Title: Change point estimation of service rate in an M/M/1/m queue

Authors: Sarat Kumar Acharya; César Emilio Villarreal-Rodríguez

Addresses: Departament of Statistics, Sambalpur University, Jyoto Vihar-768019, Sambalpur, Orissa, India ' Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, A. P. 66-F, Ciudad Universitaria 66455 San Nicolás de los Garza, N.L., Mexico

Abstract: The paper is concerned with the maximum likelihood estimation of the change point of arrival rate for an M/M/1/m queueing system. It is assumed that the change takes place after a fixed unknown number of completed services. We also calculate the maximum likelihood estimators of the traffic intensities after and before the change point and we prove that these estimators are weakly consistent. This work is applicable in planning economic models, social events and service to customers, where the service rate changes due to fatigue of the server or there is a shift change policy after a fixed amount of services done.

Keywords: change point; maximum likelihood estimation; M/M/1/m queues; service rate; arrival rate; traffic intensity; loglikelihood function.

DOI: 10.1504/IJMOR.2013.050515

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.1, pp.110 - 120

Published online: 31 Mar 2014 *

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