An iterative scheme for signal settings and network flows

An area traffic control optimization is considered where the signal setting variables and link flows are simultaneously determined. The optimal signal settings and network flows (OPSF) can be formulated as a mathematical program with equilibrium constraints (MPEC) where the user equilibrium is expressed as a variational inequality problem. Due to the non-differentiability of the perturbed solutions in equilibrium constraints, a non-smooth model is established. A Quasi–Newton subgradient projection is presented to effectively solve the OPSF with global convergence. Numerical calculations are conducted on an example network where promising results are obtained.