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.
This work was supported by the Federal Ministry for Research and Technology of Germany (BMFT) and by the German Research Society (DFG) under grants ITR9003 and Ho 1257/2-1, respectively.
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Lindemann, C. (1991). Employing The Randomization Technique for Solving Stochastic Petri Net Models. In: Lehmann, A., Lehmann, F. (eds) Messung, Modellierung und Bewertung von Rechensystemen. Informatik-Fachberichte, vol 286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76934-4_21
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DOI: https://doi.org/10.1007/978-3-642-76934-4_21
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