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=>M and prove that the RANDOM is the only non-preemptive, non-priority, probabilistic discipline that fulfils the M=>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.
On the characterization of probabilistic queueing disciplines.
BALSAMO, Maria Simonetta;MARIN, Andrea
2009-01-01
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=>M and prove that the RANDOM is the only non-preemptive, non-priority, probabilistic discipline that fulfils the M=>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.File | Dimensione | Formato | |
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