Vacation Queueing Models

Theory and Applications

By: Naishuo Tian, Zhe George Zhang

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Hardcover | 23 August 2006

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404 Pages

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A classical queueing model consists of three parts - arrival process, service process, and queue discipline. However, a vacation queueing model has an additional part - the vacation process which is governed by a vacation policy - that can be characterized by three aspects: 1) vacation start-up rule; 2) vacation termination rule, and 3) vacation duration distribution. Hence, vacation queueing models are an extension of classical queueing theory.

Vacation Queueing Models: Theory and Applications discusses systematically and in detail the many variations of vacation policy. By allowing servers to take vacations makes the queueing models more realistic and flexible in studying real-world waiting line systems. Integrated in the book's discussion are a variety of typical vacation model applications that include call centers with multi-task employees, customized manufacturing, telecommunication networks, maintenance activities, etc. Finally, contents are presented in a "theorem and proof" format and it is invaluable reading for operations researchers, applied mathematicians, statisticians; industrial, computer, electrical and electronics, and communication engineers; computer, management scientists; and graduate students in the above disciplines.

Industry Reviews

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"This book provides a comprehensive, up-to-date treatment of various queueing systems with server vacations. ... The book can be used as a reference on vacation queueing systems by both researchers and practitioners." (Dieter Fiems, Journal of the American Statistical Association, Vol. 103 (484), December, 2008)

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Non-Fiction Mathematics Applied Mathematics Stochastics Business & Management Operational Research Computing & I.T.Computer Networking & Communications Computer Science Probability & Statistics Economics Management & Management Techniques

Management of Specific Areas Production of Quality Control Management

Introduction	p. 1
Queueing Systems with Server Vacations	p. 1
Vacation Policies	p. 3
Stochastic Decomposition in Vacation Models	p. 4
Bibliographic Notes	p. 5
M/G/1 Type Vacation Models: Exhaustive Service	p. 9
M/G/1 Queue with Multiple Adaptive Vacations	p. 10
Classical M/G/1 Queue	p. 10
Multiple Adaptive Vacation Model	p. 12
Some Classical M/G/1 Vacation Models	p. 19
Multiple Vacation Model	p. 19
Single Vacation Model	p. 21
Setup Time Model	p. 24
M/G/1 Queue with Threshold Policy	p. 27
N-Threshold Policy Model	p. 27
Other Threshold Policy Models	p. 32
Discrete-Time Geo/G/1 Queue with Vacations	p. 35
Classical Geo/G/1 Queue	p. 36
Geo/G/1 Queue with MAVs	p. 37
Special Cases of the MAV Model	p. 43
MAP/G/1 Vacation Models	p. 46
General-Service Bulk Queue with Vacations	p. 54
M[superscript X]/G/1 Queue with Vacations	p. 54
M/G[superscript X]/1 Queue with Vacations	p. 59
Finite-Buffer M/G/1 Queue with Vacations	p. 69
Bibliographic Notes	p. 73
M/G/1 Type Vacation Models: Nonexhaustive Service	p. 77
Regeneration Cycle Method	p. 77
Nonexhaustive Service and Service Cycle	p. 77
A Renewal-Reward Theorem	p. 78
Gated Service M/G/1 Vacation Models	p. 81
Gated Service Multiple Vacation Model	p. 81
Gated Service Single Vacation Model	p. 84
Binomial Gated Service Vacation Model	p. 86
Limited Service M/G/1 Vacation Models	p. 90
P-Limited Service Model	p. 90
G-Limited Service Model	p. 92
B-Limited Service Model	p. 98
E-Limited Service Model	p. 102
T-Limited Service Model	p. 107
Bernoulli Scheduling Service Model	p. 111
Decrementing Service M/G/1 Vacation Models	p. 115
P-Decrementing Service Model	p. 115
G-Decrementing Service Model	p. 118
Binomial Decrementing Service Model	p. 123
Bibliographic Notes	p. 126
General-Input Single Server Vacation Models	p. 129
GI/M/1 Type Structure Matrix	p. 129
Classical GI/M/1 Queue	p. 129
Matrix Geometric Solution	p. 131
GI/M/1 Queue with Multiple Vacations	p. 134
PH-Type Vacation Model	p. 134
Stochastic Decomposition Property	p. 140
Exponential Vacation Model	p. 146
GI/M/1 Queue with Single Vacation	p. 151
Embedded Markov Chain	p. 151
Stationary Distribution	p. 156
GI/M/1 Queue with N-Threshold Policies	p. 162
General-Input Bulk Queue with Vacations	p. 170
Finite-Buffer GI/M/1 Vacation Model	p. 179
Discrete-Time GI/Geo/1 Queue with Vacations	p. 183
Classical GI/Geo/1 Queue	p. 183
GI/Geo/1 Queue with Multiple Vacations	p. 184
Bibliographic Notes	p. 191
Markovian Multiserver Vacation Models	p. 193
Introduction to Multiserver Vacation Models	p. 193
Quasi-Birth-and-Death Process Approach	p. 196
QBD Process	p. 196
Conditional Stochastic Decomposition	p. 200
M/M/c Queue with Synchronous Vacations	p. 203
Multiple Vacation Model	p. 203
Single Vacation and Setup Time Models	p. 214
M/M/c Queue with Asynchronous Vacations	p. 220
Multiple Vacation Model	p. 220
Single Vacation or Setup Time Model	p. 230
M/M/c Queue with Synchronous Vacations of Some Servers	p. 235
(SY, MV, d)-Policy Model	p. 235
(SY, MV, e-d)-Policy Model	p. 245
M/M/c Queue with Asynchronous Vacations of Some Servers	p. 257
Bibliographic Notes	p. 266
General-Input Multiserver Vacation Models	p. 269
GI/M/c Queue with Exponential Vacations	p. 269
GI/M/c Type Structure Matrix	p. 269
Stationary Queue Length Distribution	p. 272
Stationary Waiting Time Distribution	p. 276
GI/M/c Queue with PH Vacations	p. 280
Stationary Distributions of Queue Length and Waiting Time	p. 285
Conditional Stochastic Decomposition Properties	p. 292
Bibliographic Notes	p. 295
Optimization in Vacation Models	p. 297
M/G/1 Queue with Threshold Policies	p. 297
Average Cost Function	p. 298
The Exponential Vacations Case	p. 302
The General Vacations Case	p. 303
Determination of Optimal Threshold Values	p. 307
The Convexity of the Average Cost function	p. 315
Dynamic Control in M/G/1 System with Vacations of Multiple Types	p. 318
The SMDP Model	p. 321
Computation of the Optimal Policy	p. 325
Numerical Examples	p. 327
M/M/c Queue with Threshold Policies	p. 330
The (d, N)-Policy Model	p. 330
Model Formulation and Performance Measures	p. 330
Searching for the Optimal Two-Threshold Policy: A Computational Example	p. 339
Bibliographic Notes	p. 341
Applications of Vacation Models	p. 343
Modeling the Flexible Production System	p. 343
Modeling the Stochastic Service System with Multitask Servers	p. 345
Modeling SVCC-Based ATM Networks	p. 350
Bibliographic Notes	p. 358
References	p. 359
Index	p. 383
Table of Contents provided by Ingram. All Rights Reserved.

Vacation Queueing Models

Theory and Applications

At a Glance

Hardcover

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