© 2007

Max-Plus Linear Stochastic Systems and Perturbation Analysis

  • Bernd Heidergott
  • Contains the most recent research results on stochastic max-plus systems

  • No other book attempts to address the interplay between perturbation analysis and max-plus systems


Part of the The International Series on Discrete Event Dynamic Systems book series (DEDS, volume 16)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Max-Plus Algebra

    1. Front Matter
      Pages 1-1
    2. Pages 59-116
  3. Perturbation Analysis

    1. Front Matter
      Pages 117-117
    2. Pages 179-263
  4. Back Matter
    Pages 266-324

About this book


During the last decade, the area of stochastic max-plus linear systems has witnessed a rapid development, which created a growing interest in this area. This book provides a thorough treatment of the theory of stochastic max-plus linear systems. Max-plus algebra is an algebraic approach to discrete event systems (DES), like queuing networks that are prone to synchronization. Perturbation analysis studies the sensitivity of the performance of DES with respect to changes in a particular system parameter.

The first part of the book addresses modeling issues and stability theory for stochastic max-plus systems. The second part of the book treats perturbation analysis of max-plus systems: a calculus for differentiation of max-plus systems is developed. This calculus leads to numerical evaluations of performance indices of max-plus linear stochastic systems, such as the Lyapunov exponent or waiting times.

This book will be of interest to researchers and professionals in the area of applied probability who are interested in numerical evaluation of stochastic max-plus linear discrete event systems.


DES Lyapunov Taylor series expansions calculus deterministic max-plus limit theory max-plus algebra measure- modeling perturbation analysis petri nets projective space queueing systems queuing systems stability analysis subadditive ergodic theory

Editors and affiliations

  • Bernd Heidergott
    • 1
  1. 1.Faculty of Economics and Business AdministrationVrije UniversiteitHV AmsterdamThe Netherlands

Bibliographic information

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From the reviews:

"This book looks at applications of the max-plus algebra in two areas of applied probability, linear stochastic systems and perturbation analysis … . In all … this book is, without a doubt, an important contribution to the literature. … it will be widely read by people working in the field." (Jonathan Golan, ACM Computing Reviews, Vol. 49 (2), February, 2008)