Queueing theory with applications to packet telecommunication / John N. Daigle.

Format:

Book

Author/Creator:

Daigle, John N.

Contributor:

Hazel M. Hussong Fund.

Language:

English

Subjects (All):

Telecommunication systems.

Queuing theory.

Physical Description:

xxi, 316 pages : illustrations ; 25 cm

Place of Publication:

New York : Springer Science+Business Media, [2005]

Summary:

Queueing Theory with Applications to Packet Telecommunication is an efficient introduction to fundamental concepts and principles underlying the behavior of queueing systems and its application to the design of packet-oriented electrical communication systems. In addition to techniques and approaches found in earlier works, the author presents a thoroughly modern computational approach based on Schur decomposition. This approach facilitates solutions to broad classes of problems wherein a number of practical modeling issues may be explored.

Key features of communication systems, such as correlation in packet arrival processes at IP switches and variability in service rates due to fading wireless links are introduced. Numerous exercises embedded within the text and problems at the end of certain chapters that integrate lessons learned across multiple sections are also included. In all cases, including systems having priority, developments lead to procedures or formulae that yield numerical results from which sensitivity of queueing behavior to parameter variation can be explored. In several cases multiple approaches to computing distributions are presented.

Queueing Theory with Applications to Packet Telecommunication is intended both for self study and for use as a primary text in graduate courses in queueing theory in electrical engineering, computer science, operations research, and mathematics. Professionals will also find this work invaluable because the author discusses applications such as statistical multiplexing, IP switch design, and wireless communication systems. In addition, numerous modeling issues, such as the suitability of Erlang-k and Pade approximations are addressed.

Contents:

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

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 Equilibrium M/M/1 Distributions 60

3.1.3 Busy Period for M/M/1 Queueing System 76

3.2 Dynamical Equations for General Birth-Death Process 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 Supplementary Problems 101

4 Advanced CTMC-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 Recursive Approach 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

6.3.1 Higher Priority Customers 238

6.3.2 Lower Priority Customers 241

6.4 Ergodic Occupancy Probabilities for Priority Queues 244

6.5 Expected Waiting Times under HOL Priority 246

6.5.1 HOL Discipline 248

6.5.2 HOL-PR Discipline 249

7 Vector Markov Chains Analysis 253

7.1 The M/G/1 and G/M/1 Paradigms 254

7.2 G/M/1 Solution Methodology 259

7.3 M/G/1 Solution Methodology 261

7.4 Application to Statistical Multiplexing 265

7.5 Generalized State Space Approach: Complex Boundaries 278

7.7 Supplementary Problems 294.

Notes:

Includes bibliographical references (pages [301]-307) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

0387228578

0387228594

OCLC:

56192241