Synthesis and Analysis of Product-form Petri Nets

  • Authors:

  • Serge Haddad;Jean Mairesse;Hoang-Thach Nguyen

  • 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;LIAFA, CNRS UMR 7089, Université Paris 7, Paris, France. {mairesse,ngthach}@liafa.jussieu.fr

  • Venue:
  • Fundamenta Informaticae - Applications and Theory of Petri Nets and Other Models of Concurrency, 2011
  • Year:
  • 2013

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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.