Determination of optimal p values for Minkowski distance Figure 2 Determination of optimal p values for Minkowski distance. travel time presents features that differ from distance, i.e., larger mean and lower range: this combination is hard to achieve by the class of metrics considered, because p values closer to 1 (Manhattan) produce larger means, whereas p values closer to 2 (Euclidean) produce lower ranges. In light of these considerations, a relatively low p value, such as p = 1.31 most closely approximates this pattern, rendering a model that is less extreme than Manhattan, as shown by a lower standard deviation. Overall the metric p = 1.31 provides a model of travel that is intermediate between measured road distance and travel time measured under optimal conditions. This is supported by almost all the descriptive statistics; the greatest shortcoming of this metric is its poor approximation of the mean. This value produces the best of all the metrics examined.