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DOI: 10.4230/LIPIcs.AofA.2018.22
Stationary Distribution Analysis of a Queueing Model with Local Choice

Authors: Plinio S. Dester, Christine Fricker, and Hanene Mohamed

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
The paper deals with load balancing between one-server queues on a circle by a local choice policy. Each one-server queue has a Poissonian arrival of customers. When a customer arrives at a queue, he joins the least loaded queue between this queue and the next one, ties solved at random. Service times have exponential distribution. The system is stable if the arrival-to-service rate ratio called load is less than one. When the load tends to zero, we derive the first terms of the expansion in this parameter for the stationary probabilities that a queue has 0 to 3 customers. We investigate the error, comparing these expansion results to numerical values obtained by simulations. Then we provide the asymptotics, as the load tends to zero, for the stationary probabilities of the queue length, for a fixed number of queues. It quantifies the difference between policies with this local choice, no choice and the choice between two queues chosen at random.
Cite as

Plinio S. Dester, Christine Fricker, and Hanene Mohamed. Stationary Distribution Analysis of a Queueing Model with Local Choice. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dester_et_al:LIPIcs.AofA.2018.22,
  author =	{Dester, Plinio S. and Fricker, Christine and Mohamed, Hanene},
  title =	{{Stationary Distribution Analysis of a Queueing Model with Local Choice}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.22},
  URN =		{urn:nbn:de:0030-drops-89152},
  doi =		{10.4230/LIPIcs.AofA.2018.22},
  annote =	{Keywords: queueing model, local choice, stationary analysis, balance equations, power series expansion}
}
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