| Abstract: | 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 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. |
