On queues with impatience: stability, and the optimality of Earliest Deadline First

In this paper, we consider a queue with impatient customers, under general assumptions. We introduce a convenient representation of the system by a stochastic recursive sequence keeping track of the remaining service and patience times of the customers. This description allows us (i) to provide a comprehensive stability condition in the general case, (ii) to give a rigorous proof of the optimality of the Earliest Deadline First (EDF) service discipline in several cases, and (iii) to show that the loss of the system follows inversely the stochastic ordering of the generic patience time distribution.