The cost of travel time variability: Three measures with properties

•Considers three types of measures of the cost of travel time variability.•Includes probably all cost measures ever used.•Clarifies the relations between these types and the restrictions embodied in each.•Clarifies restriction implied by requiring additivity or homogeneity.•Useful for choosing cost measures for applications.

This paper explores the relationships between three types of measures of the cost of travel time variability: measures based on scheduling preferences and implicit departure time choice, Bernoulli type measures based on a univariate function of travel time, and mean-dispersion measures. We characterise measures that are both scheduling measures and mean-dispersion measures and measures that are both Bernoulli and mean-dispersion. There are no measures that are both scheduling and Bernoulli. We consider the impact of requiring that measures are additive or homogeneous, proving also a new strong result on the utility rates in an additive scheduling measure. These insights are useful for selecting cost measures to use in applications.