Applications of non-Markovian stochastic Petri nets

ABSTRACT

Petri nets represent a powerful paradigm for modeling parallel and distributed systems. Parallelism and resource contention can easily be captured and time can be included for the analysis of system dynamic behavior. Most popular stochastic Petri nets assume that all firing times are exponentially distributed. This is found to be a severe limitation in many circumstances that require deterministic and generally distributed firing times. This has led to a considerable interest in studying non-Markovian models. In this paper we specifically focus on non-Markovian Petri nets. The analytical approach through the solution of the underlying Markov regenerative process is dealt with and numerical analysis techniques are discussed. Several examples are presented and solved to highlight the potentiality of the proposed approaches.

INDEX TERMS

Primary Classification:
  D. Software
  D.2 SOFTWARE ENGINEERING
      D.2.2 Design Tools and Techniques
          Subjects: Petri nets

Additional Classification:
  F. Theory of Computation
  F.1 COMPUTATION BY ABSTRACT DEVICES
      F.1.2 Modes of Computation
          Subjects: Parallelism and concurrency

  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Markov processes; Stochastic processes

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Design, Measurement, Performance, Theory

Keywords:
Markov regenerative processes, numerical analysis, preemption policies, stochastic Petri nets