Performance evaluation of parallel systems by using unbounded generalized stochastic Petri nets

Methods of calculating efficiently the performance measures of parallel systems by using unbounded generalized stochastic Petri nets are presented. An explosion in the number of states to be analyzed occurs when unbounded places appear in the model. The state space of such nets is infinite, but it is possible to take advantage of the natural symmetries of the system to aggregate the states of the net and construct a finite graph of lumped states which can easily be analyzed. With the methods developed, the unbounded places introduce a complexity similar to that of safe places of the net. These methods can be used to evaluate models of open parallel systems in which unbounded places appear; systems which are k-bounded but are complex and have large values of k can also be evaluated in an appropriate way. From the steady-state solution of the model, it is possible to obtain automatically the performance measures of parallel systems represented by this type of net