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UBC Theses and Dissertations

Experimental evaluation of queueing theory Goyder, David

Abstract

This thesis examines methods for predicting queue length of single server queues in order to evaluate how the practitioner may achieve greatest accuracy. Because accuracy is dependent on the correct estimation of the rate parameters of the population distributions and the choice of the appropriate method of prediction, the effects of errors in both of these are examined. A computer simulation model written in GPSS/360 is used to create a real world from which data is drawn and where long run performance represents the correct solution. For four values of rho nine simulations are run, each with a unique combination of inter-arrival and service time distributions. In each of the 36 runs 10,000 arrivals are generated from which two samples of size 36 and 100 are taken and from which the generated queue statistics form the standard. A statistical analysis is used to detect samples taken from exponential distributions. The lack of a suitable test for small samples led to the development of a test based on the correlation coefficient of the sample times and pre-computed standard data. Estimates for queue length are found with classical queueing formulae and solution methods suggested by Marshall. These predictions are done without prior knowledge of rate parameters and queue type which are estimated from the samples. Then the estimated solutions are compared to the real world solution derived from the simulation. Estimation error for each method is measured and conclusions are drawn as to their accuracy in predicting queue length. It is found that accurate queue length estimation is possible using methods that can be applied without a great deal of prior mathematical knowledge. The classical formulae are accurate only when applied to queues with exponential inter-arrival times and are found to overestimate when applied to other queue types. The Increasing Failure Rate (IFR) bounds on queue length provide a satisfactory method of estimation for the general class of queues.

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