Optimal Coordination of Variable Speed Limits to Suppress Shock Waves

Abstract

A model predictive control (MPC) approach is presented to optimally coordinate variable speed limits for highway traffic. A safety constraint incorporated in the controller is formulated that prevents drivers from encountering speed limit drops larger than, say, 10 km/h. 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 is required by MPC, an adapted version of the METANET model is used 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 drivers. For the benchmark problem, the performance of the discrete controller with safety constraints is comparable with the continuous controller without constraints.