Geodesic
Mean field analysis for inhomogeneous bike sharing systems
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012).

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In the paper, bike sharing systems with stations having a finite capacity are studied as stochastic networks. The inhomogeneity is modeled by clusters. We use a mean field limit to compute the limiting stationary distribution of the number of bikes at the stations. This method is an alternative to analytical methods. It can be used even if a closed form expression for the stationary distribution is out of reach as illustrated on a variant. Both models are compared. A practical conclusion is that avoiding empty or full stations does not improve overall performance. 
@article{DMTCS_2012_special_262_a27,
     author = {Fricker, Christine and Gast, Nicolas and Mohamed, Hanene},
     title = {Mean field analysis for inhomogeneous bike sharing systems},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)},
     year = {2012},
     doi = {10.46298/dmtcs.3006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3006/}
}
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%J Discrete mathematics & theoretical computer science
%D 2012
%V DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)
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Fricker, Christine; Gast, Nicolas; Mohamed, Hanene. Mean field analysis for inhomogeneous bike sharing systems. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) (2012). doi : 10.46298/dmtcs.3006. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3006/

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