EURO Working Group on Stochastic Modelling

FIRST MEETING: 19-21 APRIL 2006, AMSTERDAM

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Abstracts

Misja Nuyens, The tail of the sojourn time in GI/GI/1 queues

One of the most important quantities in a queueing model is the sojourn time, the time a job spends in the system. In this talk, I want to give an overview of and intuition behind recent results describing the tail of the sojourn-time distribution in GI/GI/1 queues. This is done for a number of different scheduling disciplines, and both for heavy and light-tailed service times.
In particular, for light-tailed service times, the tail of the sojourn-time distribution decays exponentially fast, and hence it may be characterised by its so-called decay rate. It turns out that there are two numbers a < b such that for all work-conserving scheduling disciplines, the decay rate of the sojourn time is either a or b. All scheduling disciplines? Well....