M-timed Petri nets and Markov chains in modelling of computer systems
W.M. Zuberek · 1986
It is shown that the behavior of enhanced free-choice bounded M-timed Petri nets, i.e., Petri nets with two classes of transitions, immediate and timed ones, and with exponentially distributed firing times of timed transitions, can be represented by state-transition graphs which are finite continuous-time homogeneous Markov chains. Moreover, for each finite continuous-time homogeneous Markov chain there exists an enhanced free-choice bounded M-timed Petri net with the state-transition graph isomorphic to this chain. These two classes of models are thus equivalent. A straight-forward application of (enhanced) M-timed Petri nets is modelling and performance evaluation of Markovian queueing systems, and in particular closed-network models of computer systems. Simple models of interactive systems are used as an illustration of modelling. as an illustration of modelling.