We present a simple method of estimating mean delay (sojourn time in queueing terminology) of a call-processing processor in communication switching systems by observing actual behavior of the systems. We show Little's formula leads to the estimation of the mean delay from the number of arrivals and departures. Hence, counters for the number of arrival and departures are required for our method. This is easy to apply to real systems because measuring times of arrivals and departures, which are difficult for a call-processing processor, are not required. Furthermore, the accuracy of this method is evaluated for an M/G/1 queue.