Computing response time distributions using stochastic Petri nets and matrix diagrams

In this paper, we consider random variables expressed in terms of the time required for the state of a stochastic Petri net to pass from a set of starting markings to a set of stopping markings. These random variables have continuous phase-type distributions when the all transitions have exponentially-distributed firing delays. We demonstrate how to numerically compute the distribution of the random variable using both explicit techniques and an implicit approach based on multi-way decision diagrams and matrix diagrams. We present an efficient matrix-vector multiplication algorithm for matrix diagrams that is necessary for numerical solution. We demonstrate the efficiency of our approaches using several models. The lower storage requirements of the implicit approach effectively increases the size of models that can be analyzed by about an order of magnitude.