Heavy-traffic analysis of a non-preemptive multi-class queue with relative priorities

Ane Izagirre 1 Urtzi Ayesta 1 Ina Maria Verloop 2
1 LAAS-SARA - Équipe Services et Architectures pour Réseaux Avancés
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
2 IRT
IRIT - Institut de recherche en informatique de Toulouse, ENSEEIHT - Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications
Abstract : We study the steady-state queue-length vector in a multi-class single-server queue with relative priorities. Upon service completion, the probability that the next customer to be served is from class k is controlled by class- dependent weights. Once a customer has started service, it is served without interruption until completion. This is a generalization of the random-order-of-service discipline. We investigate the system in a heavy-traffic regime. We first establish a state-space collapse for the scaled queue length vector, that is, in the limit the scaled queue length vector is distributed as the product of an exponentially distributed random variable and a deterministic vector. As a direct consequence, we obtain that the scaled number of customers in the system reduces as classes with smaller mean service requirement obtain relatively larger weights. We then show that the scaled waiting time of a class-k customer is distributed as the product of two exponentially distributed random variables. This allows us to determine the value of the weights that minimize the m-th moment of the scaled waiting time for a customer of arbitrary class. We simulate a system with two different classes of customers in order to numerically verify some of the analytical results.
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Article dans une revue
Probability in the Engineering and Informational Sciences, Cambridge University Press (CUP), 2015, 29 (2), pp.153-180
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Dernière modification le : samedi 4 février 2017 - 01:06:07
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Ane Izagirre, Urtzi Ayesta, Ina Maria Verloop. Heavy-traffic analysis of a non-preemptive multi-class queue with relative priorities. Probability in the Engineering and Informational Sciences, Cambridge University Press (CUP), 2015, 29 (2), pp.153-180. <hal-00790846v2>

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