Modeling Travel Time Distributions on a Road Network

In transportation networks, it is more useful to think of costs on links as travel times as opposed to distances. Furthermore, while distances are usually constant, deterministic values, between nodes, travel times often vary substantially, as a result of incidents, road conditions, weather, traffic volume and drivers' preferences, among others. Recent research has developed a variety of algorithms for routing in these non-deterministic networks, but less has been done in identifying the proper functional forms to describe these travel times distributions. Moreover, most of the routing algorithms rely on the assumption that travel time distributions are independent random variables between links. In this paper, recently available data obtained from drivers using in-vehicle route guidance systems is used to empirically analyze the behavior of travel times on the US road network. Normal, lognormal, gamma and Weibull distributions are fitted to these travel times and it is concluded that the lognormal model provides the better fit. The data is then used to test the assumption of independence between arcs. A road segment comprised of eight links is selected and the correlation between travel times on the links is obtained. The correlations for consecutive links are compared, as well as for links separated by one or more links. The issue of convoluting travel time distributions when these times are not independent is analyzed. For this purpose, Reciprocal Gamma distributions are used, which have been proven to represent the infinite sum of correlated lognormal distributions. Arroyo, S. Kornhauser, A. L.