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 form 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.
On the Product Form Solution for Stochastic Petri Nets
DONATELLI, Susanna;SERENO, Matteo
1992-01-01
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 form 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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