Tight polynomial bounds for steady-state performance of marked graphs

The problem of computing both upper and lower bounds for the steady-state performance of timed and stochastic marked graphs is studied. In particular, linear programming problems defined on the incidence matrix of the underlying Petri nets to compute tight (i.e. reachable) bounds for the throughput of transitions for live and bounded marked graphs with time associated with transitions are considered. These bounds 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). Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed