A Theory of Traffic-Measurement Errors for Loss Systems With Renewal Input

In the Bell System, there are a number of traffic measurements which can be made on any given trunk group. For a standard time interval (0, t] of one hour, the three most important measurements are: (i) A(t), the number of attempts (peg count); (ii) 0(t), the number of unsuccessful attempts (overflow count); and (Hi) Ld(t), an estimate of usage based on 36 discrete samples (TUR measurement). When all three measurements are available, several statistics can be formed to estimate traffic parameters of interest. For instance, the 967 968 THE BELL SYSTEM TECHNICAL JOURNAL, J U L Y - A U G U S T 1 9 7 3 ratio 0(t)/A{t) is an estimate of call congestion. Two other important parameters are the peakedness (variance-to-mean ratio) and the load of the input traffic. An estimate of the load is given by the function = Ld(t)/ 36 A{t) while an estimate of peakedness is a complicated function of A{t), 0(t), and Ld(t) which is usually obtained by iteration using the Equivalent Random method. 1 Since the trunk-engineering procedures are based on such estimates, it is important to know their statistical accuracy. For instance, it would be useful to know the error inherent in a prediction of the required size of a trunk group (to obtain a specified grade of service) based on the estimates of offered load and peakedness of the input traffic. Such a result could be used to determine the number of singlehour measurements necessary to ensure a desired accuracy in the prediction, to determine the optimum number of measurements from a cost-effectiveness point of view, or to evaluate the consequences for trunk provisioning of using a given number of measurements.