Retrial Queues describes from a unified point of view basic methods of analysis and the most important results of the theory of retrial queues. These are characterized by the fact that a customer arriving when all accessible servers are busy leaves the service area, but after some random time repeats the demand. This  feature plays a special role in several computer and computer and communication networks, at airport with stacked aircraft waiting to land and in retail shopping queues – thus the possible applications of such systems are numerous.

This book is the first to consider retrial queues in full detail, and many of the results have previously been published only in Russian. It includes analysis of single-server retrial queues (stationary and transient distribution of the number in the system, busy periods, waiting time process, limit theorems, stochastic inequalities, traffic measurement, etc.), and analysis of multiserver retrial queues (ergodicity, explicit formulae, algorithmic solutions, limit theorems, approximations, etc.). The book then moves on to more advanced single-server and multiserver retrial queues.

Those familiar with methods of probability theory, Markov chains and queueing theory will find this book a good introduction to the subject and lecturers, researchers and students in probability, statistics, operations research, telecommunications and computer systems modeling analysis will find Retrial Queues an invaluable source.

Gennadi Falin is Professor in the Department of Probability Theory at Moscow State University, Russia, where he has lectured since 1979.

James G.C.Templeton is Professor Emeritus in the Department of Mechanical and Industrial Engineering at the University of Toronto, Canada, where he has lectured since 1966.

Contents

Preface

Chapter 1. The main single-server model

1.1 Description of the main model of M/G/1 type
1.2 Joint distribution of the server state and the queue length in the steady state
1.3 The embedded Markov chain
1.4 Limit theorems for the stationary distribution of the queue length
1.5 Stochastic inequalities
1.6 The busy period
1.7 The number of customers in the system in the nonstationary regime
1.8 The waiting time process
1.9 The departure process
1.10 Estimation of retrial rate in the case of exponential service

Chapter 2.The main multiserver model

2.1 Description of the model
2.2 Ergodicity
2.3 Explicit formulas for the main performance characteristics
2.4 Truncated model
2.5 Generalized truncated models
2.6 Numerical calculation of the stationary characteristics of the main model
2.7 Limit theorems
2.8 Approximations

Chapter 3. Advanced single-server models

3.1 A single-server batch arrival retrial queue
3.2 A single-server model with priority subscribers
3.3 A single-server model with impatient subscribers
3.4 A single-server multiclass retrial queue

Chapter 4. Advanced multiserver models

4.1 A Multiserver model with priority subscribers
4.2 A Multiserver model with impatient subscribers
4.3 A Multiserver Retrial Queue with A Finite Number of Sources of Primary Calls

Chapter 5. Bibliographical remarks

5.1 The main single-server model
5.2 The main multichannel model
5.3 Advanced single-server models
5.4 Advanced multiserver models

References
Author  index
Subject  index

 

Мой соавтор, Джим Темплетон, рассказывает об истории написания этой книги и её содержании в  статье:иВ

J.G.C.Templeton. Retrial queues. TOP, 1999, vol.7, no.2, pp.351-353 DOI 10.1007/BF02564732

 

Назад, на  Стохастические модели

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Назад, на  Стохастические модели

 

G.I. Falin, J.G.C. Templeton.

Retrial Queues

Chapman & Hall/CRC Monographs on Statistics & Applied Probability (Vol.75), 1997

ISBN 10: 0412785501, ISBN 13: 9780412785504

 

Вы можете найти эту книгу в Научной библиотеке МГУ

 

 

Работа над книгой в моем офисе в университете Торонто, июль  1994