On the use of partial symmetries for lumping Markov chains

Abstract

In this paper a method is proposed, to exploit partially symmetric behavior of systems for efficient performance evaluation. The method works on performance models described with the Stochastic Well-Formed Nets (SWN) formalism: it allows to automatically discover partial symmetries in the model behavior, and directly derive a lumped Markov chain from it, suitable for performance analysis purposes. With respect to previous works on automatic exploitation of symmetries in SWNs, the proposed approach allows a significantly higher reduction of the state space size in many practical cases.