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

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 ∼ 29min, while the time required when using the alternative arterial road path has two different characteristic times Ta ∼ 13 and 41min and follows a power law for times larger than 50min. 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 5 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New Journal of Physics 16 (2014) 013012 1367-2630/14/013012+11$33.00 © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft New J. Phys. 16 (2014) 013012 P Wang et al results, we assign a more realistic travel cost to long-range connections in twodimensional square lattices, observing dramatically different minimum average shortest path 〈l〉 but similar optimal navigation conditions.