Description framework for proxel-based simulation of a general class of stochastic models

The motivation for this paper is to raise the recently introduced proxel-based simulation method to a higher level by defining its own model description framework, which at the same time would allow us to enhance the description and analysis of discrete stochastic models beyond the potential of stochastic Petri nets. The Proxel-based method is designed for transient analysis of discrete stochastic models, which are commonly described using stochastic Petri nets (SPNs). The approach is based on the method of supplementary variables, meaning it performs the analysis in a deterministic manner. It, however, works in a purely algorithmic style, without employing partial differential equations. Experiments and applications have so far shown the method to be promising, especially in analysing classes of models which are known to be difficult or problematic to be deterministically analysed using standard methods (such as Markov chains and partial differential equations). Infinite state space models, such as queuing systems with unbounded queues (with generally distributed arrivals and processing times) where servers can fail, and the number of failures and servers' age determine the parameters of the distribution function of the processing time, is one of those problematic cases. As mentioned, up to now, a starting point for the proxel-based analysis was the Petri net model of the system to be simulated. The models, however, had to be adapted, using hard coding, to transform them into an appropriate input for the proxel-based simulator, mainly for efficiency reasons, but also for allowing properties that were not supported by SPNs. The transformation was implicitly the model description approach that we present and formalise in this paper. We believe that the modelling framework that we describe here will be able to exploit all or most of the beneficial properties of the proxel-based method and describe the model in a way that is directly analysable by the proxel-based simulator. The framework is based upon Petri net features and modifies and extends them according to the properties and needs of the proxel-based method. Our approach is supported and demonstrated by experiments and characteristic examples, as well as comparison to the formalism of SPNs.