Change point estimation of service rate in an M/M/1/\(m\) queue (Q1753780)

Summary: 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.