Estimating travel distances by the weighted lp norm

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 the authors consider the problem of fitting the weighted lp 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 lp 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.