A Heavy Traffic Approximation for Workload Processes with Heavy Tailed Service Requirements

A system with heavy tailed service requirements under heavy load having a single server has an equilibrium waiting time distribution which is approximated by the Mittag-Leffler distribution. This fact is understood by a direct analysis of the weak convergence of a sequence of negative drift random walks with heavy right tail and the associated all time maxima of these random walks. This approach complements the recent transform view of Boxma and Cohen (1997).