CONFIDENCE BAND LIMITS ON AN ESTIMATE OF MEAN QUEUE LENGTH FROM A SERIES OF OBSERVATIONS FOR A SIMPLE QUEUING MODEL.

The queuing process considered is one generated by a system that the MM1 model describes well. The queue discipline is first-come, first-served. The statistic used to estimate the mean queue length is the equally weighted average of observed queue lengths. The observatiosn are considered to be made serially in time during operation of the queuing system. It is assumbed that the queuing process is stationary in the wide sense. A correlation factor, R, is defined as the ratio of the sample sizes of serially correlated and independent random observations yielding the same variance for estimate of mean queue length. Its limiting value, A, is obtained in close form for a class of sampling schemes. The central limit theorem for dependent variables is applied to obtain confidence band limits on the estimate of mean queue length. The results obtained find application in simulations, model validation, and process control. Author