The value of travel time unreliability

Adopting the distinction between the concepts of travel time reliability (associated with expected delays of moderate duration) and travel time unreliability (associated with unexpected delays of longer duration), the contribution of this paper is to derive and quantify the value of travel time unreliability. Extensive empirical studies show that the long tail of the travel time distribution and corresponding unexpected delay can have much more serious consequences than expected delay. However, unexpected delay due to unreliability has received limited attention in previous studies of the value of travel time variability. Methodologically, we define the summation of all unexpected delays as the unreliability area of the travel time distribution and show that this is captured by two existing well defined reliability for quantifying travel time variability. We then formally derive the value of unreliability (VOU), show that it is distinct from the more established value of reliability (VOR), and combine the VOU and VOR in an overall VOV. We prove theoretically that the VOV exhibits diminishing marginal benefit in terms of the traveler punctuality requirements under a validity condition, implying that it may be economically inefficient for travelers to blindly pursue a higher probability of not being late. We then proceed to develop the concept of the travel time variability ratio, which gives the implicit cost of the punctuality requirement imposed on any given trip. Numerical examples reveal that the travel time unreliability cost can account for more than 10% of the trip cost, such that its omission could introduce non-trivial bias into route choice models and transportation appraisal more generally.