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Optimal allocation of area in hierarchical road networks

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  • 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

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  • 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
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    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, Fall.
    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.
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    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

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