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Stochastic Petri Nets with Low Variation Matrix Exponentially Distributed Firing Time

Volume 7, Number 5, September 2011 - Paper 4 - pp. 441-454

P. BUCHHOLZ1, A. HORVÁTH2and M. TELEK3

1 Informatik IV, TU Dortmund,D-44221 Dortmund, Germany
2 Dipartimento di Informatica, Università di Torino, I-10149 Torino, Italy
3 Department of Telecommunications, Technical University of Budapest, H-1521 Budapest, Hungary

(Received on November 21, 2010 and revised on May 18, 2011)


Abstract:

Matrix exponential (ME) distributions with low squared coefficient of variation (scv) are such that the density function becomes zero at some points in(0,). For such distributions there is no equivalent finite dimensional PH representation, which inhibits the application of existing methodologies for the numerical analysis of stochastic Petri nets (SPNs) with this kind of ME distributed firing time. To overcome the limitations of existing methodologies we apply the flow interpretation of ME distributions and study the transient and the stationary behaviour of stochastic Petri nets with ME distributed firing times via ordinary differential and linear equations, respectively. The main result of this study is a theory stating that all kinds of ME distributions can be used like phase type (PH) distributions in stochastic Petri nets and the numerical computation of transient or stationary measures is possible with methods similar to those used for Markov models.

 

References: 11

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