Passage times in colored stochastic Petri nets

Passage times in colored stochastic Petri nets correspond to delays in discrete-event stochastic systems. Formal definition of a sequence of passage times in a colored stochastic Petri net is in terms of the underlying general state space Markov chain of the marking process. Using symmetry of the net with respect to color, the authors provide conditions under which a sequence of passage times is a regenerative process in discrete time with finite cycle-length moments. The regenerative property implies time-average convergence, convergence in distribution, and a central limit theorem for sequences of passage times. It follows that strongly consistent point estimates and asymptotic confidence intervals for general characteristics of passage times can be obtained by simulating a finite portion of a single sample path of the underlying general state space Markov chain. Using regenerative structure of the marking process and a version of Little’s Law given by Glynn and Whitt, the authors also obtain conditions under which a sequence of passage times converges in a time-average sense and the limit can be expressed as a ratio of expected values. The resulting estimation procedure for the limiting average passage time requires no measurement of individual passage times and is valid even if there are no regeneration points for the sequence of passage times.