Empirical study of long-range connections in a road network offers new ingredient for navigation optimization models

Abstract

Navigation problem in lattices with long-range connections has been widely studied to understand the design principles for optimal transport networks; however, the travel cost of long-range connections was not considered in previous models. We define long-range connection in a road network as the shortest path between a pair of nodes through highways and empirically analyze the travel cost properties of long-range connections. Based on the maximum speed allowed in each road segment, we observe that the time needed to travel through a long-range connection has a characteristic time Th ~ 29 min, while the time required when using the alternative arterial road path has two different characteristic times Ta ~ 13 and 41 min and follows a power law for times larger than 50 min. Using daily commuting origin–destination matrix data, we additionally find that the use of long-range connections helps people to save about half of the travel time in their daily commute. Based on the empirical results, we assign a more realistic travel cost to long-range connections in two-dimensional square lattices, observing dramatically different minimum average shortest path 〈l〉 but similar optimal navigation conditions.