A theory of traffic-measurement errors for loss systems with renewal input

A theory of traffic-measurement errors for loss systems with renewal input is developed. The results provide an accurate approximation for the variance of any differentiable function of one or more of the following basic traffic measurements taken during a given time interval: (i) The total number of attempts (peg count) (ii) The number of unsuccessful attempts (overflow count) (iii) The usage based on discrete samples (TUR measurement) or on continuous scan. The approximation is given in terms of the individual variances and covariance functions of the three measurements. Asymptotic approximations for these moments are obtained using the concept of a generalized renewal process, and are shown to be sufficiently accurate for telephone traffic-engineering purposes. As an application of the theory, we examine the variances of the standard estimates of the load and peakedness (variance-to-mean ratio) of an input traffic stream for a time interval of one hour. Other possible applications to Bell System trunking problems are discussed.