Empirical Study on Route-Length Efficiency of Road Networks - Spring 2012 VIGRE Project Report

What does it mean to say that a physical network (such as a road network, electricity grid, or telephone network) is optimal? Different optimality criteria for different networks have been developed and studied. In the case of road networks connecting cities, an intuitive notion of an “optimal” network is one that provides the shortest routes between any two cities in the network while requiring a minimal total road network length. Some recent theoretical work of Aldous has focused on the properties of optimal random spatial networks (see [6] for an introduction). The mathematical models studied in this work place cities at random positions and the authors examine the tradeoffs between the route-lengths and the total network length as the number of cities in the network tends to ∞. While it is not possible to study the optimality of real-world road networks on an infinite number of cities, [6] introduces two statistics (see Section II for an explanation) that can summarize the inefficiency and total length (representative of a “cost”) of a road network. Using these two statistics to judge optimality of networks, do real road networks come close to being optimal? Previous undergraduate projects (see [4,5]) have attempted to answer this question by collecting road network data via the web and comparing the inefficiency and network length of these real networks to theoretically optimal random networks. These projects looked at networks on the 20 most populated cities within different states in the USA. One issue prevented the projects from analyzing larger networks: the data collection and calculation of the total network length was not fully automated. In this project, we attempt to resolve this issue by writing R programs that perform these two tasks. One program accesses the web and collects detailed information about the routes between any two pairs of cities in the network, while a second program uses the collected data to compute the total network length. Using these two programs, we then examine road networks on the 40 most populated cities within different states in the USA. We also look at the road network on the 200 most populated cities throughout the entire USA.