Decomposition methods based on the hierarchical partitioning of
the state space of queueing network models offer powerful evaluation
tools for the performance analysis of computer systems and
communication networks. These methods being conventionally
implemented capture the exact solution of separable queueing network
models but their credibility differs when applied to general queueing
networks. This thesis provides a universal information theoretic
framework for the implementation of hierarchical decomposition
schemes, based on the principle of minimum relative entropy given
fully decomposable subset and aggregate utilization, mean queue
length and flow-balance constraints. This principle is used, in
conjuction with asymptotic connections to infinite capacity queues,
to derive new closed form approximations for the conditional and
marginal state probabilities of general queueing network models. The
minimum relative entropy solutions are implemented iteratively at
each decomposition level involving the generalized exponential (GE)
distributional model in approximating the general service and
asymptotic flow processes in the network. It is shown that the
minimum relative entropy joint state probability, subject to mean
queue length and flow-balance constraints, is identical to the exact
product-form solution obtained as if the network was separable. An
investigation into the effect of different couplings of the resource
units on the relative accuracy of the approximation is carried out,
based on an extensive experimentation. The credibility of the method
is demonstrated with some illustrative examples involving
first-come-first-served general queueing networks with single and
multiple servers and favourable comparisons against exact solutions
and other approximations are made.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/4212 |
| Date | January 1989 |
| Creators | Tomaras, Panagiotis J. |
| Contributors | Kouvatsos, Demetres D. |
| Publisher | University of Bradford, Postgraduate School of Studies in 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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