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Approximate Formulas for Average Distances Associated with Zones

Author

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  • Rodney Vaughan

    (Department of Civil Engineering, University of Toronto, Toronto, Canada)

Abstract

This paper develops formulas for estimating average distances associated with zones. The average distance between two points, one located at random in a zone and another located at random in another, is first investigated. The average distance from a fixed point to a point located at random in a zone, and the average distance between two points located at random in the same zone, are also examined. The accuracy of the approximations for these average distances are found by examining some simple cases.

Suggested Citation

  • Rodney Vaughan, 1984. "Approximate Formulas for Average Distances Associated with Zones," Transportation Science, INFORMS, vol. 18(3), pages 231-244, August.
    • Handle: RePEc:inm:ortrsc:v:18:y:1984:i:3:p:231-244
    DOI: 10.1287/trsc.18.3.231
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    Cited by:

    1. Carrizosa, E. & Munoz-Marquez, M. & Puerto, J., 1998. "The Weber problem with regional demand," European Journal of Operational Research, Elsevier, vol. 104(2), pages 358-365, January.
    2. Uster, Halit & Love, Robert F., 2003. "Formulation of confidence intervals for estimated actual distances," European Journal of Operational Research, Elsevier, vol. 151(3), pages 586-601, December.
    3. Jing Yao & Alan T. Murray, 2014. "Serving regional demand in facility location," Papers in Regional Science, Wiley Blackwell, vol. 93(3), pages 643-662, August.
    4. Luca Quadrifoglio & Randolph W. Hall & Maged M. Dessouky, 2006. "Performance and Design of Mobility Allowance Shuttle Transit Services: Bounds on the Maximum Longitudinal Velocity," Transportation Science, INFORMS, vol. 40(3), pages 351-363, August.
    5. Heather S. Lutz & Trevor S. Hale & Faizul Huq, 2020. "Technical note: the expected length of an orderly path," Annals of Operations Research, Springer, vol. 289(2), pages 463-472, June.
    6. Ellegood, William A. & Campbell, James F. & North, Jeremy, 2015. "Continuous approximation models for mixed load school bus routing," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 182-198.
    7. Di Huang & Weiping Tong & Lumeng Wang & Xun Yang, 2019. "An Analytical Model for the Many-to-One Demand Responsive Transit Systems," Sustainability, MDPI, vol. 12(1), pages 1-17, December.
    8. Tirachini, Alejandro, 2015. "Probability distribution of walking trips and effects of restricting free pedestrian movement on walking distance," Transport Policy, Elsevier, vol. 37(C), pages 101-110.
    9. 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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