Fluid Limits for an ALOHA-type Model with Impatient Customers

Details Fluid Limits for an ALOHA-type Model with Impatient Customers Fluid Limits for an ALOHA-type Model with Impatient Customers

2011-05-11

arxiv.org/abs/1105.2133v1

Mathematics

Probability

26 pages

Scientific paper

In the present paper we consider an ALOHA-type random-multiple-access protocol where users are allowed to renege before transmission completion. We focus on the scenario which leads to overload in the absence of impatience. Under mild assumptions we show that the fl uid limit of the system workload coincides a.s. with the unique solution to a certain integral equation. Finally we demonstrate that the fl uid limits for distinct initial conditions converge to the same value as time tends to in?nity.

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