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Representative Queueing Network Models of Computer Systems in Terms of Time Delay Probability Distributions

Peter G. Harrison

PhD Thesis
1979
Abstract

In order to obtain a good representation of Computer Systems for performance evaluation, conventional analytic models requirement improvement from two points of view.

First there has been a tendency to concentrate on known analytic results and their extensions, obtaining representation of a specific system by a choice of model parameter values. It is argued here that a truly representative model is best achieved by studying the properties of the real system first, and the determining the appropriate model type and structure from them.

Secondly, the most crucial performance measures for both management and users, are the time delays that relate to the rate at which individual tasks are being processed. Conventional models predict only overall resource utilsation and queue lengths.

Much of this thesis is concerned with distributions of time delays in queueing networks. An approximate method for their determination is presented which is applicable to a very general class of networks and gives an efficient implementation. Exact results are then derived for cycle time distribution, first in cyclic and then in more general tree-like networks. Validation of both methods is by comparison with simulated results, sufficiently detailed data from real systems being unavailable.

Subject to adequate precision, approximate methods are, in general, more feasible as tools because of their greater generalty and superior efficiency. We view and apply the exact method as a standard by which to assess the accuracy of various approximations whilst also recognising its potential as a practical tool for simple cases.

Finally, the thesis addresses the almost universal assumption of "equilibrium", that is the assumption that the state space probability distribution is time independent. The time periods over which this assumption can or should not be made are quantified via time-dependent analysis that is applicable to a very general class of networks and relevant in many transient situations.

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