The Accuracy of Call-Congestion Measurements for Loss Systems with Renewal Input

In a communication network, the proportion of unsuccessful attempts on a trunk group during a specified interval of time is called the measured call-congestion, and is used to estimate the single-hour blocking probability for many of the trunk groups in the Bell System network. In order to determine how many measurements should be taken to properly assess system performance, one needs to know the statistical accuracy of the estimated blocking probability. In the context of telephone traffic-engineering, the measured callcongestion is an unbiased estimate of the blocking probability, and hence we use its variance as an indicator of the precision of the measurements. For loss systems with exponentially-distributed service times, the variance has previously been studied under the assumption that calls originate according to a Poisson process.1 However, attempts on a trunk group are well approximated by a Poisson process only for those groups which do not serve overflow traffic from subtending groups, so 2197