G.S. van de Weg, A. Hegyi, S.P. Hoogendoorn, and B. De Schutter, "Efficient freeway MPC by parameterization of ALINEA and a speed-limited area," IEEE Transactions on Intelligent Transportation Systems, vol. 20, no. 1, pp. 16-29, Jan. 2019.
Freeway congestion can reduce the freeway throughput due to the capacity drop or due to blocking caused by spillback to upstream ramps. Research has shown that congestion can be reduced by the application of ramp metering and variable speed limits. Model predictive control is a promising strategy for the optimization of the ramp metering rates and variable speed limits to improve the freeway throughput. However, several challenges have to be addressed before it can be applied for the control of freeway traffic. This paper focuses on the challenge of reducing the computation time of MPC strategies for the integration of variable speed limits and ramp metering. This is realized via a parameterized control strategy that optimizes the upstream and downstream boundaries of a speed-limited area and the parameters of the ALINEA ramp metering strategy. Due to the parameterization, the solution space reduces substantially, leading to an improved computation time. More specifically, the number of optimization variables for the variable speed limit strategy becomes independent of the number of variable message signs, and the number of optimization variables for the ramp metering strategy becomes independent of the prediction horizon. The control strategy is evaluated with a macroscopic model of a two-lane freeway with two on-ramps and off-ramps. It is shown that parameterization realizes improved throughput when compared to a non-parameterized strategy when using the same amount of computation time.