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. / Algerian government
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/4214 |
| Date | January 1989 |
| Creators | Tabet Aouel, Nasreddine |
| Contributors | Kouvatsos, Demetres D. |
| Publisher | University of Bradford, Department of Computing |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Thesis, doctoral, PhD |
| Rights | <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>. |
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