Some general results on the optimal ramp control problem

In an effort to relieve peak hour congestion on freeways, various ramp metering algorithms have been employed to regulate the inputs to freeways from entry ramps. In this paper, we consider a freeway system comprised of a freeway section and its entry/exit ramps, and formulate the ramp control problem as a dynamic optimal process to minimize the total time spent in this system. Within this framework, we are able to show when ramp metering is beneficial to the system in terms of total time savings, and when it is not, under the restriction that the controlled freeway has to serve all of its ramp demand, and the traffic flow process follows the rules prescribed by the LWR theory with a triangular flow-density relationship. We also provide solution techniques to the problem and present some preliminary numerical results and empirical validation.