On the Timing of the Peak Mean and Variance for the Number of Customers in an M(t)/M(t)/1 Queueing System

Abstract

This paper examines the time lag between the peak in the arrival rate and the peaks in the mean and variance for the number of customers in an M(t)/M(t)/1l system. We establish a necessary condition for the time at which the peak in the mean is achieved. In cases in which system utilization exceeds one during some period, we show that the peak in the mean occurs after the end of this period.