A bilevel dynamic signal timing optimization problem

This paper formulates the dynamic signal timing optimization (DSTO) problem as a bilevel model. In the upper level, total network travel time is minimized subject to some necessary signalisation constraints. In the lower level, the dynamic user-optimal route choice is formulated as a variational inequality model, which complies with the dynamic extension of Wardrop's first principle. The sensitivity analysis using a generalized inverse approach performed in the link variable is adopted to solve the DSTO problem. It is not required to generate further a nondegenerate extreme path solution from the link flow solution obtained by the FW method in the sensitivity analysis. This is the case as any path flow solution can be readily accommodated for use. Four heuristics with the same framework of the nested diagonalization (ND) method, but differing in updating decision variable or determining step size, are proposed and compared in terms of both computational performance and precision level. Numerical examples show that all four heuristics algorithms can obtain equilibrium solutions in compliance with the dynamic extension of War drop's first principle. However, considering a balance between precision level and computational performance, the Armijo-based method is recommended.