Modelling with GSPNs - MODELLING WITH GENERALISED...

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Unformatted text preview: MODELLING WITH GENERALISED STOCHASTIC PETRI NETS MODELLING WITH GENERALISED STOCHASTIC PETRI NETS M. Ajmone Marsan Politecnico di Torino Gianfranco Balbo Universit` a di Torino Gianni Conte Universit` a di Parma Susanna Donatelli Universit` a di Torino Giuliana Franceschinis Universit` a del Piemonte Orientale Dipartimento di Informatica Contents 1 INTRODUCTION 15 1.1 Shared Resources . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2 Fork and Join . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3 Kanban Process . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4 Token Ring LAN . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 PETRI NETS AND THEIR PROPERTIES 29 2.1 Petri Net Models . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 Models, Systems, and Nets . . . . . . . . . . . . . . . . . . . 32 2.3 System Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3.1 Enabling and firing rules . . . . . . . . . . . . . . . . . 34 2.3.2 Reachability set and reachability graph . . . . . . . . 36 2.3.3 Modelling issues . . . . . . . . . . . . . . . . . . . . . 39 2.3.4 Typical situations in the PN system evolution . . . . . 42 2.4 Properties of Petri Nets . . . . . . . . . . . . . . . . . . . . . 47 2.5 Structural Analysis Techniques . . . . . . . . . . . . . . . . . 49 2.5.1 Linear algebraic techniques . . . . . . . . . . . . . . . 50 2.5.2 Graph-based structural techniques . . . . . . . . . . . 58 2.6 State Space Analysis Techniques . . . . . . . . . . . . . . . . 61 3 TIME IN PETRI NETS 65 3.1 The Motivations for Timing . . . . . . . . . . . . . . . . . . . 65 3.2 Timed Transitions . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2.1 Immediate transitions . . . . . . . . . . . . . . . . . . 69 3.2.2 Two examples . . . . . . . . . . . . . . . . . . . . . . 70 3.3 Parallelism and Conflict . . . . . . . . . . . . . . . . . . . . . 72 3.4 Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4.1 An example with the enabling memory policy . . . . . 77 3.4.2 An example with the age memory policy . . . . . . . . 79 3.5 Multiple Enabling . . . . . . . . . . . . . . . . . . . . . . . . 79 3.6 A Timed PN Model Example . . . . . . . . . . . . . . . . . . 84 3.7 Performance Measures . . . . . . . . . . . . . . . . . . . . . . 84 1 2 CONTENTS 4 PETRI NETS WITH PRIORITY 87 4.1 Definition and Dynamics . . . . . . . . . . . . . . . . . . . . . 87 4.2 Conflicts, Confusion and Priority . . . . . . . . . . . . . . . . 91 4.3 Properties of Priority PN Models . . . . . . . . . . . . . . . . 95 4.4 Structural Analysis Techniques . . . . . . . . . . . . . . . . . 98 4.4.1 Linear algebraic techniques . . . . . . . . . . . . . . . 98 4.4.2 Graph based analysis . . . . . . . . . . . . . . . . . . . 99 4.5 Reachability Analysis Techniques . . . . . . . . . . . . . . . . 101 5 GSPN BASICS 107 5.1 Exponential Distributions for Transition Delays . . . . . . . . 107 5.2 Mixing Exponentially Distributed and Null Delays . Mixing Exponentially Distributed and Null Delays ....
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This note was uploaded on 04/08/2010 for the course COMPUTER E 409232 taught by Professor Mohammadabdolahiazgomiph.d during the Spring '10 term at Islamic University.

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Modelling with GSPNs - MODELLING WITH GENERALISED...

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