Efficient Controls for Traffic Flow on Networks

We study traffic flow models for road networks in vector-valued optimization statement, where the flow is controlled at the nodes of the network. We consider the case where an objective mapping possesses a weakened property of upper semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for the existence of efficient controls of the traffic problem and discuss the scalarization approach to its solution. We also prove the existence of the so-called generalized efficient controls.