The Role of Volume-delay Functions in Forecast and Evaluation of Congestion Charging Schemes, Application to Stockholm

The Role of Volume-delay Functions in Forecast and Evaluation of Congestion Charging Schemes, Application to Stockholm


L Engelson, KTH, SE; D van Amelsfort, WSP/KTH, SE


Comparison of forecasts and actual effects of Stockholm congestion charging. The effect on volume is overestimated and on travel time underestimated. We test steeper VDFs and its effect on volumes, travel time and CBA.


This paper uses observations from before and during the Stockholm congestion charging trial in order to validate and improve a transportation model for Stockholm. The validation demonstrates that the model overestimates the impacts of the charges on traffic flows and at the same time substantially underestimates the impacts on travel times. The forecast of change in volumes across the cordon is about -29% while the measured change in volumes is -13%. With regards to speeds, the forecast shows a 5.3% increase while 13% increase in speeds was measured. The deviation of effects in volume changes can be explained by a number of differences between how the charges are implemented and how they are modeled, as well as differences between the short term effect measurements and the long term effect modeling. However, if we would address the issues in the model and forecast more appropriate demand levels, then the error in travel time changes would only increase. This leads to considerable error in calculation of economic benefits which are dominated by travel time savings. The source of these errors lies in the static assignment that is used in the model.
In this study we test the effects of steeper volume-delay functions up to 10 times steeper in the neighborhood of the volume in the baseline scenario. We demonstrate that this modification of the static model just marginally improves the quality of forecast but strongly impacts the result of benefit calculations. With the 10 times steeper functions, the forecast effect on volumes reduces to -26% and the change in speeds increases to +15%. Such function is however not reasonable to apply in practice. The benefits from the congestion charges (changes in consumer surplus plus revenues) triple when comparing the 10 times steeper functions to the original functions.

We then compare alternative congesting charging schemes and demonstrate that the ranking of alternatives schemes changes with the slope of volume-delay functions is changed and that even sign change of benefit occurs for one alternative. The benefit calculations are thus largely driven by which volume-delay functions are used in the model.

We conclude that the static assignment used to assess the effects of congestion charging in Stockholm is not capable to reproduce the actual effects of the system. The dynamics of congestion are insufficiently covered by the model and a dynamic assignment is required to assess the effects of measures that aim at relieving congestion. However, in the absence of such a calibrated dynamic model for a city, we recommend that at least a sensitivity analysis is conducted with respect to the slope of volume-delay functions in order to test the robustness of the ranking of different schemes under investigation according to cost and benefit criteria.


Association for European Transport