Structural Characterization of Decomposition in Rate-insensitive Stochastic Petri Nets
نویسندگان
چکیده
This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al. as SΠ nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of T -invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its T -invariants.
منابع مشابه
A P- and T-invariant characterization of product form and decomposition in stochastic Petri nets
Structural product form and decomposition results for stochastic Petri nets are surveyed, unified and extended. The contribution is threefold. First, the literature on structural results for product form over the number of tokens at the places is surveyed and rephrased completely in terms of T -invariants. Second, based on the underlying concept of group-local-balance, the product form results ...
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