Scheduling in a queuing system with impatience and setup costs

Alain Jean-Marie 1, 2 Emmanuel Hyon 3, 4
1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
2 APR - Algorithmes et Performance des Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
4 RO - Recherche Opérationnelle
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We consider a single server queue in discrete time, in which customers must be served before some limit sojourn time of geometrical distribution. A customer who is not served before this limit leaves the system: it is impatient. The fact of serving customers and the fact of losing them due to impatience induce costs. The purpose is to decide when to serve the customers so as to minimize costs. We use a Markov Decision Process with infinite horizon and discounted cost. We establish the structural properties of the stochastic dynamic programming operator, and we deduce that the optimal policy is of threshold type. In addition, we are able to compute explicitly the optimal value of this threshold according to the parameters of problem.
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Alain Jean-Marie, Emmanuel Hyon. Scheduling in a queuing system with impatience and setup costs. 2010 MSOM Annual Conference and the Special Interest Group Conferences, Yale T. Herer, Jun 2010, Haifa, Israel. ⟨hal-00864151⟩

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