Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T09:17:36.627Z Has data issue: false hasContentIssue false
  • English
  • Français

A STOCHASTIC ANALYSIS OF BIKE-SHARING SYSTEMS

Published online by Cambridge University Press:  27 July 2020

Shuang Tao  and
Jamol Pender Open the ORCID record for Jamol Pender [Opens in a new window]
Shuang Tao
Affiliation:
School of Operations Research and Information Engineering, Cornell University, 293 Rhodes Hall, Ithaca, NY14853, USA E-mail: [email protected]; [email protected]
Jamol Pender
Affiliation:
School of Operations Research and Information Engineering, Cornell University, 293 Rhodes Hall, Ithaca, NY14853, USA E-mail: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

As more people move back into densely populated cities, bike sharing is emerging as an important mode of urban mobility. In a typical bike-sharing system (BSS), riders arrive at a station and take a bike if it is available. After retrieving a bike, they ride it for a while, then return it to a station near their final destinations. Since space is limited in cities, each station has a finite capacity of docks, which cannot hold more bikes than its capacity. In this paper, we study BSSs with stations having a finite capacity. By an appropriate scaling of our stochastic model, we prove a mean-field limit and a central limit theorem for an empirical process of the number of stations with k bikes. The mean-field limit and the central limit theorem provide insight on the mean, variance, and sample path dynamics of large-scale BSSs. We also leverage our results to estimate confidence intervals for various performance measures such as the proportion of empty stations, the proportion of full stations, and the number of bikes in circulation. These performance measures have the potential to inform the operations and design of future BSSs.

