A methodology for solving markov models of parallel systems

Abstract

The purpose of this paper is to present the ideas and algorithms that are used in the package for the Performance Evaluation of Parallel Systems (PEPS). This package uses a description of the system as a network of synchronized automata. This representation is called Stochastic Automata Network (SAN). A SAN is studied under Markovian assumptions. The Markov chain matrix can be expressed in terms of generalized tensor product, using the modularity of the SAN models. In this paper, it is shown that this formulation allows the matrix to be stored with considerable memory savings. It is also used to improve the complexity of the vector-matrix multiplication in the power method. An example is given to illustrate the methodology.