Combining Proxels and Discrete Phases

The analysis of discrete stochastic models such as generally distributed stochastic Petri nets can be done by using state spacebased methods. They describe the behavior of a model by a Markov chain that can be solved mathematically. Formerly this approach often had to be discarded as unfeasible due to high memory and runtime costs. The recently developed Proxel-based algorithm is a state space-based simulation method, and has already performed well in several application fields. Experiments suggest, that the selective use of discrete phase approximations could further improve the method, because they can often represent infinite support distribution functions with considerably fewer Markov chain states than proxels. By replacing certain on-the-fly proxel approximations by predetermined phase-type approximations, the total runtime and memory requirement of the simulation method could be drastically reduced for some test models. An efficient algorithm for the approximation of discrete phase-type distributions based on common optimization methods was recently introduced. The formal inclusion of discrete phases into the proxel paradigm is another step toward a practically usable state spacebased simulation method. Our hope is that such a combination of both approaches will lead to a competitive simulation algorithm.