Step tolling with bottleneck queuing congestion
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.
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- Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
- Chen-Hsiu Laih, 2004. "Effects of the optimal step toll scheme on equilibrium commuter behaviour," Applied Economics, Taylor & Francis Journals, vol. 36(1), pages 59-81.
- Fosgerau, Mogens, 2011.
"How a fast lane may replace a congestion toll,"
42271, University Library of Munich, Germany.
- Richard Arnott & Andre de Palma & Robin Lindsey, 1985.
"Economics of a Bottleneck,"
636, Queen's University, Department of Economics.
- Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-79, June.
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