## Electronic Theses and Dissertations

1981

Dissertation

Ph.D.

#### Department

Mathematics and Statistics

Mathematics.

CC BY-NC-ND 4.0

#### Abstract

Most of the papers published, in the area of parameter estimation in queueing theory, deal with the estimation of continuous parameters. Namely, the problem of estimating the arrival rate, service rate, or mean waiting time for a single server or multiserver queueing system is considered. The theory of Billingsley is thus directly applicable. The first half of this dissertation discusses similar problems. In one of the chapters, the properties of these estimators are discussed. The concept of stopping time and Renyi's theorem for the limit of a random sum of random variables are used to investigate some of these properties. In another chapter, an estimation problem for the arrival rate for the system M/G/l is considered. This problem leads to a new concept of conditional sufficient statistic, which turns out to be useful in many situations. However, it may happen that the arrival and service rates of a multiserver queueing system are known and that estimators for the number of servers are required. In this case, the problem of estimating discrete parameters, which take on integral values only, should be investigated. The later part of the dissertation deals with the estimation of discrete parameters, namely the number of servers or machines subject to failure. In Chapter Four the multiserver system with infinite waiting room (M/M/m) is considered. Two methods are proposed for estimating the number of servers. One method is the maximum likelihood method. This is useful for estimating the number of servers when m is small but is not accurate enough for estimaing large values of m. The second method overcomes this difficulty and is useful for all cases. Simulation is used to investigate the accuracy of the two estimators and to compare them. In the last chapter, the maximum likelihood method and a direct method are used to estimate the number of servers for the finite capacity Markovian system M/M/m/n assuming that the arrival rate, service rate, and the waiting room capacity are known. The same analysis is applied to estimate the number of machines attended by a single repairman. Simulation is also used to compare these estimators and to investigate their accuracy. A general background and literaure review is given in the first chapter.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1981 .S252. Source: Dissertation Abstracts International, Volume: 42-08, Section: B, page: 3297. Thesis (Ph.D.)--University of Windsor (Canada), 1981.

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