Traffic control and travelers’ behavior are two mutually influential processes with different objectives. Decisions made in traffic control influence travelers’ possibilities in choosing their preferred mode, route, and time of departure; and the choices made by travelers influence the optimization possibilities for traffic control. This research presents the results of simulation studies and a mathematical analysis of this bilevel optimization problem. Under certain conditions, multiple stable situations are possible, but some of these situations are sensitive to small disturbances by which the system moves away from the original equilibrium state. There appears to be a nonlinear relationship between system parameters and the character and location of the equilibrium situations. The details of the travel time model appear to have a large influence. If road authorities want to optimize traffic control, they have to anticipate the reaction of travelers. This makes the optimization process much more complicated. Iterative optimization, where traffic control is adjusted as soon as traffic conditions change, generally does not lead to a system optimum. Methods are therefore necessary that allow for the optimization of traffic control while taking into account that traffic flows will change as a result of traffic control.
A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems