Regeneration and Networks of Queues

  • Gerald S. Shedler

Part of the Applied Probability book series (APPLIEDPROB, volume 3)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Gerald S. Shedler
    Pages 1-19
  3. Gerald S. Shedler
    Pages 20-57
  4. Gerald S. Shedler
    Pages 58-136
  5. Gerald S. Shedler
    Pages 137-195
  6. Back Matter
    Pages 196-224

About this book

Introduction

Networks of queues arise frequently as models for a wide variety of congestion phenomena. Discrete event simulation is often the only available means for studying the behavior of complex networks and many such simulations are non­ Markovian in the sense that the underlying stochastic process cannot be repre­ sented as a continuous time Markov chain with countable state space. Based on representation of the underlying stochastic process of the simulation as a gen­ eralized semi-Markov process, this book develops probabilistic and statistical methods for discrete event simulation of networks of queues. The emphasis is on the use of underlying regenerative stochastic process structure for the design of simulation experiments and the analysis of simulation output. The most obvious methodological advantage of simulation is that in principle it is applicable to stochastic systems of arbitrary complexity. In practice, however, it is often a decidedly nontrivial matter to obtain from a simulation information that is both useful and accurate, and to obtain it in an efficient manner. These difficulties arise primarily from the inherent variability in a stochastic system, and it is necessary to seek theoretically sound and computationally efficient methods for carrying out the simulation. Apart from implementation consider­ ations, important concerns for simulation relate to efficient methods for generating sample paths of the underlying stochastic process. the design of simulation ex­ periments, and the analysis of simulation output.

Keywords

Markov chain Markov process Stochastic processes regenerative process stochastic process

Authors and affiliations

  • Gerald S. Shedler
    • 1
  1. 1.IBM Almaden Research CenterSan JoseUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1050-4
  • Copyright Information Springer-Verlag New York Inc. 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6997-7
  • Online ISBN 978-1-4612-1050-4
  • Series Print ISSN 0937-3195
  • About this book