New performance bounds and asymptotic properties of stochastic timed event graphs
Résumé
This paper addresses the performance evaluation and asymptotic properties of stochastic timed event graphs. The transition firing times are generated by random variables with general distribution. New upper bounds of the average cycle time are obtained by applying large deviation theory. Asymptotic properties with respect to the net structure, the transition firing times and the initial marking are then established on the basis of these new bounds and the existing ones. We propose in particular sufficient conditions under which the average cycle time tends to a finite positive value as the number of transitions tends to infinity. The convergence of the average cycle time, when the variances of the average cycle time, when the variances of the firing times decrease, is established. We also prove that, by putting enough tokens in all places, it is always possible to approach as close as possible to the minimum average cycle time which is equal to the maximum of the average transition firing times. Applications to manufacturing systems are presented. We prove in particular a conjecture which claims that the throughput rate of a transfer line decreases to a positive value when the number of machines increases.