A. Hegyi, B. De Schutter, and J. Hellendoorn, "Optimal coordination of variable speed limits to suppress shock waves," Transportation Research Record, no. 1852, pp. 167-174, 2003.
We present a model predictive control (MPC) approach to optimally coordinate variable speed limits for highway traffic. A safety constraint is formulated that prevents drivers from encountering speed limit drops larger than, say, 10 km/h, which is incorporated in the controller. The control objective is to minimize the total time that vehicles spend in the network. This approach results in dynamic speed limits that reduce or even eliminate shock waves. To predict the evolution of the traffic flows in the network, which MPC requires, we use an adapted version of the METANET model that takes the variable speed limits into account. The performance of the discrete-valued and safety-constrained controllers is compared with the performance of the continuous-valued unconstrained controller. It is found that both types of controllers result in a network with less congestion, a higher outflow, and hence a lower total time spent. For our benchmark problem, the performance of the discrete controller with safety constraints is comparable to the continuous controller without constraints.