Transactions on Transport Sciences 2025, 16(1):4-13 | DOI: 10.5507/tots.2024.019

A comparative study of gravity models to assess the evolution of urban bicycle mobility

Bertrand Jouvea, Paul Rochetb, Mohamadou Salifouab
a. LISST, University of Toulouse Jean Jaurès, CNRS, University of Toulouse
b. Federation ENAC ISAE-SUPAERO ONERA, University of Toulouse, France

Gravity models are extensively used tools to understand mobility, providing an approximation of the volume of a flow as a function of distance and population density. In particular, specific gravity models have been proposed in the literature for studying the bike sharing systems (BSS) in urban areas. In this paper, we show how robustness to scale change in data pre-processing can be used as a criterion to select the best model for BSS usage, in addition to the usual criteria of quality of fit. In a second stage, the study of the recent evolution of BSS uses in large cities via a dynamical application of gravity models over rolling time windows. Exploiting the good interpretability of gravity models, this methodology produces a time series for each parameter, that can be analysed to study the evolution of local policies and users' habits.

Keywords: gravity model; urban mobility; robustness; time series; bike sharing system

Received: July 12, 2024; Revised: July 12, 2024; Accepted: September 24, 2024; Prepublished online: December 2, 2024; Published: April 26, 2025  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Jouve, B., Rochet, P., & Salifou, M. (2025). A comparative study of gravity models to assess the evolution of urban bicycle mobility. Transactions on Transport Sciences16(1), 4-13. doi: 10.5507/tots.2024.019
Download citation

