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Mathematical principles of road congestion pricing

WJ Pienaar, JH Nel

Abstract


This paper briefly considers the objectives of road congestion pricing and identi es prereq-uisites to the successful application of such a pricing scheme. The paper is divided into two sections. In the rst section, a mathematical analysis of the constituents of an optimal road congestion price is o ered. 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 di erence between the areas of a rect-
angle (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.

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ORiON: The Journal of ORSSA.   ISSN: 0529-191-X