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Scheduling services in a queuing system with impatience and setup costs

Alain Jean-Marie 1, 2 Emmanuel Hyon 3 
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
3 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 sys- tem. The fact of serving customers, holding them in queue or losing them induce costs. The purpose is to decide when to serve the customers so as to minimize these costs. We use a Markov Decision Process with infinite horizon and discounted criterion. We establish the structural properties of the stochastic dynamic programming operator, and we deduce that the optimal policy is of threshold type, and we compute the threshold explicitly.
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Alain Jean-Marie, Emmanuel Hyon. Scheduling services in a queuing system with impatience and setup costs. 25th International Symposium on Computer and Information Sciences, Gökce Görbil and Shahareen Hilmy, Sep 2010, London, United Kingdom. pp.45-50, ⟨10.1007/978-90-481-9794-1_9⟩. ⟨hal-00863216⟩



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