The role of volume-delay functions in forecasting and evaluating congestion charging schemes: the Stockholm case

This paper uses observations from before and during the Stockkholm congestion charging trial in order to validate and improve a transportation model for Stockholm. The model overestimates the impact of the charges on traffic volumes while at the same time it substantially underestimates the impact on travel times. These forecast errors lead to considerable underestimation of economic benefits which are dominated by travel time savings. The source of error lies in the static assignment that is used in the model. Making the volume-delay functions (VDFs) steeper only marginally improves the quality of forecast but strongly impacts the result of benefit calculations. We therefore conclude that the dynamic assignment is crucial for an informed decision on introducing measures aimed at relieving congestion. However, in the absence of such a calibrated dynamic model for a city, we recommend that at least a sensitivity analysis with respect to the slope of VDFs is performed.     

Optimal toll locations and toll levels in congestion pricing schemes: a case study of Stockholm

As congestion pricing has moved from theoretical ideas in the literature to real-world implementation, the need for decision support when designing pricing schemes has become evident. This paper deals with the problem of finding optimal toll levels and locations in a road traffic network and presents a case study of Stockholm. The optimisation problem of finding optimal toll levels, given a predetermined cordon, and the problem of finding both optimal toll locations and levels are presented, and previously developed heuristics are used for solving these problems. For the Stockholm case study, the possible welfare gains of optimising toll levels in the current cordon and optimising both toll locations and their corresponding toll levels are evaluated. It is shown that by tuning the toll levels in the current congestion pricing cordon used in Stockholm, the welfare gain can be increased significantly, and furthermore improved by allowing a toll on a major bypass highway. It is also shown that, by optimising both toll locations and levels, a congestion pricing scheme with welfare gain close to what can be achieved by marginal social cost pricing can be designed with tolls being located on only a quarter of the tollable links.     

Stockholm congestion charging: an assessment with METROPOLIS and SILVESTER

This paper reviews and compares the performance of two dynamic transportation models – METROPOLIS and SILVESTER – which are used to predict the impacts of congestion charging for Stockholm. Both are mesoscopic dynamic models treating accumulation and dissipation of traffic queues, route choice, modal split and departure time choice. The models are calibrated independently for the baseline situation without charges and applied to forecast the effects of congestion charging. The results obtained from the two models are mutually compared and validated against the actual outcome of the Stockholm congestion charging scheme. Both models successfully predict the outcomes of the congestion charging trial at both aggregate and disaggregate levels. Results of welfare analysis, however, differ substantially due to differences in model specification.     

Seasonal variability of the Black Sea chlorophyll-a concentration

The optimal spectral decomposition (OSD) method is used to reconstruct seasonal variability of the Black Sea horizontally averaged chlorophyll-a concentration from data collected during the NATO SfP-971818 Black Sea Project in 1980–1995. During the reconstruction, quality control is conducted to reduce errors caused by measurement accuracy, sampling strategy, and irregular data distribution in space and time. A bi-modal structure with winter/spring (February–March) and fall (September–October) blooms is uniquely detected and accurately documented. The chlorophyll-a enriched zone rises to 15 m depth in winter and June, and deepens to 40 m in April and 35 m in August. The June rise of the chlorophyll-a enriched zone is accompanying by near-continuous reduction of upper layer maximum chlorophyll-a concentration.     

The value of travel time variance

This paper considers the value of travel time variability under scheduling preferences that are defined 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 fixed 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.     

Additive measures of travel time variability

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.