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

Haddad, Serge; Moreaux, Patrice; Chiola, Giovanni

Haddad, Serge; Moreaux, Patrice; Chiola, Giovanni (1997), Efficient Handling of Phase-Type Distributions in Generalized Stochastic Petri Nets, in 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

Conference title

ICATPN'97 Eighteenth International Conference on Application and Theory of Petri Nets

Conference date

1997-06

Conference city

Toulouse

Conference country

France

Book title

Application and Theory of Petri Nets 1997 18th International Conference, ICATPN'97, Toulouse, France, June 23-27, 1997, Proceedings

Book author

Azema, Pierre; Balbo, Gianfranco

Publisher

Springer

Series title

Lecture Notes in Computer Science

Series number

1248

Published in

Berlin

ISBN

978-3-540-63139-2

Number of pages

467

Pages

175-194

Abstract (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.

Subjects / Keywords

Tensor algebra; Stochastic Petri Nets; Phase-type distributions; Coxian distributions