Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters
AbstractThis paper discusses uniqueness and efficiency of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983, Transportation Science) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths but identical disutility functions from time costs. We first show, by example, that his result may not apply in general networks if disutility functions are allowed to differ. However, for "simple" transportation networks, we can show that user equilibrium is always unique and weakly Pareto efficient (cf. the Braess example) for a general class of utility functions. We investigate if this result applies to more general networks. We also show that user equilibrium is unique in a dynamic bottleneck model with a simple network. We discuss an interesting relationship between the following two problems: the existence of user equilibrium in a finite model and the uniqueness of user equilibrium in a continuum model. In the appendix, we also provide a proof of a slightly generalized version of Daganzo's theorem.
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Bibliographic InfoPaper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 494.
Length: 57 pages
Date of creation: 14 Mar 2001
Date of revision: 14 Nov 2002
Publication status: Published, Transportation Science, 38, 315-330, 2004
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Postal: Boston College, 140 Commonwealth Avenue, Chestnut Hill MA 02467 USA
Web page: http://fmwww.bc.edu/EC/
More information through EDIRC
transportation network; user equilibrium; heterogeneous commuters; uniqueness; efficiency; bottleneck model; game theory;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- R40 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - General
- R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion
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