Timed Petri nets in modelling and evaluation of multiprocessor systems

Abstract

Timed Petri nets discussed in this paper are extended Petri nets with exponentially distributed firing times. Interrupt arcs are introduced as an extension of inhibitor arcs to allow modelling of preemptions. Since the behavior of extended free- choice timed Petri nets can be represented by probabilistic Qs-tate graphs, stationary probabilities of states can be obtained by standard techniques used for analysis of continuous-time homogeneous Markov chains. An immediate application of such a model is performance analysis of queueing systems with exponentially distributed service and interarrival times, and in particular distributed computer systems. Places of Petri nets model systems queues, transitions represent servers, inhibitor arcs are used to model priorities of simultaneous events, and interrupt arcs provide preemption of servers. Simple models of multiprocessor systems are used as an illustration of modelling and performance evaluation.