In: Rapports de recherche 1433, INRIA, Rocquencourt. 1991.
Abstract: This paper focuses on stochastic comparison problems arising in the analysis of Stochastic Decision Free Petri Nets (SDFPN). The analysis is based on the evolution equations satified by firing times. Various structural properties are obtained including the association of the firing times and their stochastic and convex monotonicity with respect to the holding time sequences and to the initial marking. The association and the stochastic monotonicity properties are extended to the counters using an inversion relation. It is also proved that the counters and the throughput are stochastically concave in the initial marking provided the holding times are i.i.d and belong to a subclass of log-concave distribution functions that is introduced in the paper. Various bounds for the asymptotic cycle time and the throughput are then derived from these stochastic ordering results. Finally, results are presented concerning the stochastic and convex monotonicity of the transient.