Evaluating mean sojourn time estimates for the M/M/1 queue

Mean sojourn time is one of the most important performance measures for queueing systems. It is difficult to obtain the real sojourn time of a customer directly, so it is also difficult to estimate the mean sojourn time. In this paper, we propose a new and relatively simple estimate of the mean sojourn time in a single server queue, using the number of arrivals and the number of departures. This method can be used for evaluating the quality and the performance of call processing in communication switching systems, for example. We evaluate the accuracy of this estimate for an M/M/1 queue, using some results obtained by Jenkins. This estimate is compared with two other standard estimates of the mean sojourn time obtained from the sequence of actual arrival and departure times.