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Estimating travel distances by the weighted l p norm
Author(s) -
Brimberg Jack,
Love Robert F.
Publication year - 1991
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199104)38:2<241::aid-nav3220380209>3.0.co;2-z
Subject(s) - range (aeronautics) , norm (philosophy) , computer science , mathematical optimization , travel time , mathematics , algorithm , transport engineering , political science , law , materials science , composite material , engineering
Empirical distance functions are used to estimate actual travel distances in a transportation network, to verify the accuracy of road mileage data, and to formulate continuous location models. In this article we consider the problem of fitting the weighted l p norm to a given network. Mathematical properties are derived for two fitting criteria found in the literature. These properties are used to develop an accurate and efficient methodology to solve for the best‐fitting parameter values. The directional bias of the l p norm is analyzed for its effect on the range of search for the optimal p value. Concepts and methodology are applied to a case study of the road system in Southern Ontario. In conclusion, a general framework for other types of distance functions is briefly discussed.