Modelling Reliability As Expected Lateness: a Schedule-based Approach for User Benefit Analysis

Modelling Reliability As Expected Lateness: a Schedule-based Approach for User Benefit Analysis


J P Franklin, Royal Institute of Technology, SE


We develop a model for unstandardized mean lateness, based on scheduling theory, as a means of estimating the value of travel time reliability, and we compare the results to prior approaches that use the standard deviation of travel time.


Recent literature has suggested that the reliability of travel time, as distinct from travel time in itself, is valued by travellers when making such decisions as mode, route, and departure time choice. Much of the literature that attempts to account for the value of reliability has used the standard deviation of travel time as a proxy for reliability. Another stream of literature uses a scheduling approach to describe the value of reliability in terms of lateness-avoidance. This latter approach is attractive because it provides a behavioural explanation for the value of reliability.

Recently, theoretical work has shown that these two streams of literature can be reconciled by defining a quantity known as the ?mean lateness?, which is the average time late, given late, computed from the standardized distribution of travel time. Empirical evidence has shown that the mean lateness varies considerably by time of day and location. By controlling for this factor, in principle, one can estimate the value of reliability by computing the product of three terms: a cost parameter for lateness, beta, a model prediction for the standard deviation of travel time, sigma, and a model prediction for the mean lateness, H. The preference parameter can be straightforwardly obtained through stated preference surveys, while reasonably good models for standard deviation have been developed. However, no standard models have been developed for predicting mean lateness, and the only known attempts have not produced any models reasonable predictive power. Hence, even when attempting to control for mean lateness, the results are subject to considerable error due to unexplained variations in mean lateness. Moreover, studies that do not at all control for the mean lateness risk introducing even greater error by implicitly holding it constant across very different contexts.

The above experiences have pointed to an alternate approach to modelling reliability where we take a purely scheduling-based approach, rather than adapting the standard-deviation-based approach for a scheduling context. In essence, rather than attempt to separately model the standard deviation, sigma, and the (standardized) mean lateness, H, here we attempt to model the combined product of sigma and H. We define this quantity as the unstandardized mean lateness, K, which can easily be interpreted as the average time late, given late, computed from the real (i.e. unstandardized) travel time distribution. This can be seen by redefining H as the standardized mean lateness, H = K / sigma. Our paper first develops the theory and intuition behind the unstandardized mean lateness, drawing connections to the scheduling model and to the theory of standardized mean lateness. Next, we characterize variations in unstandardized mean lateness using data from a sample of arterials in the Stockholm, Sweden metropolitan area. We then proceed to identify and estimate a predictive model for unstandardized mean lateness based roadway features, traffic flow characteristics, and time of day, and we conclude by comparing the predictive power of this approach to an alternate approach where standard deviation and standardized mean lateness are modelled separately.


Association for European Transport