In: IBM Research Report RJ 6764, pages 1-24 pp.. IBM Almaden Research Center, San Jose, CA, 1989.
Abstract: We show that the marking process of a stochastic Petri net is a time homogeneous continuous time Markov chain with countable state space, provided that the clock associated with the firing of each timed transition is always set according to a fixed exponential distribution. The result rests on a representation of the conditional distribution of the vector of clock readings, given the `partial history' of the process. We also investigate the modelling power of Markovian stochastic Petri nets. The main result is that for any (possibly non-Markovian) finite state generalized semi-Markov process with exponential clock-setting distributions there exists a Markovian stochastic Petri net with deterministic transitions and unit speeds having a marking process with the same finite-dimensional distributions.
Keywords: stochastic Petri nets; continuous time Markov chains; general state space Markov chains; random polling systems; modelling power.