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Modelling the Tendency of Buses to Form Pairs

Author

Listed:
  • R. A. Chapman

    (University of Newcastle upon Tyne, England)

  • J. F. Michel

    (University of Newcastle upon Tyne, England)

Abstract

The paper describes a simple mathematical model of the behaviour of buses, on a relatively frequent service, after one has arrived at a stop at a time different from that scheduled. The model is similar to that used in some earlier papers on the pairing of buses, but derives a different objective function. Results are presented in terms of parameters relating to the scheduled headway ( h ) and the size of the initial deviation from it ( hd ), the usual time spent by a bus at a stop, and the ratio ( k ) of the passenger arrival rate to the boarding rate. A graphical method was employed to find P , the number of the stop at which the first two buses form a pair. For the typical values of parameters used the relationship P = 1/6 dk was deduced which, although no generality is claimed, can be used to set operational limits so that the bunching of buses does not occur. Limitations of the model are discussed.

Suggested Citation

  • R. A. Chapman & J. F. Michel, 1978. "Modelling the Tendency of Buses to Form Pairs," Transportation Science, INFORMS, vol. 12(2), pages 165-175, May.
    • Handle: RePEc:inm:ortrsc:v:12:y:1978:i:2:p:165-175
    DOI: 10.1287/trsc.12.2.165
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    Cited by:

    1. Vee-Liem Saw & Lock Yue Chew, 2020. "No-boarding buses: Synchronisation for efficiency," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-34, March.
    2. Mark D. Hickman, 2001. "An Analytic Stochastic Model for the Transit Vehicle Holding Problem," Transportation Science, INFORMS, vol. 35(3), pages 215-237, August.
    3. Viktoriya Degeler & Léonie Heydenrijk-Ottens & Ding Luo & Niels Oort & Hans Lint, 2021. "Unsupervised approach towards analysing the public transport bunching swings formation phenomenon," Public Transport, Springer, vol. 13(3), pages 533-555, October.
    4. Schmöcker, Jan-Dirk & Sun, Wenzhe & Fonzone, Achille & Liu, Ronghui, 2016. "Bus bunching along a corridor served by two lines," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 300-317.

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