Title: On completion times in a two-class priority queue with impatience

Authors: loane Muni Toke

Addresses: ERIM, University of New Caledonia, BP R4, 98851 Noumea Cedex, New Caledonia; MAS Laboratory, Ecole Centrale Paris, Grande Voie des Vignes, 92290 Chatenay-Malabry, France

Abstract: In this note, we consider a two-class priority queueing system with Poisson arrivals, general service time distribution and one server, in which customers that are not currently being served may leave the queue according to exponentially distributed patience times, i.e., a M₁, M₂/G/1 + M system using a generalised Kendall's notation. We expand the classic methodology to derive analytical formulas for the completion times in such a system, using preemptive repeat different and preemptive repeat identical disciplines. Known average completion times for priority queues without impatience are retrieved as limit cases.

Keywords: priority queues; impatience; reneging; completion times; preemptive disciplines.

DOI: 10.1504/IJMOR.2014.060855

International Journal of Mathematics in Operational Research, 2014 Vol.6 No.3, pp.377 - 392

Received: 09 Jan 2013
Accepted: 06 Mar 2013
Published online: 28 Jun 2014 *

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