Abstract
In this paper, we prove the asymptotic equivalence between closed, open and mixed multiclass BCMP queueing networks. Under the assumption that the service demands of a given station, for sufficiently large population sizes, are greater than the ones of all the other stations, we prove that as the total number of customers semi-proportionally grows to infinity the underlying Markov chain of a closed network converges to the underlying Markov chain of a suitable open or mixed network. The equivalence theorem lets us extend the state of the art exact asymptotic theory of queueing networks considering a general population growth and including the case in which stations have load-dependent rates of service, and provides a natural technique for the approximate on-line solution of closed networks with large populations. We also show the validity of Littleās law in the limit.
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Anselmi, J., Cremonesi, P. (2008). Exact Asymptotic Analysis of Closed BCMP Networks with a Common Bottleneck. In: Al-Begain, K., Heindl, A., Telek, M. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2008. Lecture Notes in Computer Science, vol 5055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68982-9_15
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DOI: https://doi.org/10.1007/978-3-540-68982-9_15
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