Introduction to Modeling and Analysis of Stochastic Systems
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 larg
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V.G. Kulkarni
Introduction to Modeling and Analysis of Stochastic Systems Second Edition
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Prof. V.G. Kulkarni University of North Carolina Department of Statistics and Operations Research Chapel Hill, NC 27599-3260 USA [email protected]
ISBN 978-1-4419-1771-3 e-ISBN 978-1-4419-1772-0 DOI 10.1007/978-1-4419-1772-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: PCN applied for c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my Sons Milind, Ashwin and Arvind
Preface to the Second Edition
What Is New in the Second Edition? Students and instructors will notice significant changes in the second edition. 1. The chapters on probability have been removed. Abbreviated versions of these chapters appear as Appendices A, B, C, and D. 2. A new chapter (Chapter 3) on Poisson processes has been added. This is in response to the feedback that the first edition did not give this important class of stochastic processes the attention it deserves. 3. A new chapter (Chapter 7) on Brownian motion has been added. This is to enable instructors who would like the option of covering this important topic. The treatment of this topic is kept at a sufficiently elementary level so that the students do not need background in analysis or measure theory to understand the material. 4. The chapters on design and control of stochastic systems in the first edition have been deleted. Instead, I have added case studies in Chapters 2, 4, 5, and 6. The instructor can use these to talk about the design aspect of stochastic modeling. The control aspect is entirely deleted. This has necessitated a change of title for the new edition. 5. Several typos from the first edition have been corrected. If there are new typos in the second edition, it is entirely my fault. I would appreciate it if the readers would kindly inform me about them. A current list of corrections is available on the Web at www.unc.edu/vkulkarn/ugcorrections2.pdf.
Who Is This Book For? This book is meant to be used as a textbook in a junior-or senior-level undergraduate course on stochastic models. The students a
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