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

Authors:
Pascal Moyal
Affiliations:
Laboratoire de Mathématiques Appliquées de Compiègne, Département Génie Informatique, Centre de Recherches de Royallieu, Université de Technologie de Compiègne, ...
Venue:
Queueing Systems: Theory and Applications
Year:
2013

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Abstract

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 abandonment probability of the system follows inversely the stochastic ordering of the generic patience time distribution.