This paper considers the value of travel time variability under scheduling preferences that are de…ned in terms of linearly time-varying utility rates associated with being at the origin and at the destination. The main result is a simple expression for the value of travel time variability that does not depend on the shape of the travel time distribution. The related measure of travel time variability is the variance of travel time. These conclusions apply equally to travellers who can freely choose departure time and to travellers who use a scheduled service with …xed headway. Depending on parameters, travellers may be risk averse or risk seeking and the value of travel time may increase or decrease in the mean travel time.

Summary.We study congestion pricing of road networks with users differing only in their time values. In particular, we analyze the marginal social cost (MSC) pricing, a tolling scheme that charges each user a penalty corresponding to the value of the delays inflicted on other users, as well as its implementation through fixed tolls. We show that the variational inequalities characterizing the corresponding equilibria can be stated in symmetric or nonsymmetric forms. The symmetric forms correspond to optimization problems, convex in the fixed-toll case and nonconvex in the MSC case, which hence may have multiple equilibria. The objective of the latter problem is the total value of travel time, which thus is minimized at the global optima of that problem. Implementing close-to-optimal MSC tolls as fixed tolls leads to equilibria with possibly non-unique class specific flows, but with identical close-to-optimal values of the total value of travel time. Finally we give an adaptation, to the MSC setting, of the Frank-Wolfe algorithm, which is further applied to some test cases, including Stockholm.

This paper compares forecasted effects of the Stockholm congestion charges with actual outcomes. The most important concerns during the design of the congestion charging scheme were the traffic reduction in bottlenecks, the increase in public transport ridership, the decrease of vehicle kilometres in the city centre, and potential traffic effects on circumferential roads. Comparisons of forecasts and actual outcomes show that the transport model predicted all of these factors well enough to allow planners to draw correct conclusions regarding the design and preparations for the scheme. The one major shortcoming was that the static assignment network model was unable to predict the substantial reductions of queuing times. We conclude that the transport model worked well enough to be useful as decision support, performing considerably better than unaided "experts' judgments", but that results must be interpreted taking the model's limitations into account. The positive experiences from the Stockholm congestion charges hence seem to be transferable to other cities in the sense that if a charging system is forecasted to have beneficial effects on congestion, then this is most likely true.

This paper derives a measure of travel time variability for travellers equipped with scheduling preferences defined in terms of time-varying utility rates, and who choose departure time optimally. The corresponding value of travel time variability is a constant that depends only on preference parameters. The measure is unique in being additive with respect to independent parts of a trip. It has the variance of travel time as a special case. Extension is provided to the case of travellers who use a scheduled service with fixed headway.

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 meandispersion measures. We characterise measures that are both scheduling measures and meandispersion 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.