A BCMP extension to multiserver stations with concurrent classes of customers
SIGMETRICS '86/PERFORMANCE '86 Proceedings of the 1986 ACM SIGMETRICS joint international conference on Computer performance modelling, measurement and evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Product Form and Local Balance in Queueing Networks
Journal of the ACM (JACM)
Modeling a new technique for accessing shared buses
Proceedings of the Computer Network Performance Symposium
A multi-class probabilistic priority scheduling discipline for differentiated services networks
Computer Communications
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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.