Synthesis and Analysis of Product-form Petri Nets

Serge Haddad (1) , Jean Mairesse (2) , Hoang-Thach Nguyen (2)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

For a large Markovian model, a ''product form'' is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here we address three relevant issues for product-form Petri nets which were left fully or partially open: (1) we provide a sound and complete set of rules for the synthesis; (2) we characterise the exact complexity of classical problems like reachability; (3) we introduce a new subclass for which the normalising constant (a crucial value for product-form expression) can be efficiently computed.

Keywords: petri nets; product-form; complexity analysis; synthesis; reachability; normalising constant

Domains: Modeling and Simulation; Discrete Mathematics [cs.DM]

Serge Haddad, Jean Mairesse, Hoang-Thach Nguyen. Synthesis and Analysis of Product-form Petri Nets. 2011. ⟨hal-00582584v2⟩