M-timed Petri nets, priorities, preemptions, and performance evaluation of systems

Abstract

In M-timed Petri nets, firing times are exponentially distributed random variables associated with transitions of a net. Several classes of M-timed Petri nets are discussed in this paper to show increasing "modelling power" of different nets. Conflict-free nets can model M and E k -type queueing systems. Free-choice nets can also represent H k -type systems. Systems with several classes of users and with service priorities assigned to user classes require nets with inhibitor arcs. Preemption of service can be represented by extended nets with escape (or generalized inhibitor) arcs. Finally, to provide flexible modelling of scheduling and decision strategies, enhanced Petri nets are introduced with two classes of transitions, immediate and timed ones, and with (exponentially distributed) firing times associated with the timed transitions. It is shown that the behaviour of bounded M-timed Petri nets can be represented by finite "state" graphs which are finite-state continuous-time homogeneous Markov processes. Stationary probabilities of states can thus be obtained by standard techniques used for analysis of Markov chains, and then operational analysis can be applied for performance evaluation. Simple models of interactive systems are used as an illustration of modelling.

Timed Petri Nets in Performance Exploration of Simultaneous Multithreading

“…The occurrence times of transitions can be either deterministic or stochastic (i.e., described by some probability distribution function); in the first case, the corresponding timed nets are referred to as D-timed nets [18], in the second, for the (negative) exponential distribution of firing times, the nets are called M-timed nets (Markovian nets [17]). In both cases, the concepts of state and state transitions have been formally defined and used in the derivation of different performance characteristics of the model [14].…”

Modified M-timed Petri nets in modelling and performance evaluation of systems

“…In fact, non-simple nets with more general conflicts can be described in a very similar way provided that the probabilities of conflicts are known and included in the net description. Some other generalizations are discussed in 1171 (limited-choice), [18] (multiple arcs) and [IQ] (enhanced nets).…”

“…The formalism described in this paper is a continuation of the approach originated by Ramchandani [12,16] and subsequently extended by multiple and inhibitor arcs [17,18]. In (basic and extended) M-timed Petri nets, however, firing transitions cannot be "interrupted", and therefore preemptive disciplines are difficult to model and analyze.…”

Synchronization models for multimedia presentation with user participation

“…Execution of a Petri net process might have to be interrupted in order to carry out another higher priority activity. Preemption of the on-going execution of a Petri net process can be modeled using escape arcs to interrupt the execution of a process [3]. In this section, we examine Petri net based models for the purpose of describing the synchronization characteristics of the multimedia components.…”

“…In [3], Zuberek has proposed a Petri net model which can handle "interrupts", called the pre-emptive Petri net. The pre-emptive Petri net proposed by…”