In: Proc. 3-rd IEEE Annual Int. Computer Performance and Dependability Symposium (IPDS'98), 7-9 September 1998, Durham, NC, pages 52-61. 1998.
Abstract: In recent years, several classes of stochastic Petri net (SPN) models have been elaborated which incorporate some non-exponential characteristics in their definition. Among the various approaches that have been proposed in the literature for handling non-exponential SPNs, the paper investigates the class of models in which the firing time associated with each transition is a discrete phase type (DPH) random variable, so that the evolution of the marking process is mapped into an expanded discrete-time Markov chain (DTMC). In order to alleviate the state space explosion problem, the expanded state space is expressed via Kronecker algebra operators, starting from the knowledge of the reachability graph of the untimed PN and the DPH random firing times assigned to each PN transition. The discrete case is very appealing sing it allows to mix distributions with finite and infinite support. However, the problem of simultaneous firings arises, and the related semantics must be carefully considered.
Keywords: Kronecker representation, discrete PH distributions, stochastic Petri nets.