The weighted sum of order p, the lbp-norm, is a generalization of the well-known lp-norm used in predicting distances in a transportation network. The properties of the directional bias function and the unit balls for the lbp-norm are of theoretical and practical interest. We investigate these properties and compare them with the properties of the lp-norm's directional bias function and the unit balls. We find that the lbp-norm is better at capturing the nonlinearity in a transportation network than the weighted lp-norm. It is also shown that, in contrast to the weighted lp-norm, where the optimal parameter p value is confined to the interval (1,2), for the lbp-norm the parameter p can have an optimal value greater than 2.
