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Synthesis and Analysis of Product-form Petri Nets

Haddad S., Mairesse J., Nguyen H. T.

Fundamenta Informaticae

2013

Vol. 122, nr 1-2

147--172

For a large Markovian model, a "product form" is an explicit description of the steadystate 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.

Deficiency Zero Petri Nets and Product Form

Mairesse J., Nguyen H-T.

Fundamenta Informaticae

2011

Vol. 105, nr 3

237-261

Consider a Markovian Petri net with race policy. The marking process has a "product form" stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the local marking. First we observe that the Deficiency Zero Theorem of Feinberg, developed for chemical reaction networks, provides a structural and simple sufficient condition for the existence of a product form. In view of this, we study the classical subclass of free-choice nets. Roughly, we show that the only Petri nets of this class which have a product form are the state machines, which can alternatively be viewed as Jackson networks.