The Effect of Execution Policies on the Semantics and Analysis of Stochastic Petri Nets

Petri nets in which random delays are associated with atomic transitions are defined in a comprehensive framework that contains most of the models recently proposed in the literature. The inclusion into the model of generally distributed firing times requires to specify the way in which the next transition to fire is chosen, and how the model keeps track of its past history; this set of specifications is called an execution policy. The paper discusses the impact that different execution policies have on the semantics of the model, as well as the characteristics of the stochastic process associated with each of these policies. When the execution policy is completely specified by the transition with the minimum delay (race policy) and the firing distributions are of the phase type, an algorithm is provided that automatically converts the stochastic process into a continuous time homogeneous Markov chain. Finally, an execution policy based on the choice of the next transition to fire independently of the associated delay (preselection policy) is introduced, and its semantics is discussed together with possible implementation strategies.