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Structured Characterization of the Markov Chain of Phase-Type SPN

Donatelli, Susanna; Haddad, Serge; Moreaux, Patrice (1998), Structured Characterization of the Markov Chain of Phase-Type SPN, in Serra, Bartomeu; Savino, Nunzio N.; Puigjaner, Ramon, Computer Performance Evaluation Modelling Techniques and Tools 10th International Conference, Tools’98 Palma de Mallorca, Spain September 14–18, 1998 Proceedings, Springer : Berlin, p. 243-254. http://dx.doi.org/10.1007/3-540-68061-6_20

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Type
Communication / Conférence
Date
1998
Conference title
10th International Conference for Computer Performance Evaluation (TOOLS 1998)
Conference date
1998-09
Conference city
Palma de Majorque
Conference country
Espagne
Book title
Computer Performance Evaluation Modelling Techniques and Tools 10th International Conference, Tools’98 Palma de Mallorca, Spain September 14–18, 1998 Proceedings
Book author
Serra, Bartomeu; Savino, Nunzio N.; Puigjaner, Ramon
Publisher
Springer
Series title
Lecture Notes in Computer Science
Series number
1469
Published in
Berlin
ISBN
3-540-64949-2
Pages
243-254
Publication identifier
http://dx.doi.org/10.1007/3-540-68061-6_20
Metadata
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Author(s)
Donatelli, Susanna
Haddad, Serge
Moreaux, Patrice
Abstract (EN)
This paper presents a characterization of the Markovian state space of a Stochastic Petri Nets with phase-type distribution transitions as a union of Cartesian products of a set of “components” of the net. The method uses an abstract view of the net based on the vectors of enabling degrees of phase-type transitions, as well as on the sets of “interrupted clients”. Following the decomposition used for the state space characterization, a tensor algebra expression for the infinitesimal generator (actually for its rate matrix) is given, that allows the steady state probability to be computed directly from a set of matrices of the size of the components, without the need of storing the whole infinitesimal generator.
Subjects / Keywords
Markov chain; Stochastic Petri Nets

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