Keywords

applied probabilityoperations researchprobabilistic networksqueueing theorystochastic modeling
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 4 , October 2021 , pp. 781 - 838
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ames, W.F. & Pachpatte, B.G. (1997). Inequalities for differential and integral equations, vol. 197. Elsevier.Google Scholar
Benchimol, M., Benchimol, P., Chappert, B., De La Taille, A., Laroche, F., Meunier, F., & Robinet, L. (2011). Balancing the stations of a self service “bike hire” system. RAIRO - Operations Research 45(1): 37–61.CrossRefGoogle Scholar
Chemla, D., Meunier, F., Pradeau, T., Calvo, R.W., & Yahiaoui, H. (2013). Self-service bike sharing systems: Simulation, repositioning pricing.Google Scholar
Contardo, C., Morency, C., & Rousseau, L.-M. (2012). Balancing a dynamic public bike-sharing system, vol. 4. Montreal, Canada: Cirrelt.Google Scholar
Darling, R.W.R., Norris, J.R., et al. (2008). Differential equation approximations for Markov chains. Probability Surveys 5(1): 37–79.CrossRefGoogle Scholar
DeMaio, P. (2009). Bike-sharing: History, impacts, models of provision, and future. Journal of Public Transportation 12(4): 41–56.CrossRefGoogle Scholar
Engblom, S. & Pender, J. (2014). Approximations for the moments of nonstationary and state dependent birth-death queues. Submitted for publication to Queueing Systems.Google Scholar
Ethier, S.N. & Kurtz, T.G. (2009). Markov processes: Characterization and convergence, vol. 282. John Wiley & Sons.Google Scholar
Freund, D., Henderson, S.G., & Shmoys, D.B. (2017). Minimizing multimodular functions and allocating capacity in bike-sharing systems. In International Conference on Integer Programming and Combinatorial Optimization. Cham: Springer, pp. 186–198.CrossRefGoogle Scholar
Fricker, C., Gast, N., & Mohamed, H. (2012). Mean field analysis for inhomogeneous bike sharing systems. In Discrete Mathematics & Theoretical Computer Science.CrossRefGoogle Scholar
George, D.K. & Xia, C.H. (2011). Fleet-sizing and service availability for a vehicle rental system via closed queueing networks. European Journal of Operational Research 211(1): 198–207.CrossRefGoogle Scholar
Ghosh, S., Varakantham, P., Adulyasak, Y., & Jaillet, P. (2017). Dynamic repositioning to reduce lost demand in bike sharing systems. Journal of Artificial Intelligence Research 58: 387–430.CrossRefGoogle Scholar
Hampshire, R.C. & Marla, L. (2012). An analysis of bike sharing usage: Explaining trip generation and attraction from observed demand. In 91st Annual Meeting of the Transportation Research Board, Washington, DC, pp. 12–2099.Google Scholar
Jian, N., Freund, D., Wiberg, H.M., & Henderson, S.G. (2016). Simulation optimization for a large-scale bike-sharing system. In Proceedings of the 2016 Winter Simulation Conference. IEEE Press, pp. 602–613.CrossRefGoogle Scholar
Ko, Y.M. & Pender, J. (2017). Strong approximations for time varying infinite-server queues with non-renewal arrival and service processes. Stochastic Models 34(20): 186–206.CrossRefGoogle Scholar
Ko, Y.M. & Pender, J. (2017). Diffusion limits for the (map t/ph t/∞)n queueing network. Operations Research Letters 45(3): 248–253.CrossRefGoogle Scholar
Laporte, G., Meunier, F., & Wolfler Calvo, R. (2015). Shared mobility systems. 4OR 13(4): 341–360.CrossRefGoogle Scholar
Massey, W.A. & Pender, J. (2013). Gaussian skewness approximation for dynamic rate multi-server queues with abandonment. Queueing Systems 75(2–4): 243–277.CrossRefGoogle Scholar
Nair, R. & Miller-Hooks, E. (2011). Fleet management for vehicle sharing operations. Transportation Science 45(4): 524–540.CrossRefGoogle Scholar
Nair, R. & Miller-Hooks, E. (2016). Equilibrium design of bicycle sharing systems: The case of Washington DC. EURO Journal on Transportation and Logistics 5(3): 321–344.CrossRefGoogle Scholar
Nair, R., Miller-Hooks, E., Hampshire, R.C., & Bušić, A. (2013). Large-scale vehicle sharing systems: Analysis of vélib. International Journal of Sustainable Transportation 7(1): 85–106.CrossRefGoogle Scholar
Nirenberg, S., Daw, A., & Pender, J. (2018). The impact of queue length rounding and delayed app information on Disney world queues. In Proceedings of the 2018 Winter Simulation Conference. IEEE Press, pp. 3849–3860.CrossRefGoogle Scholar
Novitzky, S., Pender, J., Rand, R.H., & Wesson, E. (2019). Nonlinear dynamics in queueing theory: Determining the size of oscillations in queues with delay. SIAM Journal on Applied Dynamical Systems 18(1): 279–311.CrossRefGoogle Scholar
O'Mahony, E.D. (2015). Smarter tools for (CITI) bike sharing. PhD thesis, Cornell University.Google Scholar
O'Mahony, E. & Shmoys, D.B. (2015). Data analysis and optimization for (CITI) bike sharing. In Twenty-ninth AAAI Conference on Artificial Intelligence, pp. 687–694.Google Scholar
Pender, J. (2014). Gram charlier expansion for time varying multiserver queues with abandonment. SIAM Journal on Applied Mathematics 74(4): 1238–1265.CrossRefGoogle Scholar
Pender, J. (2015). Nonstationary loss queues via cumulant moment approximations. Probability in the Engineering and Informational Sciences 29(01): 27–49.CrossRefGoogle Scholar
Pender, J. (2016). Sampling the functional Kolmogorov forward equations for nonstationary queueing networks. INFORMS Journal on Computing 29(1): 1–17.CrossRefGoogle Scholar
Pender, J. & Ko, Y.M. (2017). Approximations for the queue length distributions of time-varying many-server queues. INFORMS Journal on Computing 29(4): 668–704 Fall.CrossRefGoogle Scholar
Pender, J., Rand, R.H., & Wesson, E. (2017). Queues with choice via delay differential equations. International Journal of Bifurcation and Chaos 27(4): 1730016.CrossRefGoogle Scholar
Pender, J., Rand, R.H., & Wesson, E. (2018). An analysis of queues with delayed information and time-varying arrival rates. Nonlinear Dynamics 91(4): 2411–2427.CrossRefGoogle Scholar
Pfrommer, J., Warrington, J., Schildbach, G., & Morari, M. (2014). Dynamic vehicle redistribution and online price incentives in shared mobility systems. IEEE Transactions on Intelligent Transportation Systems 15(4): 1567–1578.CrossRefGoogle Scholar
Raviv, T., Tzur, M., & Forma, I.A. (2013). Static repositioning in a bike-sharing system: Models and solution approaches. EURO Journal on Transportation and Logistics 2(3): 187–229.CrossRefGoogle Scholar
Schuijbroek, J., Hampshire, R.C., & Van Hoeve, W.-J. (2017). Inventory rebalancing and vehicle routing in bike sharing systems. European Journal of Operational Research 257(3): 992–1004.CrossRefGoogle Scholar
Shaheen, S., Guzman, S., & Zhang, H. (2010). Bikesharing in Europe, the Americas, and Asia: Past, present, and future. Transportation Research Record: Journal of the Transportation Research Board 2143: 159–167.CrossRefGoogle Scholar