Stochastic automata network for modeling parallel systems

Abstract-This paper is motivated by the study of the per-formance of parallel systems. The performance models of such systems are often complex to describe and hard to solve. The method presented here uses a modular representation of the system as a network of state-transition graphs. The state space explosion is handled by a decomposition technique. The dynamic behavior of the algorithm is analyzed under Markovian assump-tions. The transition matrix of the chain is automatically derived using tensor algebra operators, under a format which involves a very limited storage cost. Index Terms-Performance evaluation, Markov chain, tensor product, parallel systems, discrete time scale