASIC M/G/1 QUEUEING SYSTEM 159
5.1 M/G/1 Transform Equations 161
5.1.1 Sojourn Time for M/G/1 165
5.1.2 Waiting Time for M/G/1 167
5.1.3 Busy Period for M/G/1 167
5.2 Ergodic Occupancy Distribution for M/G/1 170
5.2.1 Discrete Fourier Transform Approach 170
5.2.2 RecursiveApproach 180
5.2.3 Generalized State-Space Approach 183
5.3 Expected Values Via Renewal Theory 210
5.3.1 Expected Waiting and Renewal Theory 210
5.3.2 Busy Periods and Alternating Renewal Theory 216
5.4 Supplementary Problems 219
6. THE M/G/1 QUEUEING SYSTEM WITH PRIORITY 225
6.1 M/G/1 Under LCFS-PR Discipline 226
6.2 M/G/1 System Exceptional First Service 229
6.3 M/G/1 under HOL Priority 236