Optimal aggregated control of in- and outflows for a congested area

:A continuous dynamical model is used in order to find an optimal control policy that minimizes the total delay while limiting the net inflow to a congested area. The problem is reduced to a single intersection problem, and an analytical solution is given. The optimal control is different for the four principal control constraint cases. The optimal solutions found from the Pontryagin maximum principle satisfy the sufficient conditions for optimality.