Abstract
Probabilistic queueing disciplines are used for modeling several system behaviors. In particular, under a set of assumptions, it has been proved that if the choice of the customer to serve after a job completion is uniform among the queue population, then the model has a BCMP-like product-form solution. In this paper we address the problem of characterizing the probabilistic queueing disciplines that can be embedded in a BCMP queueing network maintaining the product-form property. We base our result on Muntz’s property \(M\Rightarrow M\) and prove that the RANDOM is the only non-preemptive, non-priority, probabilistic discipline that fulfils the \(M\Rightarrow M\) property with a class independent exponential server. Then we observe that the FCFS and RANDOM discipline share the same product-form conditions and a set of relevant performance indices when embedded in a BCMP queueing network. We use a simulator to explore the similarities of these disciplines in non-product-form contexts, i.e., under various non-Poisson arrival processes.
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Balsamo, S., Marin, A. (2009). On the Characterization of Product-Form Multiclass Queueing Models with Probabilistic Disciplines. In: Al-Begain, K., Fiems, D., Horváth, G. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2009. Lecture Notes in Computer Science, vol 5513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02205-0_15
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DOI: https://doi.org/10.1007/978-3-642-02205-0_15
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