Ebook: Max-Plus Linear Stochastic Systems and Perturbation Analysis
Author: Bernd Heidergott (eds.)
- Tags: Probability and Statistics in Computer Science, Math Applications in Computer Science, Symbolic and Algebraic Manipulation
- Series: The International Series on Discrete Event Dynamic Systems 16
- Year: 2007
- Publisher: Springer US
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Max-Plus Linear Stochastic Systems....Pages 3-58
Ergodic Theory....Pages 59-116
Front Matter....Pages 117-117
A Max-Plus Differential Calculus....Pages 119-150
Higher-Order D-Derivatives....Pages 151-177
Taylor Series Expansions....Pages 179-263
Back Matter....Pages 266-324
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.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Max-Plus Linear Stochastic Systems....Pages 3-58
Ergodic Theory....Pages 59-116
Front Matter....Pages 117-117
A Max-Plus Differential Calculus....Pages 119-150
Higher-Order D-Derivatives....Pages 151-177
Taylor Series Expansions....Pages 179-263
Back Matter....Pages 266-324
....