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Elements of Queueing Theory

Palm Martingale Calculus and Stochastic Recurrences

  • François Baccelli
  • Pierre Brémaud

Part of the Applications of Mathematics book series (SMAP, volume 26)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. François Baccelli, Pierre Brémaud
    Pages 1-74
  3. François Baccelli, Pierre Brémaud
    Pages 75-180
  4. François Baccelli, Pierre Brémaud
    Pages 181-258
  5. François Baccelli, Pierre Brémaud
    Pages 259-315
  6. Back Matter
    Pages 317-334

About this book

Introduction

The Palm theory and the Loynes theory of stationary systems are the two pillars of the modern approach to queuing. This book, presenting the mathematical foundations of the theory of stationary queuing systems, contains a thorough treatment of both of these.

This approach helps to clarify the picture, in that it separates the task of obtaining the key system formulas from that of proving convergence to a stationary state and computing its law.

The theory is constantly illustrated by classical results and models: Pollaczek-Khintchin and Tacacs formulas, Jackson and Gordon-Newell networks, multiserver queues, blocking queues, loss systems etc., but it also contains recent and significant examples, where the tools developed turn out to be indispensable.

Several other mathematical tools which are useful within this approach are also presented, such as the martingale calculus for point processes, or stochastic ordering for stationary recurrences.

This thoroughly revised second edition contains substantial additions - in particular, exercises and their solutions - rendering this now classic reference suitable for use as a textbook.

Keywords

Markovian systems Martingale Palm probability theory linear optimization mathematical statistics point process quenes queueing theory queues

Authors and affiliations

  • François Baccelli
    • 1
  • Pierre Brémaud
    • 2
  1. 1.Ecole Normale Supérieure, LIENSINRIA-ENSParis Cedex 05France
  2. 2.School of Computer and Communications SystemsÉcole Polytechnique Fédérale de LausanneÉcublensSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-11657-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08537-6
  • Online ISBN 978-3-662-11657-9
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site