. PR ] 5 A ug 2 00 3 The maximum queue length for heavy tailed service times
نویسنده
چکیده
In this article we study the maximum queue length M in a busy cycle in the M/G/1 queue. Assume that the service times have a logconvex density. For such (heavy tailed) service time distributions the Foreground Background service discipline is optimal. This discipline gives service to those customer(s) that have received the least amount of service so far. It will be shown that under this discipline M has an exponentially decreasing tail. From the behaviour of M we obtain asymptotics for the maximum queue length M (t) over the interval (0, t) for t → ∞.
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