Abstract
The problem of determining the equilibrium distribution of the traffic flow in a city network is studied when the traffic demands on a set of given routes are known. The problem is formulated in terms of a nonlinear variational inequality over a polyhedron and a solving procedure, different from those shown in [1], [3], [4], is exhibited. This procedure is based on a very simple, necessary, and sufficient condition for a solution of the variational inequality to lie on a face of the polyhedron. Moreover, it is also compared, by means of numerical examples, with the procedures formulated in [1], [3], and [4] (see expressions (1.2) and (3.5) for a significant valuation).
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Communicated by A. V. Balakrishman
Supported by M.P.I. and C.N.R.
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Maugeri, A. Convex programming, variational inequalities, and applications to the traffic equilibrium problem. Appl Math Optim 16, 169–185 (1987). https://doi.org/10.1007/BF01442190
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DOI: https://doi.org/10.1007/BF01442190