EQUILIBRIUM FLOWS IN A NETWORK WITH CONGESTED LINKS

Abstract

The existing traffic assignment technique which employs a link cost function, f(x), such that f(x) tends to infinity as the flow approaches the capacity only yields an approximate solution to the problem which is produced by adding explicit capacity restraints to the mathematical programming problem, p-1, for obtaining the equilibrium flow pattern. P-1 is not necessarily effective if the network involves some link(s) where the flow is in the congested flow regime since the maximum solution of p-1 can offer the equilibrium flow pattern if all paths between each origin-destination pair are utilized. For this reason it is proposed to deal with the dual problem, d-1, of p-1 whose maximum solution is proved to offer the equilibrium flow pattern. If the congested flow regime is taken into account, the equilibrium flow pattern is not unique since the objective function of d-1 is not concave and further we can produce many different d-1's depending on the combinations of links in the congested flow regime. (Author/TRRL)

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