Proprietes de Comparaison Stochastique dans les Graphes d'Evenements Aleatoires(Comparison Properties of Stochastic Decision Free Petri Nets)

摘要

Stochastic comparison problems arising in the analysis of stochastic decisionfree Petri nets are addressed. The analysis is based on the evolution equations satisfied 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. The counters and the throughput are proved to be stochastically concave in the initial marking provided the holding times are i.i.d. and belong to a subclass of log-concave distribution functions. Various bounds for the asymptotic cycle time and the throughput are then derived from these stochastic ordering results. Results concerning the stochastic and convex monotonicity of the transient and the stationary marking distributions are presented.