An Equivalent Random Method with hyper-exponential service

The Equivalent Random Method (ERM) has been widely used to predict blocking probabilities at overflow service stations. The method assumes that service times follow an exponential distribution. While this may be a reasonable assumption for voice traffic, it is not a good assumption for dial-up Internet traffic, where service times typically have a coefficient of variation (standard deviation/mean) greater than 1. In this paper, we give a modified ERM for two-term hyper-exponential service distributions. The method is based on an efficient algorithm to estimate the peakedness of the overflow process of an M/H2/S/S queue. Finally, we investigate the accuracy of the modified ERM using simulation and also compare systems with hyper-exponential service to systems with heavy-tailed service.