The Stability of a Dynamic Model of Traffic Assignment—An Application of a Method of Lyapunov

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Abstract
This paper considers a dynamic model of traffic assignment in which drivers change their route choices to take advantage of cheaper routes. Using a method due to Lyapunov, we show that if the cost-flow function is monotone and there are no explicit capacity restrictions then any solution trajectory of our dynamical system converges to the set of Wardrop equilibria as time passes.

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