Entropy Maximisation and Open Queueing Networks with Priority and Blocking.
Kouvatsos, Demetres D. Awan, Irfan U.
Kouvatsos, Demetres D.
Awan, Irfan U.
Publication Date
2003
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Keywords
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
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Abstract
A 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.
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published version paper
Citation
Kouvatsos, D.D. and Awan, I.U. (2003). Entropy Maximisation and Open Queueing Networks with Priority and Blocking. Performance Evaluation. Vol. 51, No. 2-4, pp. 191-227.
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