Haas P. - Stochastic Petri nets. Modelling, stability, simulation.pdf - Stochaistic Processes and Differential Equations - Kuya

Stochastic Petri Nets:

Modelling, Stability,

Simulation

Peter J. Haas

Springer

Springer Series in Operations Research

Editors:

Peter W. Glynn Stephen M. Robinson

Peter J. Haas

Stochastic Petri Nets

Modelling, Stability, Simulation

With 71 Illustrations

Peter J. Haas

IBM Research Division

San Jose, CA 95120-6099

USA

peterh@almaden.ibm.com

Series Editors:

Peter W. Glynn

Stephen M. Robinson

Department of Management Science

Department of Industrial Engineering

and Engineering

University of Wisconsin–Madison

Terman Engineering Center

Madison, WI 53706-1572

Stanford University

USA

Stanford, CA 94305-4026

USA

Library of Congress Cataloging-in-Publication Data

Haas, Peter J. (Peter Jay)

Stochastic Petri nets : modelling, stability, simulation / Peter J. Haas.

p. cm. — (Springer series in operations research)

Includes bibliographical references and index.

ISBN 0-387-95445-7 (alk. paper)

1. Petri nets. 2. Stochastic analysis. I. Title. II. Series.

QA267 .H3 2002

511.3—dc21

2002019559

Printed on acid-free paper.

2002 Springer-Verlag New York, Inc.

written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York,

NY 10010, 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.

Manufacturing supervised by Jerome Basma.

Camera-ready copy prepared from the author’s LaTeX2e files using Springer’s macros.

Printed and bound by Maple-Vail Book Manufacturing Co., York, PA.

Printed in the United States of America.

987654321

ISBN 0-387-95445-7

SPIN 10867072

Springer-Verlag New York Berlin Heidelberg

A member of BertelsmannSpringer Science

Business Media GmbH

Preface

This book was motivated by a desire to bridge the gap between two impor-

tant areas of research related to the design and operation of engineering

and information systems. The ﬁrst area concerns the development of mathe-

matical tools for formal speciﬁcation of complex probabilistic systems, with

an eye toward subsequent simulation of the resulting stochastic model on

a computer. The second area concerns the development of methods for

analysis of simulation output.

Research on modelling techniques has been driven by the ever-increasing

size and complexity of computer, manufacturing, transportation, workﬂow,

and communication systems. Many engineers and systems designers now

recognize that the use of formal models has a number of advantages over

simply writing complicated simulation programs from scratch. Not only

is it much easier to generate software that is free of logical errors, but

various qualitative system properties—absence of deadlock, impossibility of

reaching catastrophic states, and so forth—can be veriﬁed far more easily

for a formal model than for an ad-hoc computer program. Indeed, certain

system properties can sometimes be veriﬁed automatically.

Our focus is on systems that can be viewed as making state transitions

when events associated with the occupied state occur. More speciﬁcally,

we consider discrete-event systems in which the stochastic state transi-

tions occur only at an increasing sequence of random times. The “Bedi-

enungsprozess” (service process) framework, developed by Konig, Matthes,

and Nawrotzki in the 1960s and early 1970s, provided the ﬁrst set of build-

ing blocks for formal modelling of general discrete-event systems. The mod-

ern incarnation of the Bedienungsprozess is the “generalized semi-Markov

Haas P. - Stochastic Petri nets. Modelling, stability, simulation.pdf

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