Optimal traffic signal control under dynamic user equilibrium and link constraints in a general network

In this study, an optimal traffic signal control framework is proposed for finding the signal control settings that minimize the total travel time in a road network with traffic lights. A novel aspect of this framework is its integration of the continuous-time double queue traffic flow model in a signal controlled traffic network to capture queue spillbacks in continuous-time. Furthermore, drivers' long term responses to changes in traffic signal control settings are captured by their route choices following Wardrop's first principle, which results in the dynamic user equilibrium state. Two signal control strategies, the fixed-timing control and the adaptive signal control, are considered. A continuous approximation method for the signal control is applied to eliminate integer variables and enhance the computational efficiency. A heuristic genetic algorithm based solution procedure is proposed to solve the proposed nonlinear programming problem with time-varying delay terms. Numerical tests are conducted in two testing networks and the results show that adaptive control with drivers taking into account signal timing on their route travel times performs best, and in some cases nearly as well as the benchmark performance derived from system optimal control without equilibrium constraints. The results also show that the advantage of adaptive over fixed-time signal control is more pronounced under UE than SO routing behavior.