Valuing Reliability: Characteristics of Travel Time Distribution on an Urban Road

Valuing Reliability: Characteristics of Travel Time Distribution on an Urban Road


M Fosgerau, Technical University of Denmark, DK; D Fukuda, Tokyo Institute of Technology, JP


Is the distribution of standardised travel times stable over the day? Is it a stable distribution? Can the distribution be aggregated from link to network level?


Travel time reliability is increasingly recognised as an important issue for transport planning and policy evaluation. Based on Small's scheduling model, Fosgerau & Karlstrom have shown that the value of reliability may be expressed as a constant times the standard deviation of travel time. This summary measure of reliability is available from traffic models, making feasible the application of the theoretical result.

In the theoretical model, the mean and standard deviation of travel time may depend on the time of day, such that it is possible to take into account that both vary with demand over the day.

An important assumption in the theoretical model is that the standardised travel time distribution is constant over the day. Then it is sufficient to account for the variation in the mean and standard deviation.

The point of this paper is to provide a detailed empirical examination of this assumption. The paper uses minute by minute observations of average travel times on four sections of a major radial road in Copenhagen, collected over a period of three months.

The distribution of travel times is evaluated using a range of nonparametric techniques. One finding is that the standardised distribution of travel times seems to be similar to a stable distribution. The family of stable distributions include the normal distribution as a special case and result from a general central limit theorem, where disturbances do not necessarily have finite variance. The nonparametric techniques employed allow for this.

The paper fits stable distributions to the standardised travel time distributions and examines whether they share a common shape parameter. It will be quite important if this emerges as a stylised fact, since it would allow for easy aggregation of results from links to the network level.


Association for European Transport