Comparative tests of multimodal traffic equilibrium methods

In this study we proceeded to test the relative efficiencies of the two main computational techniques now available for calculating the traffic equilibrium in multimodal networks, namely, the relaxation and projection methods. Since both of these methods solve at each step a mathematical programming problem, we first set out to test the Frank-Wolfe algorithm and the Dafermos-Sparrow algorithm and found the latter to be the more efficient algorithm. As expected, this was also the case when these algorithms were used to solve the mathematical programming problem at each step of the relaxation method. We then investigated how different versions of the projection method enhance its performance. Subsequently, we proceeded to our main goal to compare the best projection method with the relaxation method. We tested multimodal networks with three different classes of monotone travel cost functions and found that the form of the travel cost functions affects the performance of the two basic techniques available for computing the multimodal equilibrium.