TRANSIENT ANALYSIS OF A PREEMPTIVE RESUME M/D/l/2/2 THROUGH PETRI NETS

Abstract

Stochastic Petri Nets (SPN) are usually designed to support exponential distributions only, with the consequence that their modelling power is restricted to Markovian systems. In recent years, some attempts have appeared in the literature aimed to define SPN models with generally distributed firing times. A particular subclass, called Deterministic and Stochastic Petri Nets (DSPN), combines into a single model both exponential and deterministic transitions. The available DSPN implementations require simplifying assumptions which limit the applicability of the model to preemptive repeat different service mechanisms only. The present paper discusses a semantical generalization of the DSPNs by including preemptive mechanisms of resume type. This generalization is crucial in connection with fault tolerant systems, where the work performed before the interruption should not be lost. By means of this new approach, the transient analysis of a M/D/1/2/2 queue (with 2 customers, 1 server, exponential thinking and deterministic service time) is fully examined under different preemptive resume policies.