Variances of link travel time estimates: Implications for optimal routes

In this paper, we explore the consequences of using link travel time estimates with high variance to compute the minimum travel time route between an origin and destination pair. Because of platoon formation or for other reasons, vehicles on a link separated by small headways tend to have similar travel times. In other words, the covariance of link travel times of distinct vehicles which are close together may not be zero. It follows that the variance of the mean of travel times obtained from a sample of n vehicles on a same link over small time intervals is of the form a + b/n where a and b would usually be positive. This result has an important implication for the quality of road network travel time information given by Intelligent Transportation Systems (ITS) – that the variance of the estimate of mean travel time does not go to zero with increasing n. Thus the quality of information disseminated by ITS is not necessarily improved by increasing the market penetration of vehicles monitoring the system with the necessary equipment (termed probe vehicles). Estimates of a and b for a set of links are presented in the paper and consequences for probe-based ITS are explored by means of a simulation of such a system which is operational on an actual network.