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Employing The Randomization Technique for Solving Stochastic Petri Net Models

  • Christoph Lindemann
Part of the Informatik-Fachberichte book series (INFORMATIK, volume 286)

Abstract

In this paper we propose to employ the randomization technique improved by a numerically stable calculation of Poisson probabilities for computing transient solutions of Markov chains underlying stochastic Petri net models. It is shown how to employ this numerical method for calculating the time-dependent quantities required by the solution process of DSPN models. The benefit of the described method is illustrated by stochastic Petri net models for two queueing systems. The evaluation of the transient behavior of the M/M/l/K queue is performed by means of a GSPN model. The steady-state solution of the E10/D/1/K queue is obtained using a DSPN model. The presented results show that the model solutions are calculated with significantly less computational effort and a better error control by the refined randomization method than by an adaptive matrix exponentiation method implemented in the version 1.4 of the software package GreatPN.

Keywords

Numerical Analysis of Markov Chains Stochastic Petri Nets Performance Evaluation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Christoph Lindemann
    • 1
  1. 1.Institut für Technische Informatik, Fachgebiet Prozeßdatenverarbeitung und Robotik (Real-Time Systems and Robotics)Technische Universität BerlinBerlin 10Deutschland

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