Springer Max-Plus Linear Stochastic Systems and Perturbation Analysis: 15 (The International Series on Discrete Event Dynamic Systems, 15)

This book provides a thorough review and explanation of the theory of stochastic max-plus linear systems, which has seen rapid advances in the last decade. The coverage includes modeling issues and stability theory for stochastic max-plus systems, perturbation analysis of max-plus systems, developing a calculus for differentiation of max-plus systems. This leads to numerical evaluations of performance indices of max-plus linear stochastic systems, such as the Lyapunov exponent or waiting times. Review 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) From the Back Cover 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.