Synthesis and analysis of product-form petri nets

Authors:
S. Haddad;J. Mairesse;H.-T. Nguyen
Affiliations:
ENS Cachan, LSV, CNRS UMR 8643, INRIA, Cachan, France;Université Paris 7, LIAFA, CNRS UMR 7089, Paris, France;Université Paris 7, LIAFA, CNRS UMR 7089, Paris, France
Venue:
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
Year:
2011

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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.