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.

On the relations between BCMP queueing networks and product form solution stochastic Petri nets

BALBO, Gianfranco;SERENO, Matteo
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.
10-th International Workshop on Petri Nets and Performance Models (PNPM '03)
Urbana-Champaign, Illinois, USA
2-5 Settembre 2003
Proceedings of the 10-th International Workshop on Petri Nets and Performance Models (PNPM '03)
IEEE Computer Society
103
112
9780769519760
Queueing networks; Multiclass queueing networks; Product form; Stochastic Petri nets; Generalized stochastic Petri nets; Equivalence between formalisms
G. BALBO; S. C. BRUELL; M. SERENO
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/20000
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