Frequency of probe reports and variance of travel time estimates

An important design issue relating to probe-based Advanced Traveler Information Systems (ATISs) and Advanced Traffic Management systems is the sample size of probes (or the number of link traversals by probe vehicles) per unit time used in order to obtain reliable network information in terms of link travel time estimates. The variance of the mean of travel times obtained from n probes for the same link over a fixed time period may be shown to be of the form a + b/n where a and b are link-specific parameters. Using probe travel time data from a set of signalized arterials, it is shown that a is positive for well-traveled signalized links. This implies that the variance does not go to zero with increasing n. Consequences of this fact for probe-based systems are explored. While the results presented are for a specific set of links, we argue that because of the nature of the underlying travel time process, the broad conclusions would hold for most well-traveled links with signal control.