Properties and steady-state performance bounds for Petri nets with unique repetitive firing count vector

The problem of computing both upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is studied. In particular, linear programming problems defined on the incidence matrix of underlying Petri net are used to compute bounds for the throughput of transitions for live and bounded nets with a unique possibility of steady-state behavior. These classes of nets are defined and their characteristics are studied. The bounds proposed here depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases); moreover they can be also computed for non-ergodic models. Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed