Queueing Theory with Applications to Packet Telecommunication

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Springer Science & Business Media, Sep 24, 2004 - Mathematics - 316 pages
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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 solution of 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.

  

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Contents

TERMINOLOGY AND EXAMPLES
1
11 The Terminology of Queueing Systems
2
12 Examples of Application to System Design
9
122 Multiplexing Packets at a Switch
11
123 CDMABased Cellular Data
14
13 Summary
17
REVIEW OF RANDOM PROCESSES
19
21 Statistical Experiments and Probability
20
44 Supplementary Problems
156
THE BASIC MG1 QUEUEING SYSTEM
159
51 MG1 Transform Equations
161
511 Sojourn Time for MG1
165
512 Waiting Time for MG1
167
52 Ergodic Occupancy Distribution for MG1
170
522 Recursive Approach
180
523 Generalized StateSpace Approach
183

212 Conditioning Experiments
22
22 Random Variables
27
23 Exponential Distribution
33
24 Poisson Process
39
25 Markov Chains
45
ELEMENTARY CTMCBASED QUEUEING MODELS
57
31 MM1 Queueing System
58
312 Stochastic Equilibrium MM1 Distributions
60
313 Busy Period for MM1 Queueing System
76
32 Dynamical Equations for General BirthDeath Process
81
33 TimeDependent State Probabilities for FiniteState Systems
83
331 Classical Approach
84
332 Jensens Method
88
34 Balance Equation Approach for Systems In Equilibrium
91
35 Probability Generating Function Approach
98
36 Supplementary Problems
101
ADVANCED CTMCBASED QUEUEING MODELS
107
41 Networks
108
Fixed Routing
109
412 Arbitrary Open Networks
110
413 Closed Networks of Single Servers
111
42 PhaseDependent Arrivals and Service
122
421 Probability Generating Function Approach
124
422 Matrix Geometric Method
138
423 Rate Matrix Computation via Eigenanalysis
143
424 Generalized StateSpace Methods
146
43 PhaseType Distributions
152
53 Expected Values Via Renewal Theory
210
532 Busy Periods and Alternating Renewal Theory
216
54 Supplementary Problems
219
THE MG1 QUEUEING SYSTEM WITH PRIORITY
225
61 MG1 Under LCFSPR Discipline
226
62 MG1 System with Exceptional First Service
229
63 MG1 under HOL Priority
236
631 Higher Priority Customers
238
632 Lower Priority Customers
241
64 Ergodic Occupancy Probabilities for Priority Queues
244
65 Expected Waiting Times for under HOL Priority
246
651 HOL Discipline
248
652 HOLPR Discipline
249
VECTOR MARKOV CHAIN ANALYSIS
253
71 The MG1 and GM1 Paradigms
254
72 GM1 Solution Methodology
259
73 MG1 Solution Methodology
261
74 An Application to Statistical Multiplexing
265
Complex Boundaries
278
76 Summary
290
77 Supplementary Problems
294
CLOSING REMARKS
297
References
301
Index
309
About the Author
315
Copyright

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About the author (2004)

John N. Daigle is Professor of Electrical Engineering, The University of Mississippi, University, MS.

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