Elements of Queueing Theory - Palm Martingale Calculus and Stochastic Recurrences

François Baccelli, Pierre Brémaud

348 pages, parution le 31/12/2002 (2^eme édition)

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Résumé

The Palm theory and the Loynes theory of stationary systems L are the two pillars of the modern approach to queueing. This book, presenting the mathematical foundations of the theory of stationary queueing 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 Taca s 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.

Contents

1. The Palm Calculus of Point Processes

Palm Probability
Basic Formulas of Palm Calculus
Examples.
Local Aspect of Palm Probability
Ergodicity of a Point Process
Palm Theory in Discrete Time
Stochastic Intensity
Palm Probability and Stochastic Intensity
Solutions to Exercises
Bibliographical Comments

2. Stationarity and Coupling

Stability of the Single Server Queue
Proof of Loynes' Theorem
The Multiserver Queue
Coupling
Stochastic Recurrences and Their Stationary Regimes
Stability of the G/G/1/0 Queue
The Fluid Queue
Other Queueing Systems
Stability of Queueing Networks via Coupling
Queueing Network Stability via Recurrence Equations
Non-Expansive Stochastic Recurrences
Solutions to Exercises
Bibliographical Comments

3. Formulas

The Little Formula
Other Applications of Campbell's Formula
Other Applications of Campbell's Formula
Event and Time Averages
Formulas Derived from Conservation Equations
Applications of the Stochastic Intensity Integration Formula
Solutions to Exercises
Bibliographical Comments

4. Stochastic Ordering of Queues

Comparison of Service Disciplines
Comparison of Queues
Association Properties of Queues
Stochastic Comparison of Time-Stationary Queues
Solutions to Exercises
Bibliographical Comments

L'auteur - François Baccelli

Paris, France

L'auteur - Pierre Brémaud

CNRS/ESE, Gif-sur-Yvette, France

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	François Baccelli, Pierre Brémaud
Parution	31/12/2002
Édition	2^eme édition
Nb. de pages	348
Format	16 x 24
Couverture	Relié
Poids	641g
Intérieur	Noir et Blanc
EAN13	9783540660880