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Expected Impulse Rewards in Markov Regenerative Stochastic Petri Nets.

German, Reinhard; van Moorsel, Aad P. A.; Qureshi, Muhammad; Sanders, William H.

In: Lecture Notes in Computer Science, Vol. 1091; Proc. 17th International Conference in Application and Theory of Petri Nets (ICATPN'96), Osaka, Japan, pages 172-191. Springer-Verlag, June 1996.

Abstract: Reward structures provide a versatile tool for the definition of performance and dependability measures in stochastic Petri nets. In this paper we derive formulas for the computation of expected reward measures in Markov regenerative stochastic Petri nets, which allow for transitions with non-exponentially distributed firing times. The reward measures may be composed of rate rewards which are obtained in certain markings and of impulse rewards which are obtained when transitions fire. The main result of the paper is the derivation of formulas for the expected impulse reward of transitions with non-exponentially distributed firing times. The analysis is based on the method of supplementary variables. Numerical examples are given for an M/D/1/K queueing system with service breakdowns.

Keywords: Markov regenerative stochastic Petri nets; method of supplementary variables; rate and impulse reward measures.

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