References

  1. Barbieri, D. M., Lou, B., Passavanti, M., Hui, C., Hoff, I., Lessa, D. A., Sikka, G., Chang, K., Gupta, A., Fang, K., et al. (2021). Impact of covid-19 pandemic on mobility in ten countries and associated perceived risk for all transport modes. PloS one, 16(2): e0245886. Go to original source...
  2. Bert, J., Schellong, D., Hagenmaier, M., Hornstein, D., Wegschei-der, A. K., Palme, T., et al. (2020). How covid-19 will shape urban mobility. https://www.bcg.com/publications/2020/how-covid-19-will-shape-urban-mobility.
  3. Bouchard, R. J. and Pyers, C. E. (1965). Use of gravity model for describing urban travel. Highway Research Record, 88(196):5.
  4. Buehler, R. and Pucher, J. (2023). Covid-19 and cycling: a review of the literature on changes in cycling levels and government policies from 2019 to 2022. Transport Reviews, 44:299-344. Go to original source...
  5. Chai, X., Guo, X., Xiao, J., and Jiang, J. (2020). Analysis of spatial-temporal behavior pattern of the share bike usage during covid-19 pandemic in Beijing. arXiv preprint arXiv:2004.12340. Go to original source...
  6. Chan, H. F., Skali, A., Savage, D. A., Stadelmann, D., and Torgler, B. (2020). Risk attitudes and human mobility during the covid-19 pandemic. Scientific reports, 10(1):1-13. Go to original source...
  7. Chen, Y. (2015). The distance-decay function of geographical gravity model: Power law or exponential law? Chaos, Solitons & Fractals, 77:174-189. Go to original source...
  8. DeMaio, P. (2009). Bike-sharing: History, impacts, models of provision, and future. Journal of public transportation, 12(4):3. Go to original source...
  9. Dobson, A. J. and Barnett, A. G. (2018). An introduction to generalized linear models. Chapman and Hall/CRC.
  10. Eren, E. and Uz, V. E. (2020). A review on bike-sharing: The factors affecting bike-sharing demand. Sustainable Cities and Society, 54:101882. Go to original source...
  11. Fishman, E. (2019). Bike Share. Routledge.
  12. Flowerdew, R. and Aitkin, M. (1982). A method of fitting the gravity model based on the poisson distribution. Journal of Regional Science, 22(2):191-202. Go to original source...
  13. Furno, A., Jouve, B., Revelli, B., and Rochet, P. (2023). Impact of the COVID-19 pandemic on bike-sharing uses in two French towns: the cases of Lyon and Toulouse. working paper or preprint.
  14. Goh, S., Lee, K., Park, J. S., and Choi, M. Y. (2012). Modification of the gravity model and application to the metropolitan seoul subway system. Phys. Rev. E, 86:026102. Go to original source...
  15. Heinen, E., Van Wee, B., and Maat, K. (2010). Commuting by bicycle: an overview of the literature. Transport reviews, 30(1):59-96. Go to original source...
  16. Hu, S., Xiong, C., Liu, Z., and Zhang, L. (2021). Examining spatiotemporal changing patterns of bike-sharing usage during covid-19 pandemic. Journal of Transport Geography, 91:102997. Go to original source...
  17. Kou, Z. and Cai, H. (2021). Comparing the performance of different types of bike share systems. Transportation research part D: transport and environment, 94:102823. Go to original source...
  18. Kwon, O.-H., Hong, I., Jung, W.-S., and Jo, H.-H. (2023). Multiple gravity laws for human mobility within cities.
  19. Li, A., Zhao, P., He, H., and Axhausen, K. W. (2020). Understanding the variations of micro-mobility behavior before and during covid-19 pandemic period. Arbeitsberichte Verkehrs-und Raumplanung, 1547.
  20. Li, H., Zhang, Y., Zhu, M., and Ren, G. (2021a). Impacts of covid-19 on the usage of public bicycle share in london. Transportation Research Part A: Policy and Practice, 150:140-155. Go to original source...
  21. Li, R., Gao, S., Luo, A., Yao, Q., Chen, B., Shang, F., Jiang, R., and Stanley, H. E. (2021b). Gravity model in dockless bike-sharing systems within cities. Physical Review E, 103(1):012312. Go to original source...
  22. M´edard De Chardon, C. (2021). Bicycle Sharing, volume 6, pages 19-30. Elsevier, 1 edition. Go to original source...
  23. Pase, F., Chiariotti, F., Zanella, A., and Zorzi, M. (2020). Bike sharing and urban mobility in a post-pandemic world. Ieee Access, 8:187291-187306. Go to original source...
  24. Pucher, J., Dill, J., and Handy, S. (2010). Infrastructure, programs, and policies to increase bicycling: an international review. Preventive medicine, 50:106-125. Go to original source...
  25. Shaheen, S., Guzman, S., and Zhang, H. (2012). Bike sharing across the globe. City cycling, 183.
  26. Shang, W.-L., Chen, J., Bi, H., Sui, Y., Chen, Y., and Yu, H. (2021). Impacts of covid-19 pandemic on user behaviors and environmental benefits of bike sharing: A big-data analysis. Applied Energy, 285:116429. Go to original source...
  27. Simini, F., Barlacchi, G., Luca, M., and Pappalardo, L. (2021). A deep gravity model for mobility flows generation. Nature Communications, 12. Go to original source...
  28. Song, J., Zhang, L., Qin, Z., and Ramli, M. A. (2021). Where are public bikes? the decline of dockless bike-sharing supply in Singapore and its resulting impact on ridership activities. Transportation Research Part A: Policy and Practice, 146:72-90. Go to original source...
  29. Song, J., Zhang, L., Qin, Z., and Ramli, M. A. (2022). Spatiotemporal evolving patterns of bike-share mobility networks and their associations with land-use conditions before and after the covid-19 outbreak. Physica A: Statistical Mechanics and its Applications, 592:126819. Go to original source...
  30. Sung, H. (2022). Causal impacts of the coronavirus-19 pandemic on daily ridership of public bicycle sharing in seoul. SSRN Electronic Journal, 89:104344. Go to original source...
  31. Teixeira, J., Silva, C., and Moura e Sa´, F. (2023). Potential of bike sharing during disruptive public health crises: A review of covid-19 impacts. Transportation Research Record Journal of the Transportation Research Board, pages 1-13. Go to original source...
  32. Teixeira, J. F. and Lopes, M. (2020). The link between bike sharing and subway use during the covid-19 pandemic: The case-study of new York's city bike. Transportation research interdisciplinary perspectives, 6:100166. Go to original source...
  33. Teixeira, J. F., Silva, C., and e S´a, F. M. (2021a). The motivations for using bike sharing during the covid-19 pandemic: Insights from Lisbon. Transportation research part F: traffic psychology and behaviour, 82:378-399. Go to original source...
  34. Teixeira, J. F., Silva, C., and Moura e Sa´, F. (2021b). Empirical evidence on the impacts of bike sharing: a literature review. Transport reviews, 41(3):329-351. Go to original source...
  35. Thompson, C., Saxberg, K., Lega, J., Tong, D., and Brown, H. (2019). A cumulative gravity model for inter-urban spatial interaction at different scales. Journal of Transport Geography, 79:102461. Go to original source...
  36. Wang, H. and Noland, R. B. (2021). Bikeshare and subway ridership changes during the covid-19 pandemic in New York city. Transport policy, 106:262-270. Go to original source...
  37. Zhang, S., Chen, L., and Li, Y. (2021). Shared bicycle distribution connected to subway line considering citizens' morning peak social characteristics for urban low-carbon development. Sustainability, 13(16):9263. Go to original source...
  38. Zhao, P., Hu, H., Zeng, L., Chen, J., and Ye, X. (2023). Revisiting the gravity laws of inter-city mobility in megacity regions. Science China Earth Sciences, 66(2):271-281. Go to original source...
  39. Zipf, G. K. (1946). The p1 p2 d hypothesis: On the intercity movement of persons. American Sociological Review, 11:677. Go to original source...

This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.