Letter to the Editor—Some Confidence Intervals for Queues

Abstract

It is possible to calculate for many queuing situations, in the steady state, the state probabilities, the expected number of units in the system or in the queue, the proportion of idle time per channel, and other quantities of interest. These quantities are calculated as a function of the number of channels, the queuing discipline, and the parameters of the distributions of arrival and service times. If the parameters of the distributions are known exactly, then the results are exact. In many cases of interest, however, the parameters are not known exactly and estimates must be used. In such situations one obtains estimates rather than exact values for the state probabilities, expected number of units in the queue, and the other quantities. In order to make use of these estimates it is important to know the precision of the estimates as measured by their respective confidence intervals. In this paper confidence intervals are calculated for several cases of interest.

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