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Introduction to Modeling and Analysis of Stochastic Systems

  • V. G.┬áKulkarni

Part of the Springer Texts in Statistics book series (STS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. V. G. Kulkarni
    Pages 1-4
  3. V. G. Kulkarni
    Pages 5-58
  4. V. G. Kulkarni
    Pages 59-83
  5. V. G. Kulkarni
    Pages 85-145
  6. V. G. Kulkarni
    Pages 147-187
  7. V. G. Kulkarni
    Pages 189-245
  8. V. G. Kulkarni
    Pages 247-280
  9. Back Matter
    Pages 281-313

About this book

Introduction

This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany the this book can be downloaded from http://www.unc.edu/~vkulkarn/Maxim/maxim.zip. A graphical user interface to access the above files can be downloaded from http://www.unc.edu/~vkulkarn/Maxim/maximgui.zip . The second edition incorporates several changes. First its title reflects the changes in content: the chapters on design and control have been removed. The book now contains several case studies that teach the design principles. Two new chapters have been added. The new chapter on Poisson processes gives more attention to this important class of stochastic processes than the first edition did. The new chapter on Brownian motion reflects its increasing importance as an appropriate model for a variety of real-life situations, including finance. V. G. Kulkarni is Professor in the Department of Statistics and Operations Research in the University of North Carolina, Chapel Hill. He has authored a graduate-level text Modeling and Analysis of Stochastic Systems and dozens of articles on stochastic models of queues, computer and communications systems, and production and supply chain systems. He holds a patent on traffic management in telecommunication networks, and has served on the editorial boards of Operations Research Letters, Stochastic Models, and Queueing Systems and Their Applications.

Keywords

Brownian Motion Markov Chains Poisson Processes Renewal Processes Stochastic Models

Authors and affiliations

  • V. G.┬áKulkarni
    • 1
  1. 1., Dept. of Operations ResearchUniversity of North CarolinaChapel HillUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-1772-0
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-1771-3
  • Online ISBN 978-1-4419-1772-0
  • Series Print ISSN 1431-875X
  • Buy this book on publisher's site
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