IDEAS home Printed from https://ideas.repec.org/a/spr/anresc/v53y2014i2p617-630.html
   My bibliography  Save this article

Optimal allocation of area in hierarchical road networks

Author

Listed:
  • Masashi Miyagawa

Abstract

This paper deals with the hierarchical road network design using a continuous model. The model is based on a grid road network where roads are classified into three types: access roads, minor arterial roads, and major arterial roads. Using a continuous approximation in which the distance is measured as the rectilinear distance, we obtain a simple approximation for the total travel time. We then find the optimal allocation of area taken up by roads at each level of the hierarchy so as to minimize the sum of the travel and construction costs. The result demonstrates how the total traffic volume, the traffic composition, and the unit construction cost affect the optimal road area. The optimal area of major arterial roads increases with the total traffic volume and the proportions of inward, outward, and through traffic and decreases with the unit construction cost. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Masashi Miyagawa, 2014. "Optimal allocation of area in hierarchical road networks," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(2), pages 617-630, September.
    • Handle: RePEc:spr:anresc:v:53:y:2014:i:2:p:617-630
    DOI: 10.1007/s00168-014-0635-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00168-014-0635-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00168-014-0635-z?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1994. "A Dual-Based Algorithm for Multi-Level Network Design," Management Science, INFORMS, vol. 40(5), pages 567-581, May.
    2. Sancho, N. G. F., 1995. "A suboptimal solution to a hierarchial network design problem using dynamic programming," European Journal of Operational Research, Elsevier, vol. 83(1), pages 237-244, May.
    3. Current, John R. & ReVelle, Charles S. & Cohon, Jared L., 1986. "The hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 27(1), pages 57-66, October.
    4. Bigotte, João F. & Krass, Dmitry & Antunes, António P. & Berman, Oded, 2010. "Integrated modeling of urban hierarchy and transportation network planning," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(7), pages 506-522, August.
    5. Robert F. Love & James G. Morris, 1979. "Mathematical Models of Road Travel Distances," Management Science, INFORMS, vol. 25(2), pages 130-139, February.
    6. Current, John & Pirkul, Hasan, 1991. "Theory and methodologyThe hierarchical network design problem with transshipment facilities," European Journal of Operational Research, Elsevier, vol. 51(3), pages 338-347, April.
    7. Hasan Pirkul & John Current & V. Nagarajan, 1991. "The Hierarchical Network Design Problem: A New Formulation and Solution Procedures," Transportation Science, INFORMS, vol. 25(3), pages 175-182, August.
    8. Daganzo, Carlos F., 2010. "Structure of competitive transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 434-446, May.
    9. Masashi Miyagawa, 2009. "Optimal hierarchical system of a grid road network," Annals of Operations Research, Springer, vol. 172(1), pages 349-361, November.
    10. Obreque, Carlos & Donoso, Macarena & Gutiérrez, Gabriel & Marianov, Vladimir, 2010. "A branch and cut algorithm for the hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 28-35, January.
    11. John R. Current, 1988. "The Design of a Hierarchical Transportation Network with Transshipment Facilities," Transportation Science, INFORMS, vol. 22(4), pages 270-277, November.
    12. C. E. M. Pearce, 1974. "Locating Concentric Ring Roads in a City," Transportation Science, INFORMS, vol. 8(2), pages 142-168, May.
    13. Aldaihani, Majid M. & Quadrifoglio, Luca & Dessouky, Maged M. & Hall, Randolph, 2004. "Network design for a grid hybrid transit service," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(7), pages 511-530, August.
    14. Tönu Puu, 1997. "Mathematical Location and Land Use Theory," Advances in Spatial Science, Springer, number 978-3-662-03439-2, december.
    15. Miyagawa, Masashi, 2011. "Hierarchical system of road networks with inward, outward, and through traffic," Journal of Transport Geography, Elsevier, vol. 19(4), pages 591-595.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Masashi Miyagawa, 2017. "Continuous location model of a rectangular barrier facility," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 95-110, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Miyagawa, Masashi, 2011. "Hierarchical system of road networks with inward, outward, and through traffic," Journal of Transport Geography, Elsevier, vol. 19(4), pages 591-595.
    2. Gollowitzer, Stefan & Gouveia, Luis & Ljubić, Ivana, 2013. "Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities," European Journal of Operational Research, Elsevier, vol. 225(2), pages 211-222.
    3. Obreque, Carlos & Donoso, Macarena & Gutiérrez, Gabriel & Marianov, Vladimir, 2010. "A branch and cut algorithm for the hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 28-35, January.
    4. Eduardo Álvarez-Miranda & Ivana Ljubić & S. Raghavan & Paolo Toth, 2015. "The Recoverable Robust Two-Level Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 1-19, February.
    5. Masashi Miyagawa, 2009. "Optimal hierarchical system of a grid road network," Annals of Operations Research, Springer, vol. 172(1), pages 349-361, November.
    6. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    7. M-G Yoon & J Current, 2008. "The hub location and network design problem with fixed and variable arc costs: formulation and dual-based solution heuristic," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(1), pages 80-89, January.
    8. Souza, Fernanda S.H. & Gendreau, Michel & Mateus, Geraldo R., 2014. "Branch-and-price algorithm for the Resilient Multi-level Hop-constrained Network Design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 84-93.
    9. Sancho, N. G. F., 1997. "The hierarchical network design problem with multiple primary paths," European Journal of Operational Research, Elsevier, vol. 96(2), pages 323-328, January.
    10. Bigotte, João F. & Krass, Dmitry & Antunes, António P. & Berman, Oded, 2010. "Integrated modeling of urban hierarchy and transportation network planning," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(7), pages 506-522, August.
    11. Luo, Sida & Nie, Yu (Marco), 2020. "Paired-line hybrid transit design considering spatial heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 320-339.
    12. Chen, Peng (Will) & Nie, Yu (Marco), 2018. "Optimal design of demand adaptive paired-line hybrid transit: Case of radial route structure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 110(C), pages 71-89.
    13. Lin, Cheng-Chang, 2010. "The integrated secondary route network design model in the hierarchical hub-and-spoke network for dual express services," International Journal of Production Economics, Elsevier, vol. 123(1), pages 20-30, January.
    14. 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.
    15. van de Leensel, R.L.J.M. & Flippo, O.E. & Koster, Arie M.C.A. & Kolen, A.W.J., 1996. "A dynamic programming algorithm for the local access network expansion problem," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1998. "Designing Hierarchical Survivable Networks," Operations Research, INFORMS, vol. 46(1), pages 116-136, February.
    17. Masashi Miyagawa, 2017. "Continuous location model of a rectangular barrier facility," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 95-110, April.
    18. Chen, Peng Will & Nie, Yu Marco, 2017. "Analysis of an idealized system of demand adaptive paired-line hybrid transit," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 38-54.
    19. Crainic, Teodor Gabriel & Gendron, Bernard & Akhavan Kazemzadeh, Mohammad Rahim, 2022. "A taxonomy of multilayer network design and a survey of transportation and telecommunication applications," European Journal of Operational Research, Elsevier, vol. 303(1), pages 1-13.
    20. Karatas, Mumtaz & Eriskin, Levent, 2023. "Linear and piecewise linear formulations for a hierarchical facility location and sizing problem," Omega, Elsevier, vol. 118(C).

    More about this item

    Keywords

    R41; R53; C61;
    All these keywords.

    JEL classification:

    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise
    • R53 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Regional Government Analysis - - - Public Facility Location Analysis; Public Investment and Capital Stock
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:spr:anresc:v:53:y:2014:i:2:p:617-630. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.