Abstract
If each car in an urban road network is equipped with a device to communicate with the control center, a route guidance system which takes into account each driver's objective can be constructed for easing up traffic congestion.
This paper deals with a dynamic assignment problem of traffic flows for such a system.
It is shown that, based on the observed data of actual traffic flows, the problem may be formulated as a nonlinear optimal control problem may with constraints.
Then, two methods for approximate solutions are proposed; one is an application of a gradient method for optimal control problems with constraints, and another is a combination of linear approximation of the state equation and penalization of constraints, which constructs a problem similar to a linear tracking problem. The two methods are compared by solving an example problem.
The example shows that the gradient method provides a better value of performance index than the linear approximation method. However, the latter may also provide a good result if short time spans of assignment are connected in series.
