Stationary Distribution Analysis of a Queueing Model with Local Choice

Plinio Dester 1 Christine Fricker 2 Hanene Mohamed 3
2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : The paper deals with load balancing in a set of N queues on a line by a local choice policy. Each one-server queue has a Poissonian arrival of customers. When a customer arrives at queue i, he joins the least loaded queue between queues i and i + 1. When the load tends to zero, we obtain an asymptotic for the steady-state probability that a queue has m customers. It quantifies the difference between this local choice, no choice and the choice between two queues chosen at random.
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Plinio Dester, Christine Fricker, Hanene Mohamed. Stationary Distribution Analysis of a Queueing Model with Local Choice. 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)., Jun 2018, Uppsala, Sweden. ⟨10.4230/LIPIcs.AofA.2018.22⟩. ⟨hal-01666326v2⟩

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