Nonlinear Road Pricing for Congestion and the Environment
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2012-03-30
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Alternative Title:Final report to the Center for Multimodal Solutions for Congestion Mitigation (CMS)
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Edition:Final report.
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NTL Classification:NTL-ECONOMICS AND FINANCE-ECONOMICS AND FINANCE;NTL-ENERGY AND ENVIRONMENT-ENERGY AND ENVIRONMENT;NTL-OPERATIONS AND TRAFFIC CONTROLS-Congestion;
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Abstract:Under nonlinear road pricing (or tolling), the price charged is not strictly proportional to the distance travelled inside a tolling area, the generalized travel cost is not link-wise additive, and finding a user equilibrium distribution is typically formulated as a complementarity problem. The latter is a difficult problem to solve in mathematical programming. In this report, we use piecewise linear functions to determine tolls and show that finding a user equilibrium distribution with such functions can be formulated as a convex optimization problem that is based on path flows and solvable by traditional algorithms such as simplicial decomposition. For area-based and two-part pricing schemes, the tolling function consists of only one linear piece and finding a user equilibrium distribution reduces to a convex optimization problem formulated in terms of link flows and solvable by any software for linearly constrained convex programs.
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