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Analysis of Phase-Type Stochastic Petri Nets with Discrete and Continuous Timing: by Robert L. Jones

By Jones, Robert L. (Robert Lewis)

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Book Id: WPLBN0000659877
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Title: Analysis of Phase-Type Stochastic Petri Nets with Discrete and Continuous Timing: by Robert L. Jones  
Author: Jones, Robert L. (Robert Lewis)
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Language: English
Subject: Government publications, National Aeronautics and Space Administration (U.S.), NASA reference publication
Collections: NASA Publication Collection
Historic
Publication Date:
Publisher: National Aeronautics and Space Administration Publication

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L. (Robert Lewis, J. R. (n.d.). Analysis of Phase-Type Stochastic Petri Nets with Discrete and Continuous Timing. Retrieved from http://www.ebooklibrary.org/


Excerpt
Description: This document contains information regarding the Example Petri net model, Reach ability graph of example PN model, and Examples of possible Petri net and stochastic confusion...

Table of Contents
Contents 1 Introduction 4 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Organization and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Background 7 2.1 Petri Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1 Discrete-Time Markov Chains . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Continuous-Time Markov Chains . . . . . . . . . . . . . . . . . . . . 15 2.3 Phase-Type Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Semi-Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 Semi-Regenerative Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.6 Generalized Semi-Markov Models . . . . . . . . . . . . . . . . . . . . . . . . 35 3 Proposed Research 39 4 Preliminary Research 41 4.1 Analyzing the Underlying Stochastic Process . . . . . . . . . . . . . . . . . . 41 4.1.1 Theory Applied to PDPNs in General . . . . . . . . . . . . . . . . . . 44 4.1.2 Isochronous PDPNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.1.3 Synchronous PDPNs . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1.4 Mixed PDPNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.5 Asynchronous PDPNs . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.2 PDPN Stationary Solution Algorithm . . . . . . . . . . . . . . . . . . . . . . 53 4.2.1 Embedding with Elimination . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.2 Conversion Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.3 Presentation of the Algorithm . . . . . . . . . . . . . . . . . . . . . . 65 4.3 Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.4 Summary of Current Accomplishments . . . . . . . . . . . . . . . . . . . . . 81 5 Future Work 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

 

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