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
TypeCommunication / Conférence
Conference title22nd International Conference on Application and Theory of Petri Nets (ICATPN 2001)
Conference cityNewcastle upon Tyne
Book titleApplications and Theory of Petri Nets 2001 22nd International Conference, ICATPN 2001 Newcastle upon Tyne, UK, June 25-29, 2001 Proceedings
Book authorColom, Jose-Manuel; Koutny, Maciej
Series titleLecture Notes in Computer Science
Number of pages403
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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 / KeywordsStochastic Petri Nets
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