# Mathematical principles of road congestion pricing

 dc.contributor.author Pienaar, Wessel J. en_ZA dc.contributor.author Nel, J. Hannelie en_ZA dc.date.accessioned 2012-07-16T09:40:26Z dc.date.available 2012-07-16T09:40:26Z dc.date.issued 2009 dc.identifier.citation Pienaar, W. J. & Nel, J. H. 2009. Mathematical principles of road congestion pricing. ORiON, 25(1):45-51, doi:10.5784/25-1-71 en_ZA dc.identifier.issn 2224-0004 (online) dc.identifier.issn 0259-191X (print) dc.identifier.other doi:10.5784/25-1-71 dc.identifier.uri http://hdl.handle.net/10019.1/21709 dc.description CITATION: Pienaar, W. J. & Nel, J. H. 2009. Mathematical principles of road congestion pricing. ORiON, 25(1):45-51, doi:10.5784/25-1-71. dc.description The original publication is available at http://orion.journals.ac.za dc.description.abstract This paper briefly considers the objectives of road congestion pricing and identifies prerequisites to the successful application of such a pricing scheme. The paper is divided into two sections. In the first section, a mathematical analysis of the constituents of an optimal road en_ZA congestion price is offered. The eliminated inefficiency loss achieved by the introduction of a congestion levy is usually evaluated by means of an integral involving marginal trip cost, travel demand and average trip cost in two-dimensional (travel time, traffic flow)-space. In this section we show that this loss may, in fact, be evaluated more easily for a general marginal trip cost function and a linear demand function as the difference between the areas of a rectangle (representing the part of road agency revenue that lies below the original trip cost) and a triangle (representing the loss of consumer surplus of the reduced traffic) in (travel time, traffic flow)-space, eliminating the need to use integration. The next section deals with the application of the illustrated mathematical principles and proofs to a hypothetical case study relating to road congestion pricing in Cape Town. dc.description.uri http://orion.journals.ac.za/pub/article/view/71 dc.format.extent 8 pages ; illustrations dc.language.iso en_ZA en_ZA dc.publisher Operations Research Society of South Africa dc.subject Traffic congestion -- Costs -- Cape Town (South Africa) en_ZA dc.subject Traffic congestion -- Costs -- Statistical methods en_ZA dc.title Mathematical principles of road congestion pricing en_ZA dc.type Article en_ZA dc.description.version Publisher's version en_ZA dc.rights.holder ORiON
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