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Documents authored by Fricker, Christine

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DOI: 10.4230/LIPIcs.AofA.2022.13
Mean Field Analysis of an Incentive Algorithm for a Closed Stochastic Network

Authors: Bianca Marin Moreno, Christine Fricker, Hanene Mohamed, Amaury Philippe, and Martin Trépanier

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)

Abstract
The paper deals with a load-balancing algorithm for a closed stochastic network with two zones with different demands. The algorithm is motivated by an incentive algorithm for redistribution of cars in a large-scale car-sharing system. The service area is divided into two zones. When cars stay too long in the low-demand zone, users are encouraged to pick them up and return them in the high-demand zone. The zones are divided in cells called stations. The cars are the network customers. The mean-field limit solution of an ODE gives the large scale distribution of the station state in both clusters for this incentive policy in a discrete Markovian framework. An equilibrium point of this ODE is characterized via the invariant measure of a random walk in the quarter-plane. The proportion of empty and saturated stations measures how the system is balanced. Numerical experiments illustrate the impact of the incentive policy. Our study shows that the incentive policy helps when the high-demand zone observes a lack of cars but a saturation must be prevented especially when the high-demand zone is small.
Cite as

Bianca Marin Moreno, Christine Fricker, Hanene Mohamed, Amaury Philippe, and Martin Trépanier. Mean Field Analysis of an Incentive Algorithm for a Closed Stochastic Network. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{moreno_et_al:LIPIcs.AofA.2022.13,
  author =	{Moreno, Bianca Marin and Fricker, Christine and Mohamed, Hanene and Philippe, Amaury and Tr\'{e}panier, Martin},
  title =	{{Mean Field Analysis of an Incentive Algorithm for a Closed Stochastic Network}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.13},
  URN =		{urn:nbn:de:0030-drops-160998},
  doi =		{10.4230/LIPIcs.AofA.2022.13},
  annote =	{Keywords: Large scale analysis, mean-field, car-sharing, incentive algorithm, stochastic network, cluster, load balancing, closed Jackson networks, product-form distribution}
}
Document
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.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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