A comparison of user-optimum versus system-optimum traffic assignment in transportation network design

In this report, we compare the computational efficiency and results of solving two alternative models for the problem of determining improvements to an urban road network. Using a 1462 link, 584 node test network of the north Dallas area, we compare a model which assumes user-optimum behavior of travelers with a model which assumes system-optimum flows. Both of these models allow improvements to the road network to take on any nonnegative value, rather than requiring discrete improvement values. Investment costs are modeled by functions with decreasing marginal costs. Unfortunately, the user-optimum model, which is much more realistic than the system-optimum one, normally cannot be solved optimally. However, the simpler system-optimum model can be optimally solved, provided that investment costs are approximated by linear functions. Thus, for this network design problem we compare an accurate representation which can be solved only approximately with an approximate representation which can be solved optimally. Our computational testing showed that the system-optimum model produces solutions as good as those from the user-optimum model, and thus seems justified when favored by other considerations, such as ease of coding, availability of “canned” programs, etc.