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Entropy Maximisation and Open Queueing Networks with Priority and Blocking.

By Demetres D. Kouvatsos and Irfan U. Awan

Abstract

NoA review is carried out on the characterisation and algorithmic implementation of an extended product-form approximation, based on the principle of maximum entropy (ME), for a wide class of arbitrary finite capacity open queueing network models (QNMs) with service and space priorities. A single server finite capacity GE/GE/1/N queue with R (R>1) distinct priority classes, compound Poisson arrival processes (CPPs) with geometrically distributed batches and generalised exponential (GE) service times is analysed via entropy maximisation, subject to suitable GE-type queueing theoretic constraints, under preemptive resume (PR) and head-of-line (HOL) scheduling rules combined with complete buffer sharing (CBS) and partial buffer sharing (PBS) management schemes stipulating a sequence of buffer thresholds {N=(N1,¿,NR),0<Ni¿Ni¿1,i=2,¿,R}. The GE/GE/1/N queue is utilised, in conjunction with GE-type first two moment flow approximation formulae, as a cost-effective building block towards the establishment of a generic ME queue-by-queue decomposition algorithm for arbitrary open QNMs with space and service priorities under repetitive service blocking with random destination (RS-RD). Typical numerical results are included to illustrate the credibility of the ME algorithm against simulation for various network topologies and define experimentally pessimistic GE-type performance bounds. Remarks on the extensions of the ME algorithm to other types of blocking mechanisms, such as repetitive service blocking with fixed destination (RS-FD) and blocking-after-service (BAS), are included

Topics: Queueing network models (QNMs);, Maximum entropy (ME) principle, Preemptive resume (PR) rule, Head-of-line (HOL) rule, Complete buffer sharing (CBS) scheme, Partial buffer sharing (PBS) scheme, Compound Poisson process (CPP);, Generalised exponential (GE) distribution, Blocking-after-service (BAS) mechanism, Repetitive service blocking with random (RS-RD) or fixed (RS-RD) destination mechanism
Year: 2003
OAI identifier: oai:bradscholars.brad.ac.uk:10454/3084
Provided by: Bradford Scholars
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