The metric encodes the actual cost of traversing a road segment or taking a turn. It can often be described compactly, as a function that maps (in constant time) the properties of an edge/turn into a cost.
Bibliography
Delling, Daniel, Andrew V. Goldberg, Thomas Pajor, and Renato F. Werneck. 2011. “Customizable Route Planning.” In Experimental Algorithms, edited by Panos M. Pardalos and Steffen Rebennack, 6630:376–87. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_32.