Hybrid optimization: Optimal static traffic control constrained by drivers route choice behavior

This paper considers the static traffic signal control problem in a network with the relaxation of the usual fixed flow asumption implicit in most such studies. Link flows in a traffic network are realistically assumed to be variable because given a set of network control parameters such as signal settings, drivers are free to choose among alternate paths. This is called "hybrid optimization" because it combines the usual notions of user equilibrium and system optimization. Necessary conditions for the optimum solution are derived and discussed. These conditions extend user equilibrium: not only is travel time equalized over utilized paths, but also other quantities related to the system-wide objective. Numerical algorithms are proposed.