A New Tool to Model Parallel Systems and Protocols

Abstract

We present a new performance evaluation tool based on the analysis of large Markov chains and Stochastic Automata Networks. Using some graph theoretical arguments, we show how to systematically perform state reduction. The graph properties can be checked easily because we take advantage of the tensorial construction of the Markov chain from the Stochastic Automata Network. 1 Introduction We present a new modeling tool based on Stochastic Automata Networks (SAN). Stochastic Automata Networks have been introduced as an efficient method to represent complex systems with interacting components such as parallel systems or distributed systems [Plateau et al. 1988]. This new method automatically provides an analytic derivation of the generator matrix of the Markov chain using tensor algebra. The SAN seem to be more efficient than Queueing Networks or Stochastic Petri Nets to model systems with a large number of states and complex synchronizations. Queueing Networks give a very compact repres..