Affiliations: LSV, CNRS UMR 8643, INRIA, ENS Cachan, Cachan, France. haddad@lsv.ens-cachan.fr | LIAFA, CNRS UMR 7089, Université Paris 7, Paris, France. {mairesse,ngthach}@liafa.jussieu.fr
Note: [] Address for correspondence: LSV, CNRS UMR 8643, INRIA, ENS Cachan, Cachan, France
Abstract: 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, synthesis, complexity analysis, reachability, normalising constant
