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## On the product Form Solution for Stochastic Petri Nets.

Donatelli, Susanna;
Sereno, Matteo
In:
Jensen, K.: *Lecture Notes in Computer Science, Vol. 616; 13th International Conference on Application and Theory of Petri Nets 1992, Sheffield, UK*, pages 154-172.
Springer-Verlag,
June 1992.

Abstract:
The combinatorial explosion of the state space of Stochastic Petri Nets
(SPNs) is a well known problem that inhibits the exact solution of large
SPNs, and therefore a broad use of this kind of Petri Nets as a modelling
tool. The same problem exists also for other modelling formalisms like for
example Queueing Networks (QNs). In [13,3] a class of QNs whose solution
can be computed in an easy way was defined. For this class of models the
solution can be factorized into terms that refer to each single queue of
the network. This solution is known as Product Form Solution (PFS). In
this paper we compare two different approaches to PFS for SPNs. In both
proposals the solution is obtained as a product for of terms, each term
corresponding to a place in the SPN. The first approach (by Lazar and
Robertazzi) allows the PFS to be detected at state space level by
inspecting the structure of the reachability graph. The second one (by
Henderson, Lucic and Taylor) allows the PFS to be detected at structural
level, that is to say without inspection of the reachability graph. In
this paper we try to put the two approaches into a common framework and to
show the important role played by T-invariants.

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