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.