Mean field analysis for inhomogeneous bike sharing systems

Christine Fricker; Nicolas Gast; Hanene Mohamed

doi:10.46298/dmtcs.3006

Christine Fricker ; Nicolas Gast ; Hanene Mohamed - Mean field analysis for inhomogeneous bike sharing systems

dmtcs:3006 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12) - https://doi.org/10.46298/dmtcs.3006

Mean field analysis for inhomogeneous bike sharing systems

Authors: Christine Fricker ¹; Nicolas Gast ^2,³; Hanene Mohamed ⁴

1 Networks, Algorithms and Probabilities
2 Middleware efficiently scalable
3 Ecole Polytechnique Fédérale de Lausanne
4 Modélisation aléatoire de Paris X

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.

https://doi.org/10.46298/dmtcs.3006

Source: HAL:hal-01086055v1

Volume: DMTCS Proceedings vol. AQ, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12)

Section: Proceedings

Published on: January 1, 2012

Imported on: January 31, 2017

Keywords: [INFO.INFO-PF] Computer Science [cs]/Performance [cs.PF],[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC],[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]

Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo DOI 10.1016/0167-6377(92)90009-r 10.1016/0167-6377(92)90009-r Another approach to asymptotic expansions for large closed queueing networks

15 Documents citing this article

Source : OpenCitations

Cheng, Xi; Gao, Yang, 2018, The Optimal Monthly Strategy Pricing Of Free-Floating Bike Sharing Platform, Modern Economy, 09, 02, pp. 318-338, 10.4236/me.2018.92021.

Chow, Joseph; Sayarshad, Hamid R., 2014, Symbiotic Network Design Strategies In The Presence Of Coexisting Transportation Networks, Transportation Research Part B: Methodological, 62, pp. 13-34, 10.1016/j.trb.2014.01.008.

Feng, Cheng; Hillston, Jane; Reijsbergen, DaniĂŤl, 2017, Moment-based Availability Prediction For Bike-Sharing Systems, Performance Evaluation, 117, pp. 58-74, 10.1016/j.peva.2017.09.004.

Fricker, Christine; Gast, Nicolas, 2016, Incentives And Redistribution In Homogeneous Bike-Sharing Systems With Stations Of Finite Capacity, EURO Journal On Transportation And Logistics, 5, 3, pp. 261-291, 10.1007/s13676-014-0053-5.

Fricker, Christine; Servel, Nicolas, 2015, Two-choice Regulation In Heterogeneous Closed Networks, Queueing Systems, 82, 1-2, pp. 173-197, 10.1007/s11134-015-9465-7.

Fricker, Christine; Tibi, Danielle, 2017, Equivalence Of Ensembles For Large Vehicle-Sharing Models, The Annals Of Applied Probability, 27, 2, 10.1214/16-aap1219.

Gómez Márquez, Héctor R.; López Bracho, Rafael; Ramirez-Nafarrate, Adrian, 2021, A Simulation-Optimization Study Of The Inventory Of A Bike-Sharing System: The Case Of Mexico City Ecobici’s System, Case Studies On Transport Policy, 9, 3, pp. 1059-1072, 10.1016/j.cstp.2021.01.014.

Kadri, Ahmed Abdelmoumene; Kacem, Imed; Labadi, Karim, 2018, Lower And Upper Bounds For Scheduling Multiple Balancing Vehicles In Bicycle-Sharing Systems, Soft Computing, 23, 14, pp. 5945-5966, 10.1007/s00500-018-3258-y.

Li, Quan-Lin; Fan, Rui-Na, 2021, A Mean-Field Matrix-Analytic Method For Bike Sharing Systems Under Markovian Environment, Annals Of Operations Research, 309, 2, pp. 517-551, 10.1007/s10479-021-04140-x.

Li, Quan-Lin; Fan, Rui-Na; Qian, Zhi-Yong, 2017, A Nonlinear Solution To Closed Queueing Networks For Bike Sharing Systems With Markovian Arrival Processes And Under An Irreducible Path Graph, Queueing Theory And Network Applications, pp. 118-140, 10.1007/978-3-319-68520-5_8.

Massey, William A.; Ekwedike, Emmanuel; Hampshire, Robert C.; Pender, Jamol, 2022, A Transient Symmetry Analysis For The M/M/1/k Queue, Queueing Systems, 10.1007/s11134-022-09849-5.

Nadarajah, Saralees; Garibay Cancho, Vicente; Ortega, Edwin MoisĂŠs Marcos, 2013, The Geometric Exponential Poisson Distribution, Statistical Methods & Applications, 22, 3, pp. 355-380, 10.1007/s10260-013-0230-y.

Prieto-Castrillo, Francisco; Benito, Rosa M.; Borondo, Javier, 2022, Understanding Imbalance Mechanisms In Shared Mobility Systems, Complex Networks & Their Applications X, pp. 757-768, 10.1007/978-3-030-93413-2_62.

Tao, Shuang; Pender, Jamol, 2020, A Stochastic Analysis Of Bike-Sharing Systems, Probability In The Engineering And Informational Sciences, 35, 4, pp. 781-838, 10.1017/s0269964820000297.

Waserhole, Ariel; Jost, Vincent, 2016, Pricing In Vehicle Sharing Systems: Optimization In Queuing Networks With Product Forms, EURO Journal On Transportation And Logistics, 5, 3, pp. 293-320, 10.1007/s13676-014-0054-4.

Share and export

Consultation statistics

This page has been seen 305 times.

This article's PDF has been downloaded 450 times.