Combined signal setting design and traffic assignment problem

The paper provides a comprehensive discussion about the global signal settings problem, subject to the user equilibrium constraint for traffic flows. A new algorithm that applies the Armijo rule for step size estimation to usual projected gradient algorithm is presented and compared to other usual solution procedures. Moreover, numerical experiments are performed on a test network in order to investigate the shape of the objective function and then obtain further information about mathematical properties of the problem. Issues concerning multiplicity of solutions, algorithm convergence, and sensitivity to demand patterns are also discussed.