Approximate transient analysis of large stochastic models with WinPEPSY-QNS

In this paper we present a new algorithm for the approximate transient analysis of large stochastic models. The new algorithm is based on the self-correcting analysis principle for continuous-time Markov chains (CTMC). The approach uses different time dependent aggregations of the CTMC of a stochastic model. With the method of uniformization the transient state probabilities of each aggregated CTMC for a time step are calculated. The derived probabilities are used for the construction of stronger aggregations, which are applied for the correction of the transition rates of the previous aggregations. This is done step by step, until the final time is reached. High aggregations of the original continuous-time Markov chain lead to a time and space efficient computational effort. Therefore the approximate transient analysis method based on the self-correcting aggregation can be used for models with large state spaces. For queuing networks with phase-type distributions of the service times this newly developed algorithm is implemented in WinPEPSY-QNS, a tool for performance evaluation and prediction of stochastic models based on queuing networks. It consists of a graphical editor for the construction of queuing networks and an easy-to-use evaluation component, which offers suitable analysis methods. The newly implemented algorithm is used for the analysis of several examples, and the results are compared to the results of simulation runs where exact values cannot be achieved.