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Efficient Handling of Phase-Type Distributions in Generalized Stochastic Petri Nets

Haddad, Serge; Moreaux, Patrice; Chiola, Giovanni (1997), Efficient Handling of Phase-Type Distributions in Generalized Stochastic Petri Nets, dans Azema, Pierre; Balbo, Gianfranco, Application and Theory of Petri Nets 1997 18th International Conference, ICATPN'97, Toulouse, France, June 23-27, 1997, Proceedings, Springer : Berlin, p. 175-194. http://dx.doi.org/10.1007/3-540-63139-9_36

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Type
Communication / Conférence
Date
1997
Titre du colloque
ICATPN'97 Eighteenth International Conference on Application and Theory of Petri Nets
Date du colloque
1997-06
Ville du colloque
Toulouse
Pays du colloque
France
Titre de l'ouvrage
Application and Theory of Petri Nets 1997 18th International Conference, ICATPN'97, Toulouse, France, June 23-27, 1997, Proceedings
Auteurs de l’ouvrage
Azema, Pierre; Balbo, Gianfranco
Éditeur
Springer
Titre de la collection
Lecture Notes in Computer Science
Numéro dans la collection
1248
Ville d’édition
Berlin
Isbn
978-3-540-63139-2
Nombre de pages
467
Pages
175-194
Identifiant publication
Métadonnées
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Auteur(s)
Haddad, Serge
Moreaux, Patrice
Chiola, Giovanni
Résumé (EN)
We study the introduction of transitions with Phase-type distribution firing time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works. The method is based on a structural decomposition of the net. We establish conditions under which this decomposition leads to a tensor expression of the generator of the chain. The tensor expression is used to solve the chain with an iterative method.
Mots-clés
Tensor algebra; Stochastic Petri Nets; Phase-type distributions; Coxian distributions