Timed Petri Nets Theory and Application
Driven by the request for increased productivity, flexibility, and competitiveness, modern civilization increasingly has created high-performance discrete event dynamic systems (DEDSs). These systems exhibit concurrent, sequential, competitive activities
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THE KLUWER INTERNATIONAL SERIES ON DISCRETE EVENT DYNAMIC SYSTEMS Series Editor Yu-ChiHo Harvard University GRADIENT ESTIMATION VIA PERTURBATION ANALYSIS P. Glasserman ISBN: 0-7923-9095-4 PERTURBATION ANALYSIS OF DISCRETE EVENT DYNAMIC SYSTEMS Yu-Chi Ho and Xi-Ren Cao ISBN: 0-7923-9174-8 PETRI NET SYNTHESIS FOR DISCRETE MANUFACTURING SYSTEMS MengChu Zhou and Frank DiCesare ISBN: 0-7923-9289-2
EVENT
CONTROL
OF
MODELING AND CONTROL OF LOGICAL DISCRETE EVENT SYSTEMS Ratnesh Kumar and Vijay K. Garg ISBN: 0-7923-9538-7 UNIFORM RANDOM NUMBERS: THEORY AND PRACTICE Shu Tezuka ISBN: 0-7923-9572-7 OPTIMIZATION OF STOCHASTIC MODELS: THE INTERFACE BETWEEN SIMULATION AND OPTIMIZATION Georg Ch. Pflug ISBN: 0-7923-9780-0 CONDITIONAL MONTE CARLO: OPTIMIZATION APPLICATIONS Michael FU and Jian-Qiang HU ISBN: 0-7923-9873-4
GRADIENT
ESTIMATION
AND
SUPERVISORY CONTROl, OF DISCRETE EVENT SYSTEMS USING PETRI NETS John O. Moody and Panos 1. Antsaklis ISBN: 0-7923-8199-8
TIMED PETRI NETS Theory and Application
by
Jiacun Wang Florida International University Miami, Florida
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4613-7531-9 ISBN 978-1-4615-5537-7 (eBook) DOI 10.1007/978-1-4615-5537-7
Copyright © 1998 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 1998 Softcover reprint of the hardcover Ist edition 1998 AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Medi~ LLC. Printed on acid-free paper.
CONTENTS
PREFACE
ix
1 INTRODUCTION
1
1.1 Discrete Event Dynamic Systems 1 1.2 Performance Models for Discrete Event Dynamic Systems 2 1.3 Timed Petri Nets: A Powerful Tool 4
2 PETRI NETS 2.1 2.2 2.3 2.4
Preliminary Definitions 9 Transition Firing 11 Representational Power 13 Properties of Petri Nets 15 2.4.1 Reachability 15 2.4.2 Boundedness and Safeness 17 2.4.3 Conservativeness 18 2.4.4 Liveness 19 2.5 Analysis of Petri Nets 20 2.5.1 The Coverability Tree 21 2.5.2 Incidence Matrix and State Equation 24 2.5.3 Invariant Analysis 29 2.5.4 Simple Reductions for Analysis 32 2.5.5 Simulation 34
9
CONTENTS
VI
3 DETERMINISTIC TIMED PETRI NETS
37
3.1 Deterministic Timed Transitions Petri Nets 38 3.2 Performance Analysis 40 3.2.1 Consistent Petri Nets 41 3.2.2 Decision-Free Petri Nets 42 3.2.3 Performance Evaluation 43 3.2.4 Safe Persistent Petri Nets 50 3.3 Other Types of Deterministic Timed Petri Nets 53 3.3.1 Deterministic Timed Places Petri Nets 53 3.3.2 Deterministic Timed Arcs Petri Nets 57
4 TIME PETRI NETS
63
4.1 Time Petri Nets 64 4.1.1 Time Petri Nets 64 4.1.2 States in a Time Petri Net 66 4.1.3 Enabling and Firing Conditions of Transitions 67 4.1.4 Firing Rule between States 67 4.1.5 Multiple Enablings of Tra
