Petri nets with k simultaneously enabled generally distributed timed transitions

Abstract

Stochastic Petri nets have been used to analyze the performance and reliability of complex systems comprising concurrency and synchronization. Various extensions have been proposed in literature in order to broaden their field of application to an increasingly larger range of real situations. In this paper we extend the class of Markov regenerative stochastic Petri nets ∗ (MRSPNs ∗), removing the restriction that at most one generally distributed timed transition can be enabled in any marking. This new class of Petri nets, which we call concurrent generalized Petri nets (CGPNs), allows simultaneous enabling of immediate, exponentially and generally distributed timed transitions, under the hypothesis that the latter are all enabled at the same instant. The stochastic process underlying a CGPN is shown to be still an MRGP. We evaluate the kernel distribution of the underlying MRGP and define the steps required to generate it automatically. The methodology described is used to assess the behavior of a system in both steady-state and transient functioning conditions.