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General queueing network models for computer system performance analysis. A maximum entropy method of analysis and aggregation of general queueing network models with application to computer systems.

By Mohamed A. El-Affendi

Abstract

In this study the maximum entropy formalism [JAYN 57] is suggested\ud as an alternative theory for general queueing systems of computer\ud performance analysis. The motivation is to overcome some of the\ud problems arising in this field and to extend the scope of the results\ud derived in the context of Markovian queueing theory.\ud For the M/G/l model a unique maximum entropy solution., satisfying\ud locALl balance is derived independent of any assumptions about the service\ud time distribution. However, it is shown that this solution is identical\ud to the steady state solution of the underlying Marko-v process when the\ud service time distribution is of the generalised exponential (CE) type.\ud (The GE-type distribution is a mixture of an exponential term and a unit\ud impulse function at the origin). For the G/M/1 the maximum entropy\ud solution is identical in form to that of the underlying Markov process,\ud but a GE-type distribution still produces the maximum overall similar\ud distributions.\ud For the GIG11 model there are three main achievements:\ud first, the spectral methods are extended to give exaft formulae for\ud the average number of customers in the system for any G/G/l with rational\ud Laplace transform. Previously, these results are obtainable only through\ud simulation and approximation methods.\ud (ii) secondly, a maximum entropy model is developed and used to obtain\ud unique solutions for some types of the G/G/l. It is also discussed how\ud these solutions can be related to the corresponding stochastic processes.\ud (iii) the importance of the G/GE/l and the GE/GE/l for the analysis of\ud general networks is discussed and some flow processes for these systems\ud are characterised.\ud For general queueing networks it is shown that the maximum entropy\ud solution is a product of the maximum entropy solutions of the individual\ud nodes. Accordingly, existing computational algorithms are extended to\ud cover general networks with FCFS disciplines. Some implementations are\ud suggested and a flow algorithm is derived. Finally, these results are\ud iised to improve existing aggregation methods.\ud In addition, the study includes a number of examples, comparisons,\ud surveys, useful comments and conclusions

Topics: Queueing, Network models, Performance analysis, Maximum entropy formalism, Markovian queueing theory
Publisher: Postgraduate School of Studies in Computing
Year: 1983
OAI identifier: oai:bradscholars.brad.ac.uk:10454/3743
Provided by: Bradford Scholars

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