Step by step: Revisiting step tolling in the bottleneck model

Research output: Working paperProfessional

Abstract

In most dynamic traffic congestion models, congestion tolls must vary continuously over time to achieve the full optimum. This is also the case in Vickrey's (1969) 'bottleneck model'. To date, the closest approximations of this ideal in practice have so-called 'step tolls', in which the toll takes on different values over discrete time intervals, but is constant within each interval. Given the prevalence of step tolling schemes they have received surprisingly little attention in the literature. This paper compares two step-toll schemes that have been studied using the bottleneck model by Arnott, de Palma and Lindsey (1990) and Laih (1994). It also proposes a third scheme in which late in the rush hour drivers slow down or stop just before reaching a tolling point, and wait until the toll is lowered from one step to the next step. Such behaviour has indeed been observed in reality. Analytical derivations and numerical modelling show that the three tolling schemes have different optimal toll schedules and reduce total social costs by different percentages. These differences persist even in the limit as the number of steps approaches infinity. Braking lowers the welfare gain from tolling by 14% to 21% in the numerical example. Therefore, preventing or limiting braking seems important in designing step-toll systems.
Original languageEnglish
Place of PublicationAmsterdam
PublisherTinbergen Institute
Number of pages41
Publication statusPublished - 2010

Publication series

NameTI Discussion Papers Series
No.10-118/3

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traffic congestion
congestion
modeling
social cost

Cite this

Lindsey, C. R., van den Berg, V. A. C., & Verhoef, E. T. (2010). Step by step: Revisiting step tolling in the bottleneck model. (TI Discussion Papers Series; No. 10-118/3). Amsterdam: Tinbergen Institute.
Lindsey, C.R. ; van den Berg, V.A.C. ; Verhoef, E.T. / Step by step: Revisiting step tolling in the bottleneck model. Amsterdam : Tinbergen Institute, 2010. (TI Discussion Papers Series; 10-118/3).
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abstract = "In most dynamic traffic congestion models, congestion tolls must vary continuously over time to achieve the full optimum. This is also the case in Vickrey's (1969) 'bottleneck model'. To date, the closest approximations of this ideal in practice have so-called 'step tolls', in which the toll takes on different values over discrete time intervals, but is constant within each interval. Given the prevalence of step tolling schemes they have received surprisingly little attention in the literature. This paper compares two step-toll schemes that have been studied using the bottleneck model by Arnott, de Palma and Lindsey (1990) and Laih (1994). It also proposes a third scheme in which late in the rush hour drivers slow down or stop just before reaching a tolling point, and wait until the toll is lowered from one step to the next step. Such behaviour has indeed been observed in reality. Analytical derivations and numerical modelling show that the three tolling schemes have different optimal toll schedules and reduce total social costs by different percentages. These differences persist even in the limit as the number of steps approaches infinity. Braking lowers the welfare gain from tolling by 14{\%} to 21{\%} in the numerical example. Therefore, preventing or limiting braking seems important in designing step-toll systems.",
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Lindsey, CR, van den Berg, VAC & Verhoef, ET 2010 'Step by step: Revisiting step tolling in the bottleneck model' TI Discussion Papers Series, no. 10-118/3, Tinbergen Institute, Amsterdam.

Step by step: Revisiting step tolling in the bottleneck model. / Lindsey, C.R.; van den Berg, V.A.C.; Verhoef, E.T.

Amsterdam : Tinbergen Institute, 2010. (TI Discussion Papers Series; No. 10-118/3).

Research output: Working paperProfessional

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N2 - In most dynamic traffic congestion models, congestion tolls must vary continuously over time to achieve the full optimum. This is also the case in Vickrey's (1969) 'bottleneck model'. To date, the closest approximations of this ideal in practice have so-called 'step tolls', in which the toll takes on different values over discrete time intervals, but is constant within each interval. Given the prevalence of step tolling schemes they have received surprisingly little attention in the literature. This paper compares two step-toll schemes that have been studied using the bottleneck model by Arnott, de Palma and Lindsey (1990) and Laih (1994). It also proposes a third scheme in which late in the rush hour drivers slow down or stop just before reaching a tolling point, and wait until the toll is lowered from one step to the next step. Such behaviour has indeed been observed in reality. Analytical derivations and numerical modelling show that the three tolling schemes have different optimal toll schedules and reduce total social costs by different percentages. These differences persist even in the limit as the number of steps approaches infinity. Braking lowers the welfare gain from tolling by 14% to 21% in the numerical example. Therefore, preventing or limiting braking seems important in designing step-toll systems.

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Lindsey CR, van den Berg VAC, Verhoef ET. Step by step: Revisiting step tolling in the bottleneck model. Amsterdam: Tinbergen Institute. 2010. (TI Discussion Papers Series; 10-118/3).