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Thesis (M.Sc.) -- University of Adelaide, Dept. of Applied Mathematics, 1982. / Typescript (photocopy).

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The purpose of this project is to derive the first two moments of two random variables, that is, the number served during and the length of a busy period. Two singleserver models are discussed in this project, namely, the Mb°∕Ea∕ 1 model, and the Mb∕Mb∕1 model. Moreover, in the development, standard methods such as the moment generating function technique are used, application of a computer system will also be introduced. / Thesis / Master of Science (MSc)

Parameter estimation is a long-lasting topic in queueing systems and has attracted considerable attention from both academia and industry. In this thesis, we design a parameter estimation framework for a tandem queueing system that collects end-to-end measurement data and utilizes the finite mixture model for the maximum likelihood (ML) estimation. The likelihood equations produced by ML are then solved by the iterative expectation-maximization (EM) algorithm, a powerful algorithm for parameter estimation in scenarios involving complicated distributions. We carry out a set of experiments with different parameter settings to test the performance of the proposed framework. Experimental results show that our method performs well for tandem queueing systems, in which the constituent nodes' service time follow distributions governed by exponential family. Under this framework, both the Newton-Raphson (NR) algorithm and the EM algorithm could be applied. The EM algorithm, however, is recommended due to its ease of implementation and lower computational overhead. / Graduate / hangli@uvic.ca

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Thesis (M.A.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The thesis deals with some of the mathematical techniques that are used in solving queueing theory problems. The organization of the paper is basically the same as that used by Goddard [3] in his treatment of queueing theory. The first method investigated is the analysis of queueing problems as Markovian processes. This analysis is due to D. G. Kendall [4,5] and is primarily for the case M/G/1. Formulas are found for E(n) and E(w). The limitations of this method in dealing with more general queues are mentioned. For the case M/M/s, the differential-difference equations are developed with examples of their use in machine breakdown problems and telephone trunk line congestion. The treatment is primarily for the case in which the system is in statistical equilibrium. The uses of Laplace transforms and probability generating functions are illustrated by Pollazoek's method of finding the moments of the waiting time distribution for the queue M/G/1. They are also shown in finding Pn(t) and Pn in an example of welders using a power supply. A method of expressing the distribution of the waiting time for the queue G/G/1, due to Lindley [7], is outlined at the conclusion of the paper. The result is an expression for the waiting time distribution in terms of the density function of the difference between the service time and inter-arrival time, rather than either density function separately. / 2031-01-01

In this thesis, we first study delay systems with different classes of impatient customers. We analyze the M/GI/1+M queue serving two priority classes under the static non-preemptive priority discipline. We also study the multi-server priority queue considering two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to obtain the steady-state system performance measures. In the second part, we consider the steady-state waiting time distributions of a two class M/GI/1 queue operating under a dynamic priority discipline. We find an accurate approximation for the steady-state waiting time distribution of the low-priority customers which allows us to study how they are penalized as the priority parameter increases. We also obtain bounds for the variance of the waiting time of high-priority customers.

In this thesis, we first study delay systems with different classes of impatient customers. We analyze the M/GI/1+M queue serving two priority classes under the static non-preemptive priority discipline. We also study the multi-server priority queue considering two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to obtain the steady-state system performance measures. In the second part, we consider the steady-state waiting time distributions of a two class M/GI/1 queue operating under a dynamic priority discipline. We find an accurate approximation for the steady-state waiting time distribution of the low-priority customers which allows us to study how they are penalized as the priority parameter increases. We also obtain bounds for the variance of the waiting time of high-priority customers.