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A Unifying Approach to Product-forms in Networks with Finite Capacity Constraints

Simonetta Balsamo, Peter G. Harrison, Andrea Marin

Conference or Workshop Paper
ACM Sigmetrics 2010
June, 2010
ACM SIGMETRICS Performance Evaluation Review
pp.25–36
ACM
DOI 10.1145/1811099.1811043
Abstract

In queueing networks with blocking, stations wishing to transmit customers to a full queue are blocked and need to take alternative action on completing a service. In general, product-forms, i.e. separable solutions for such a network's equilibrium state probabilities, do not exist but some product-forms have been obtained over the years in special cases, using a variety of techniques. We show that the Reversed Compound Agent Theorem (RCAT) can obtain these diverse results in a uniform way by its direct application, so unifying product-forms in networks with and without blocking. New product-forms are also constructed for a type of blocking we call `skipping', where a blocked station sends its output-customers to the queue after the one causing the blocking in that customer's path. Finally, we investigate a novel congestion management scheme for networks of finite-capacity queues in which a station with a full queue transmits signals that delete customers from upstream queues in order to reduce incoming traffic.

Keywords
Stochastic Modelling
AESOP
BibTEX file for the publication
 

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