Fluid Limits for an ALOHA-type Model with Impatient Customers

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 fluid limit of the system workload coincides a.s. with the unique solution to a certain integral equation. Finally we demonstrate that the fluid limits for distinct initial conditions converge to the same value as time tends to infinity.