IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v1y1967i4p318-361.html
   My bibliography  Save this article

Flow Dependent Traffic Assignment on a Circular City

Author

Listed:
  • Tenny N. Lam

    (Institute of Transportation and Traffic Engineering, University of California, Berkeley)

  • G. F. Newell

    (Institute of Transportation and Traffic Engineering, University of California, Berkeley)

Abstract

Consider a circular central business district of a city with n evenly spaced radial streets and m circular streets. We assume that during the evening rush hour driver origins are all inside the city and exits at the circumference with a joint distribution that depends only upon the relative angle between original and final radii, and the radial coordinate of the origin. Travel time on any directed link is assumed to be a function of the flow along that directed link and the radial coordinate of the link. For a flow of Q vehicles per hour leaving the city, our problem is to find an assignment of drivers to paths such that every driver follows a path of minimum travel time between his origin and exit. This extends some work of Smeed who considers a similar model with no flow dependence of the travel time and a uniform distribution of origins. It is first shown that this circularly symmetric system gives rise to a circularly symmetric optimal flow pattern. This flow pattern can be generated by assigning each driver to a path that uses at most one of the circular streets. Eventually the assignment is expressed explicitly as a function of 2( m - 1) unknown parameters that satisfy a system of equations and/or inequalities. The general solution of these equations were not found, but solutions were obtained for a number of special cases that showed the effect of congestion at the center and the effect of a belt expressway. Differential equations were also obtained for n (rightarrow) (infinity) and m (rightarrow) (infinity).

Suggested Citation

  • Tenny N. Lam & G. F. Newell, 1967. "Flow Dependent Traffic Assignment on a Circular City," Transportation Science, INFORMS, vol. 1(4), pages 318-361, November.
  • Handle: RePEc:inm:ortrsc:v:1:y:1967:i:4:p:318-361
    DOI: 10.1287/trsc.1.4.318
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1.4.318
    Download Restriction: no

    File URL: https://libkey.io/10.1287/trsc.1.4.318?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Zhi-Chun & Cheng, Li & de Palma, André, 2024. "Ring road investment, cordon tolling, and urban spatial structure," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    2. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Xiong, Tao & Zhang, Mengping & Choi, Keechoo, 2013. "Revisiting Jiang’s dynamic continuum model for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 96-119.
    3. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    4. Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    5. Wong, S. C., 1998. "Multi-commodity traffic assignment by continuum approximation of network flow with variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 567-581, November.
    6. Zhi-Chun Li & Li Cheng & André de Palma, 2023. "Ring road investment, cordon tolling, and urban spatial structure: Formulation and a case study," THEMA Working Papers 2023-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Jiang, Yanqun & Wong, S.C. & Ho, H.W. & Zhang, Peng & Liu, Ruxun & Sumalee, Agachai, 2011. "A dynamic traffic assignment model for a continuum transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 343-363, February.
    8. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:1:y:1967:i:4:p:318-361. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.