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Bus Frequency Optimization: When Waiting Time Matters in User Satisfaction

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 12113)

Abstract

Reorganizing bus frequency to cater for the actual travel demand can save the cost of the public transport system significantly. Many, if not all, existing studies formulate this as a bus frequency optimization problem which tries to minimize passengers’ average waiting time. However, many investigations have confirmed that the user satisfaction drops faster as the waiting time increases. Consequently, this paper studies the bus frequency optimization problem considering the user satisfaction. Specifically, for the first time to our best knowledge, we study how to schedule the buses such that the total number of passengers who could receive their bus services within the waiting time threshold is maximized. We prove that this problem is NP-hard, and present an index-based algorithm with \((1-1/e)\) approximation ratio. By exploiting the locality property of routes in a bus network, we propose a partition-based greedy method which achieves a \((1-\rho )(1-1/e)\) approximation ratio. Then we propose a progressive partition-based greedy method to further improve the efficiency while achieving a \((1\,-\,\rho )(1\,-\,1/e-\varepsilon )\) approximation ratio. Experiments on a real city-wide bus dataset in Singapore verify the efficiency, effectiveness, and scalability of our methods.

Keywords

Bus frequency scheduling optimization User waiting time minimization Approximate algorithm 

Notes

Acknowledgements

Zhiyong Peng is supported in part by the National Key Research and Development Program of China (Project Number: 2018YFB1003400), Key Project of the National Natural Science Foundation of China (Project Number: U1811263) and the Research Fund from Alibaba Group. Zhifeng Bao is supported in part by ARC DP200102611, DP180102050, NSFC 91646204, and a Google Faculty Award. Baihua Zheng is supported in part by Prime Minister’s Office, Singapore under its International Research Centres in Singapore Funding Initiative.

References

  1. 1.
    Antonides, G., Verhoef, P.C., Van Aalst, M.: Consumer perception and evaluation of waiting time: a field experiment. J. Consum. Psychol. 12(3), 193–202 (2002)CrossRefGoogle Scholar
  2. 2.
    Ceder, A., Golany, B., Tal, O.: Creating bus timetables with maximal synchronization. Transp. Res. Part A: Pol. Pract. 35(10), 913–928 (2001)Google Scholar
  3. 3.
    Constantin, I., Florian, M.: Optimizing frequencies in a transit network: a nonlinear bi-level programming approach. Int. Trans. Oper. Res. 2(2), 149–164 (1995)CrossRefGoogle Scholar
  4. 4.
    Fletterman, M., et al.: Designing multimodal public transport networks using metaheuristics. Ph.D. thesis, University of Pretoria (2009)Google Scholar
  5. 5.
    Gao, Z., Sun, H., Shan, L.L.: A continuous equilibrium network design model and algorithm for transit systems. Transp. Res. Part B: Methodol. 38(3), 235–250 (2004)CrossRefGoogle Scholar
  6. 6.
    Ibarra-Rojas, O.J., Delgado, F., Giesen, R., Muñoz, J.C.: Planning, operation, and control of bus transport systems: a literature review. Transp. Res. Part B: Methodol. 77, 38–75 (2015)CrossRefGoogle Scholar
  7. 7.
    Ibarra-Rojas, O.J., Rios-Solis, Y.A.: Synchronization of bus timetabling. Transp. Res. Part B: Methodol. 46(5), 599–614 (2012)CrossRefGoogle Scholar
  8. 8.
    Kong, M.C., Camacho, F.T., Feldman, S.R., Anderson, R.T., Balkrishnan, R.: Correlates of patient satisfaction with physician visit: differences between elderly and non-elderly survey respondents. Health Qual. Life Outcomes 5(1), 62 (2007).  https://doi.org/10.1186/1477-7525-5-62CrossRefGoogle Scholar
  9. 9.
    Lin, N., Ma, W., Chen, X.: Bus frequency optimisation considering user behaviour based on mobile bus applications. IET Intel. Transp. Syst. 13(4), 596–604 (2019)CrossRefGoogle Scholar
  10. 10.
    Martínez, H., Mauttone, A., Urquhart, M.E.: Frequency optimization in public transportation systems: formulation and metaheuristic approach. Eur. J. Oper. Res. 236(1), 27–36 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions - I. Math. Program. 14(1), 265–294 (1978).  https://doi.org/10.1007/BF01588971MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Parbo, J., Nielsen, O.A., Prato, C.G.: User perspectives in public transport timetable optimisation. Transp. Res. Part C: Emerg. Technol. 48, 269–284 (2014)CrossRefGoogle Scholar
  13. 13.
    Schéele, S.: A supply model for public transit services. Transp. Res. Part B: Methodol. 14(1–2), 133–146 (1980)CrossRefGoogle Scholar
  14. 14.
    Shafahi, Y., Khani, A.: A practical model for transfer optimization in a transit network: Model formulations and solutions. Transportation Research Part A: Policy and Practice 44(6), 377–389 (2010)Google Scholar
  15. 15.
    Tian, X., Zheng, B.: Using smart card data to model commuters’ responses upon unexpected train delays. In: Big Data, pp. 831–840. IEEE (2018)Google Scholar
  16. 16.
    Wang, S., Bao, Z., Culpepper, J.S., Sellis, T., Cong, G.: Reverse k nearest neighbor search over trajectories. IEEE Trans. Knowl. Data Eng. 30(4), 757–771 (2018)CrossRefGoogle Scholar
  17. 17.
    Wu, Y.: Combining local search into genetic algorithm for bus schedule coordination through small timetable modifications. Int. J. Intell. Transp. Syst. Res. 17(2), 102–113 (2019).  https://doi.org/10.1007/s13177-018-0165-7CrossRefGoogle Scholar
  18. 18.
    Zhang, P., Bao, Z., Li, Y., Li, G., Zhang, Y., Peng, Z.: Trajectory-driven influential billboard placement. In: SIGKDD, pp. 2748–2757. ACM (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Computer ScienceWuhan UniversityHubeiChina
  2. 2.RMIT UniversityMelbourneAustralia
  3. 3.Singapore Management UniversitySingaporeSingapore

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