In the past decades, traffic control has mainly included approaches based on ramp metering, i.e., actuation on the freeway via lights preventing a too high flow from entering the freeway during congestion times. In the last years, with the advent of distributed computing, wireless communication and ubiquitous sensing, metering can be achieved at large scale (not only locally), and can be allied with numerous other approaches such as variable speed limits, special use lanes, etc. The mathematical formulation of the underlying problems is quite challenging (for example variable speed limits changes the underlying flow model used in the problem set up). The formulation of the corresponding control problems is also quite difficult, as many times it results in nonlinear nonconvex optimization problems. Numerous approaches have been investigated to solve these problems, which include Lyapunov techniques, adjoint based optimization, and convex relaxation.
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