Using the probabilistic evaluation tool for the analytical solution of large Markov models

Stochastic Petri net-based Markov modeling is a potentially very powerful and generic approach for evaluating the performance and dependability of many different systems, such as computer systems, communication networks, manufacturing systems, etc. As a consequence of their general applicability, SPN-based Markov models form the basic solution approach for several software packages that have been developed for the analytic solution of performance and dependability models. In these tools, stochastic Petri nets are used to conveniently specify complicated models, after which an automatic mapping can be carried out to an underlying Markov reward model. Subsequently, this Markov reward model is solved by specialized solution algorithms, appropriately selected for the measure of interest. One of the major aspects that hampers the use of SPN-based Markov models for the analytic solution of performance and dependability results is the size of the state space. Although typically models of up to a few hundred thousand states can conveniently be solved on modern-day work-stations, often even larger models are required to represent all the desired detail of the system. Our tool PET (probabilistic evaluation tool) circumvents problems of large state spaces when the desired performance and dependability measure are transient measures. It does so by an approach named probabilistic evaluation.