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    General queueing networks with priorities. Maximum entropy analysis of general queueing network models with priority preemptive resume or head-of-line and non-priority based service disciplines.

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    Publication date
    2010-02-08T15:46:35Z
    Author
    Tabet Aouel, Nasreddine
    Supervisor
    Kouvatsos, Demetres D.
    Keyword
    Scheduling discipline
    Priority class
    Maximum entropy
    Preemptive resume
    Head-of-line
    Generalised exponential
    Queueing network
    Rights
    Creative Commons License
    The University of Bradford theses are licenced under a Creative Commons Licence.
    Institution
    University of Bradford
    Department
    Department of Computing
    Awarded
    1989
    
    Metadata
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    Abstract
    Priority based scheduling disciplines are widely used by existing computer operating systems. However, the mathematical analysis and modelling of these systems present great difficulties since priority schedulling is not compatible with exact product form solutions of queueing network models (QNM's). It is therefore, necessary to employ credible approximate techniques for solving QNM's with priority classes. The principle of maximum entropy (ME) is a method of inference for estimating a probability distribution given prior information in the form of expected values. This principle is applied, based on marginal utilisation, mean queue length and idle state probability constraints, to characterise new product-form approximations for general open and closed QNM's with priority (preemptive-resume, non-preemtive head-of-line) and non-priority (first-come-first-served, processor-sharing, last-come-first-served with, or without preemtion) servers. The ME solutions are interpreted in terms of a decomposition of the original network into individual stable GIG11 queueing stations with assumed renewal arrival processes. These solutions are implemented by making use of the generalised exponential (GE) distributional model to approximate the interarrival-time and service-time distributions in the network. As a consequence the ME queue length distribution of the stable GE/GEzl priority queue, subject to mean value constraints obtained via classical queueing theory on bulk queues, is used as a 'building block' together with corresponding universal approximate flow formulae for the analysis of general QNM's with priorities. The credibility of the ME method is demonstrated with illustrative numerical examples and favourable comparisons against exact, simulation and other approximate methods are made.
    URI
    http://hdl.handle.net/10454/4214
    Type
    Thesis
    Qualification name
    PhD
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    Theses

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