Abstract

In this paper a new algorithm to solve the traffic assignment problem is proposed: the Linear User Cost Equilibrium (LUCE). The main idea is to seek at every node a deterministic equilibrium for the local route choice of users directed toward a same destination among the links of its forward star. The cost function associated to each one of these travel alternatives expresses the average impedance to reach the destination by continuing the trip with that link, linearized at the current flow pattern. We prove that the solution to such linear program in terms of destination flows, recursively applied for each node, provides a descent direction with respect to the classical sumintegral objective function. The network loading is then performed through the corresponding splitting rates, thus avoiding explicit path enumeration. Exploiting the inexpensive information provided by the derivatives of the link costs with respect to link flows, LUCE achieves a very high convergence speed that compares favourably to the other methods, while it assigns the demand flow of each o-d couple on several paths at once.

Citations