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Optimum polar networks for an urban bus system with a many-to-many travel demand

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  • Vaughan, Rodney

Abstract

The spacing and headway configuration of a bus system comprising a series of ring and radial routes which minimizes travel time is found by the use of the calculus of variations. A many-to-many travel demand is described by a continuous function of the positions of a commuter's home and workplace. It is assumed that buses travel at a constant speed and are subject to a fleet size constraint. Under optimal conditions it is found that both spacing between routes and headway between buses should be inversely proportional to the cube root of the proportion of commuters joining and leaving the route. A simple numerical example is worked in which homes and workplaces are independently and uniformly distributed.

Suggested Citation

  • Vaughan, Rodney, 1986. "Optimum polar networks for an urban bus system with a many-to-many travel demand," Transportation Research Part B: Methodological, Elsevier, vol. 20(3), pages 215-224, June.
    • Handle: RePEc:eee:transb:v:20:y:1986:i:3:p:215-224
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    Cited by:

    1. Ahmed, Leena & Mumford, Christine & Kheiri, Ahmed, 2019. "Solving urban transit route design problem using selection hyper-heuristics," European Journal of Operational Research, Elsevier, vol. 274(2), pages 545-559.
    2. Gu, Weihua & Amini, Zahra & Cassidy, Michael J., 2016. "Exploring alternative service schemes for busy transit corridors," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 126-145.
    3. Badia, Hugo & Estrada, Miquel & Robusté, Francesc, 2014. "Competitive transit network design in cities with radial street patterns," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 161-181.
    4. Guo, Xin & Sun, Huijun & Wu, Jianjun & Jin, Jiangang & Zhou, Jin & Gao, Ziyou, 2017. "Multiperiod-based timetable optimization for metro transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 46-67.
    5. Chen, Haoyu & Gu, Weihua & Cassidy, Michael J. & Daganzo, Carlos F., 2015. "Optimal transit service atop ring-radial and grid street networks: A continuum approximation design method and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 755-774.
    6. Mei, Yu & Gu, Weihua & Cassidy, Michael & Fan, Wenbo, 2021. "Planning skip-stop transit service under heterogeneous demands," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 503-523.
    7. Hugo Badia, 2020. "Comparison of Bus Network Structures in Face of Urban Dispersion for a Ring-Radial City," Networks and Spatial Economics, Springer, vol. 20(1), pages 233-271, March.
    8. Moccia, Luigi & Laporte, Gilbert, 2016. "Improved models for technology choice in a transit corridor with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 245-270.
    9. Nocera, Silvio & Fabio, Alberto & Cavallaro, Federico, 2020. "The adoption of grid transit networks in non-metropolitan contexts," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 256-272.
    10. Marcos Medina-Tapia & Francesc Robusté, 2019. "Implementation of Connected and Autonomous Vehicles in Cities Could Have Neutral Effects on the Total Travel Time Costs: Modeling and Analysis for a Circular City," Sustainability, MDPI, vol. 11(2), pages 1-18, January.
    11. Amirgholy, Mahyar & Shahabi, Mehrdad & Gao, H. Oliver, 2017. "Optimal design of sustainable transit systems in congested urban networks: A macroscopic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 261-285.
    12. Badia, Hugo & Estrada, Miquel & Robusté, Francesc, 2016. "Bus network structure and mobility pattern: A monocentric analytical approach on a grid street layout," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 37-56.
    13. Moccia, Luigi & Giallombardo, Giovanni & Laporte, Gilbert, 2017. "Models for technology choice in a transit corridor with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 733-756.
    14. Cats, Oded & Vermeulen, Alex & Warnier, Martijn & van Lint, Hans, 2020. "Modelling growth principles of metropolitan public transport networks," Journal of Transport Geography, Elsevier, vol. 82(C).
    15. Masing, Berenike & Lindner, Niels & Borndörfer, Ralf, 2022. "The price of symmetric line plans in the Parametric City," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 419-443.
    16. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

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