Integrating Simulation and Numerical Analysis in the Evaluation of Generalized Stochastic Petri Nets

Abstract

The standard existing performance evaluation methods for discrete-state stochastic models such as Petri nets either generate the reachability graph followed by a numerical solution of equations or use some variant of simulation. Both methods have characteristic advantages and disadvantages depending on the size of the reachability graph and type of performance measure. This article proposes a hybrid performance evaluation algorithm for the steady-state solution of Generalized Stochastic Petri Nets that integrates elements of both methods. It automatically adapts its behavior depending on the available size of main memory and number of model states. As such, the algorithm unifies simulation and numerical analysis in a joint framework. It is proved to result in an unbiased estimator whose variance tends to zero with increasing simulation time. The article extends earlier results with an algorithm variant that starts with a small maximum number of particles and increases them during the run to increase the efficiency in cases that are rapidly solved by regular simulation. The algorithm’s applicability is demonstrated through case studies, including an example where it outperforms the standard methods.