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On the relations between BCMP Queueing Networks and Product Form Solution Stochastic Petri Nets.

Balbo, G.; Bruell, S. C.; Sereno, M.

In: 10th International Workshop on Petri Nets and Performance Models (PNPM 2003), Urbana, Illinois, USA, pages 103-113. IEEE Press, September 2003.

Abstract: In this paper we show that multi-class BCMP queueing networks can be represented by means of Product Form Solution Stochastic Petri Nets (PF-SPNs). Since the first time PF-SPNs were proposed, one of their main drawbacks concerned the fact that there was no clear relation between PF-SPNs and PF-QNs, in particular the well-known multi-class BCMP-QNs. It is important to note that the existence of the product form solution is not a property of the formalism, but of the underlying Markovian process. Hence, the fact that PF-SPNs (and also PF-GSPNs) cannot directly represent BCMP-QNs is one of the weaknesses of the SPN product-form results. The results presented in this paper overcome this weakness. In particular, we show that starting from a detailed GSPN representation of each of the BCMP station types, it is possible to derive equivalent compact PF-SPN representations for each station type.

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