  This paper addresses the problem of a boundary control design for traffic
evolving in a large-scale urban network. The traffic state is described on a
macroscopic scale and corresponds to the vehicle density, whose dynamics are
governed by a two-dimensional conservation law. We aim at designing a boundary
control law such that the throughput of vehicles in a congested area is
maximized. Thereby, the only knowledge we use is the network's topology,
capacities of its roads and speed limits. In order to achieve this goal, we
treat a 2D equation as a set of 1D equations by introducing curvilinear
coordinates satisfying special properties. The theoretical results are verified
on a numerical example, where an initially fully congested area is driven to
the state with maximum possible througput.
