Max-Plus Linear Stochastic Systems and Perturbation Analysis
Max-Plus Linear Stochastic Systems and Perturbation Analysis by Bernd Heidergott, published by Springer US on November 29, 2010, is a softcover reprint of the hardcover first edition from 2007. This book offers a comprehensive examination of the theory surrounding stochastic max-plus linear systems, an area that has seen significant advancements in recent years. It explores max-plus algebra as a method for analyzing discrete event systems, particularly in contexts such as queuing networks that require synchronization.
Readers will find a detailed discussion on modeling issues and stability theory in the first part of the book, while the second part delves into perturbation analysis, introducing a calculus for differentiating max-plus systems. This calculus facilitates numerical evaluations of performance indices relevant to max-plus linear stochastic systems, including metrics like the Lyapunov exponent and waiting times. With 320 pages, this edition serves as a valuable resource for those interested in the intersections of computer science, mathematics, and data science.
Official synopsis Publisher
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.
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