Stationary Distribution Analysis of a Queueing Model with Local Choice

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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Christine Fricker, Plinio Dester, Hanene Mohamed. Stationary Distribution Analysis of a Queueing Model with Local Choice. James Allen Fill; Mark Daniel Ward. 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)., Jun 2018, Uppsala, Sweden. Leibniz International Proceedings in Informatics , pp.22:1-22:18, 2018, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)., ⟨10.4230/LIPIcs.AofA.2018.22⟩. ⟨hal-01666326v1⟩

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