Proxel-Based Simulation of Stochastic Petri Nets Containing Immediate Transitions

This paper discusses the analysis of stochastic Petri nets using the proxelbased simulation method. The paradigm of the proxel (”probability element”) was recently introduced in order to provide a new algorithmic approach to analysing discrete-state stochastic models such as are represented by stochastic Petri nets (SPNs) or queuing systems. Proxel-based simulation is not related to either of the standard simulation approaches: it is in no way analogous to discrete-event simulation, and, although it is based on the model′s underlying stochastic process and makes use of supplementary variables, it does not require the use of differential equations. Instead, the proxels trace the movement of probability from one state of the model to another using discretised time steps. Since stochastic Petri nets are a powerful and widespread tool for modelling stochastic processes, we are interested in finding out how the proxel-based method applies to them. The analysis of SPNs using the proxel-based method is the subject of this paper, with an emphasis on the treatment of immediate transitions. 1 Goals of the Paper The goal of this paper is to extend the analysis of stochastic Petri nets using the recently introduced proxel-based method. The formal 1 Email: [email protected] 2 Email: [email protected]