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    Entropy Maximisation and Open Queueing Networks with Priority and Blocking.

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    Publication date
    2003
    Author
    Kouvatsos, Demetres D.
    Awan, Irfan U.
    Keyword
    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
    Peer-Reviewed
    Yes
    
    Metadata
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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.
    URI
    http://hdl.handle.net/10454/3084
    Version
    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.
    Link to publisher’s version
    http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V13-46WPNY4-3-J4&_cdi=5663&_user=122861&_orig=search&_coverDate=02%2F28%2F2003&_sk=999489997&view=c&wchp=dGLbVtz-zSkWz&md5=f4a7235ccba96404cf0954cf89f9cd99&ie=/sdarticle.pdf
    Type
    Article
    Collections
    Engineering and Digital Technology Publications

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