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.
This work was initiated while Reinhard German visited the University of Illinois at Urbana-Champaign. His visit was supported by Siemens Corporate, Research and Development.
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German, R., van Moorsel, A.P.A., Qureshi, M.A., Sanders, W.H. (1996). Expected impulse rewards in Markov regenerative stochastic Petri nets. In: Billington, J., Reisig, W. (eds) Application and Theory of Petri Nets 1996. ICATPN 1996. Lecture Notes in Computer Science, vol 1091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61363-3_10
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DOI: https://doi.org/10.1007/3-540-61363-3_10
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