Summary
We consider a particular class of Stochastic Petri Nets whose stationary probabilities at arbitrary instants exhibit a product form. We study these nets at specific instants in the steady state that occur directly after the firing of a transition. We focus our attention on the instant after tokens are removed from the places specified by a transition’s input bag and just before tokens are entered into the places specified by the same transition’s output bag. We show that the stationary probabilities at “arrival instants” are related to corresponding stationary probabilities at arbitrary instants in net(s) with lower load. We then show how one of the “arrival” theorems can be applied to the derivation of a formula for the mean sojourn time of a token in a place at steady state.
This work has been supported in part by the Italian National Research Council “Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo (Grant N. 92.01563.PF69),” by the ESPRIT-BRA project No.7269 “QMIPS,” and by a grant from 3M.
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© 1995 ECSC-EC-EAEC, Brussels-Luxembourg
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Balbo, G., Bruell, S.C., Sereno, M. (1995). Arrival Theorems for Product-Form Stochastic Petri Nets. In: Baccelli, F., Jean-Marie, A., Mitrani, I. (eds) Quantitative Methods in Parallel Systems. Esprit Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79917-4_19
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DOI: https://doi.org/10.1007/978-3-642-79917-4_19
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