Moment-Based Probabilistic Prediction of Bike Availability for Bike-Sharing Systems

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9826)


We study the problem of future bike availability prediction of a bike station through the moment analysis of a PCTMC model with time-dependent rates. Given a target station for prediction, the moments of the number of available bikes in the station at a future time can be derived by a set of moment equations with an initial set-up given by the snapshot of the current state of all stations in the system. A directed contribution graph with contribution propagation method is proposed to prune the PCTMC to make it only contain stations which have significant contribution to the journey flows to the target station. The underlying probability distribution of the available number of bikes is reconstructed through the maximum entropy approach based on the derived moments. The model is parametrized using historical data from Santander Cycles, the bike-sharing system in London. In the experiments, we show our model outperforms the classic time-inhomogeneous queueing model on several performance metrics for bike availability prediction.


Availability prediction PCTMC models Moment analysis Maximum entropy reconstruction 



This work is supported by the EU project QUANTICOL, 600708.


  1. 1.
    Fishman, E.: Bikeshare: a review of recent literature. Transp. Rev. 36(1), 1–22 (2015)CrossRefGoogle Scholar
  2. 2.
    Lin, J.R., Yang, T.H.: Strategic design of public bicycle sharing systems with service level constraints. Transp. Res. Part E: Logist. Transp. Rev. 47(2), 284–294 (2011)CrossRefGoogle Scholar
  3. 3.
    Pfrommer, J., Warrington, J., Schildbach, G., Morari, M.: Dynamic vehicle redistribution and online price incentives in shared mobility systems. IEEE Trans. Intell. Transp. Syst. 15(4), 1567–1578 (2014)CrossRefGoogle Scholar
  4. 4.
    Nair, R., Miller-Hooks, E.: Fleet management for vehicle sharing operations. Transp. Sci. 45(4), 524–540 (2011)CrossRefGoogle Scholar
  5. 5.
    Contardo, C., Morency, C., Rousseau, L.M.: Balancing a Dynamic Public Bike-Sharing System, vol. 4. CIRRELT, Montreal (2012)Google Scholar
  6. 6.
    Schuijbroek, J., Hampshire, R., van Hoeve, W.J.: Inventory rebalancing and vehicle routing in bike sharing systems. In: Technical report, Schuijbroek (2013)Google Scholar
  7. 7.
    Yoon, J.W., Pinelli, F., Calabrese, F.: Cityride: a predictive bike sharing journey advisor. In: 2012 IEEE 13th International Conference on Mobile Data Management (MDM), pp. 306–311. IEEE (2012)Google Scholar
  8. 8.
    Gast, N., Massonnet, G., Reijsbergen, D., Tribastone, M.: Probabilistic forecasts of bike-sharing systems for journey planning. In: The 24th ACM International Conference on Information and Knowledge Management (CIKM 2015) (2015)Google Scholar
  9. 9.
    Froehlich, J., Neumann, J., Oliver, N.: Sensing and predicting the pulse of the city through shared bicycling. IJCAI 9, 1420–1426 (2009)Google Scholar
  10. 10.
    Kaltenbrunner, A., Meza, R., Grivolla, J., Codina, J., Banchs, R.: Urban cycles and mobility patterns: exploring and predicting trends in a bicycle-based public transport system. Pervasive Mob. Comput. 6(4), 455–466 (2010)CrossRefGoogle Scholar
  11. 11.
    Guenther, M.C., Bradley, J.T.: Journey data based arrival forecasting for bicycle hire schemes. In: Dudin, A., De Turck, K. (eds.) ASMTA 2013. LNCS, vol. 7984, pp. 214–231. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Engblom, S.: Computing the moments of high dimensional solutions of the master equation. Appl. Math. Comput. 180(2), 498–515 (2006)MathSciNetMATHGoogle Scholar
  13. 13.
    Raviv, T., Kolka, O.: Optimal inventory management of a bike-sharing station. IIE Trans. 45(10), 1077–1093 (2013)CrossRefGoogle Scholar
  14. 14.
    Feng, C., Hillston, J., Galpin, V.: Automatic moment-closure approximation of spatially distributed collective adaptive systems. ACM Trans. Model. Comput. Simul. (TOMACS) 26(4), 26 (2016)CrossRefGoogle Scholar
  15. 15.
    Mead, L.R., Papanicolaou, N.: Maximum entropy in the problem of moments. J. Math. Phys. 25(8), 2404–2417 (1984)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Andreychenko, A., Mikeev, L., Wolf, V.: Model reconstruction for moment-based stochastic chemical kinetics. ACM Trans. Model. Comput. Simul. (TOMACS) 25(2), 12 (2015)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Tari, Á., Telek, M., Buchholz, P.: A unified approach to the moments based distribution estimation – unbounded support. In: Bravetti, M., Kloul, L., Zavattaro, G. (eds.) EPEW/WS-EM 2005. LNCS, vol. 3670, pp. 79–93. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Snyman, J.: Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms, vol. 97. Springer Science & Business Media, Heidelberg (2005)MATHGoogle Scholar
  19. 19.
    Reinecke, P., Krauss, T., Wolter, K.: Hyperstar: phase-type fitting made easy. In: 2012 Ninth International Conference on Quantitative Evaluation of Systems, pp. 201–202. IEEE (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Cheng Feng
    • 1
  • Jane Hillston
    • 1
  • Daniël Reijsbergen
    • 1
  1. 1.LFCS, School of InformaticsUniversity of EdinburghScotlandUK

Personalised recommendations