General Considerations on the Use of the Weighted lp Norm as an Empirical Distance Measure

Abstract

In this paper, we present a general procedure for fitting the weighted lp norm in order to estimate travel distances in a distribution system. An important finding of our study is that the search for the best-fitting value of the parameter p can be restricted to the interval (0, 2], provided the reference axes of the distance function are oriented to match the directional bias inherent in the transportation network. The advantages of our methodology and particularly the importance of properly aligning the reference axes are demonstrated through a case study of the road system in Southern Ontario. Although attention is restricted to the weighted lp norm, the concepts presented are readily extended to other distance functions such as the block norms of Ward and Wendell.

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