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Structural characterization and qualitative properties of product form stochastic Petri nets

Haddad, Serge; Moreaux, Patrice; Sereno, Matteo; Silva, Manuel (2001), Structural characterization and qualitative properties of product form stochastic Petri nets, in Colom, Jose-Manuel; Koutny, Maciej, Applications and Theory of Petri Nets 2001 22nd International Conference, ICATPN 2001 Newcastle upon Tyne, UK, June 25-29, 2001 Proceedings, Springer : Berlin, p. 164-183. http://dx.doi.org/10.1007/3-540-45740-2_11

Type
Communication / Conférence
Date
2001
Conference title
22nd International Conference on Application and Theory of Petri Nets (ICATPN 2001)
Conference date
2001-06
Conference city
Newcastle upon Tyne
Conference country
Royaume-Uni
Book title
Applications and Theory of Petri Nets 2001 22nd International Conference, ICATPN 2001 Newcastle upon Tyne, UK, June 25-29, 2001 Proceedings
Book author
Colom, Jose-Manuel; Koutny, Maciej
Publisher
Springer
Series title
Lecture Notes in Computer Science
Series number
2075
Published in
Berlin
ISBN
978-3-540-42252-5
Number of pages
403
Pages
164-183
Publication identifier
http://dx.doi.org/10.1007/3-540-45740-2_11
Metadata
Show full item record
Author(s)
Haddad, Serge
Moreaux, Patrice
Sereno, Matteo
Silva, Manuel
Abstract (EN)
The model of Stochastic Petri nets (SPN) with a product form solution (Π-net) is a class ofnets for which there is an analytic expression ofthe steady state probabilities w.r.t. markings, as for product form queueing networks w.r.t. queue lengths. In this paper, we prove new important properties ofthis kind ofnets. First we provide a polynomial time (w.r.t. the size ofthe net structure) algorithm to check whether a SPN is a Π-net. Then, we give a purely structural characterization of SPN for which a product form solution exists regardless the particular values ofprobabilistic parameters ofthe SPN. We call such nets $ \overline \prod - nets $−nets . We also present untimed properties of Π-nets and $ \overline \prod - nets $−nets such like liveness, reachability, deadlock freeness and characterization of reachable markings. The complexity ofthe reachability and the liveness problems is also addressed for Π-nets and $ \overline \prod - nets $−nets . These results complement previous studies on these classes ofnets and improve the applicability ofPro duct Form solutions.
Subjects / Keywords
Stochastic Petri Nets

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