B.S.T.J. Briefs: The Accuracy of the Equivalent Random Method With Renewal Inputs

The equivalent random method 1 (aso see Ref. 2) is widely used to approximate the blocking probabilities for non-Poisson traffic streams. Although much numerical experience and some analysis (e.g., Ref. 3) suggests that the method is usually reliable for superpositions of overflows, the reason for its accuracy (or errors) deserves further attention. The equivalent random method first determines the mean M and variance V of the number of the trunks that would be occupied if the traffic were offered to an infinite trunk group. Then an overflow process with the same M and V is offered to the finite trunk group and its blocking calculated. 1 This blocking is taken as the approximation for the blocking seen by the original traffic. In this Brief, we derive the range of the blocking probabilities which may be experienced by renewal streams characterized by the same M and V. Since this range may be rather wide, it follows that the success of equivalent random method cannot be explained solely by the constraints put on blockings by fixing M and V. Rather, one should factor in the special structure of the processes. Furthermore, it is seen that one cannot use an arbitrary renewal process to represent another process with the same mean and variance. * A version of this Brief was presented at the Seventh International Teletraffic Congress, Stockholm, June 1973. ' That is, the blocking is calculated for the specific renewal process which is the overflow process from a Poisson input. Conceivably, other types of renewal processes could be used.