Properties of Expected Travel Cost Function with Uncertain Travel Time

Abstract

The paper presents a theoretical analysis of travelers’ scheduling preferences and the resulting form of the expected utility that includes travel time reliability measures. A series of research papers and reports used the mean–standard deviation approach to evaluate policies that improve travel time reliability. Recently, this approach was theoretically substantiated under the conventional assumptions of constant marginal utility of time (MUT) at the origin, two discrete MUT values at the destination, and constant standardized travel time distribution. In this paper, properties of the minimal expected travel cost are investigated with smooth MUTs at the origin and destination of the trip. The influence of small variations in travel time on travel cost is well approximated by a term proportional to the travel time variance and independent of the distribution form of travel time. Two examples of MUT functions are provided: the minimal expected travel cost can be analytically expressed through moments or through a moment generating function of travel time, and conditions are stated guaranteeing that the expected travel cost is exactly additive by independent parts of the trip. These results provide justification in particular for the mean–variance approach to modeling drivers’ decisions under uncertain travel times. This formulation is convenient especially for scheme evaluation in large road networks because it allows the use of conventional network assignment routines by just modifying the volume delay functions to include the travel time variability term.