Speci cations and Solution Techniques for Non-Markovian Stochastic Petri Nets

Allmost all the available tools for the analysis of Stochastic Petri Nets (SPN) assume that the stochastic nature of the problem is restricted to be a Continuous Time Markov Chain (CTMC), but in reality, there are instances in which the CTMC assumption is too weak. The evolution of the stochastic systems with nonexponential timing becomes a stochastic process, for which in general, no analytical solution is available. In order to properly de ne Non-Markovian Stochastic Petri Nets special specications should be added at the PN level. These speci cations are usually referred to as the ring policy. The semantics of di erent ring policies appeared in the literature is discussed, together with their implication on the behavior of the associated marking process. Di erent approaches and numerical techniques have been explored in the literature for dealing with non-Markovian SPNs: techniques based on the theory of Markov regenerative processes; techniques based on the use of supplementary variables; techniques based on the approximation of the original non-Markovian process by means of a Markov chain de ned over an extended state space. The paper explore the background of the above solution techniques with respect to di erent classes of models.