Step tolling with bottleneck queuing congestion

Research output: Contribution to JournalArticleAcademicpeer-review

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 (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 et al. (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 'braking' behaviour has been observed in practice. 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. © 2012 Elsevier Inc.
Original languageEnglish
Pages (from-to)46-59
JournalJournal of Urban Economics
Volume72
Issue number1
DOIs
Publication statusPublished - 2012

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congestion
traffic congestion
social costs
welfare
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modeling
Queuing
Congestion
Values
time

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@article{61f88bf7b8d84519b034cb1378a4b522,
title = "Step tolling with bottleneck queuing congestion",
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 (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 et al. (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 'braking' behaviour has been observed in practice. 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. {\circledC} 2012 Elsevier Inc.",
author = "C.R. Lindsey and {van den Berg}, V.A.C. and E.T. Verhoef",
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doi = "10.1016/j.jue.2012.02.001",
language = "English",
volume = "72",
pages = "46--59",
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}

Step tolling with bottleneck queuing congestion. / Lindsey, C.R.; van den Berg, V.A.C.; Verhoef, E.T.

In: Journal of Urban Economics, Vol. 72, No. 1, 2012, p. 46-59.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

T1 - Step tolling with bottleneck queuing congestion

AU - Lindsey, C.R.

AU - van den Berg, V.A.C.

AU - Verhoef, E.T.

PY - 2012

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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 (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 et al. (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 'braking' behaviour has been observed in practice. 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. © 2012 Elsevier Inc.

AB - 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 (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 et al. (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 'braking' behaviour has been observed in practice. 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. © 2012 Elsevier Inc.

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