Regular stochastic Petri nets

An extension of regular nets, a class of coloredd nets, to a stochastic model is proposed. We show that the symmetries in this class of nets make it pos sible to developp a performance evaluation by constructingg only a graph of symbolic markings, which ver tices are classes of states, insteadd of the whole reachability graph. Usingg algebraic techniques, we prove that all the states in a class have the same probability, andd that the coefficients of the li near system describingg the lumpedd Markov process can be calculatedd directly from the graph of symb olic markings. I-INTRODUCTION As they are a function of the number andd the complexity of the processes to be represented, Petri net models of distributedd computer systems must quickly face probl ems due to the huge size of the reachability graph. The use of higher level models (e.g., coloredd nets, Pr/T nets) can make the taskk of the modeler easier. However, the existingg analysis methods often make it necessary to go backk to an equivalent ordinary net, so that there is no improvement in the complexity. In order to face the exponential increase in the numbe r of states, Jensen [Jen 81a] has introducedd in coloredd Petri nets some equivalence relations that take into account the symmetries of the model. He showedd that those relations were directly dependingg on th e type of the color functions. He also definedd analysis methods associatedd with the use of simpl e functions [Jen 81a, Hub 84].