Modelling with Stochastic Petri Nets

Abstract

Stochastic Petri nets (SPNs) are well suited to representing concurrency, synchronization, precedence, and priority. After presenting the basic SPN building blocks in Section 2.1, we give a series of examples in Section 2.2 that illustrates the use of SPNs for modelling discrete-event systems. We pay particular attention to complications that arise in the specification of new-marking probabilities. These probabilities determine the mechanism by which a transition removes tokens from a random subset of its normal input places and deposits tokens in a random subset of its output places when it fires. Consideration of a queueing system with batch arrivals shows that new-marking probabilities must be allowed to depend explicitly on the current marking; that is, the SPN formalism must include marking-dependent transitions. By means of an example, we show how new-marking probabilities for an SPN with marking-dependent transitions can be specified in a form suitable for processing by a computer program. Another complication arises when more than one transition can fire at a time point. In principle, new-marking probabilities must be defined for all possible sets of simultaneously firing transitions, and there can be an extremely large number of such sets. As shown in Section 2.3, concise specification of new-marking probabilities can be facilitated by assigning numerical “priorities” to transitions.