How heavy-tailed distributions affect simulation-generated time averages
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Queueing approximation of suprema of spectrally positive Lévy process
Queueing Systems: Theory and Applications
Convergence of the all-time supremum of a Lévy process in the heavy-traffic regime
Queueing Systems: Theory and Applications
Heavy-traffic asymptotics for the single-server queue with random order of service
Operations Research Letters
Gaussian queues in light and heavy traffic
Queueing Systems: Theory and Applications
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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).