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UBC Theses and Dissertations

General case of single channel queues Tan, Thiam Soon

Abstract

This thesis attempts to evaluate Low's hypothesis that for a single channel, single phase, steady state, infinite queue, the system length depends only on (1) the square of the coefficient of variation of the inter-arrival time distribution, C[formula omitted],(2) the square of the coefficient of variation of the service time distribution, C[formula omitted], and (3) the ratio of mean arrival rate to mean service rate [formula omitted]. In order to support the hypothesis, Low developed a set of curves by using simulation method. However, his simulation model is considered inadequate in representing actual queueing situation. A different simulation model has been employed instead and is used to test the classical queue models as well as the general arbitrary queues. The conclusion has been reached that in spite of the differences between the actual and expected results, the hypothesis is empirically true. Moreover, for any single channel queue with given values of C[formula omitted] and C[formula omitted], the system length L increases exponentially with the utilization factor, regardless of the patterns of arrival and service time distributions. The reader is expected to have a basic knowledge of standard queueing theory and some of its applications.

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