Optimal coordination of variable speed limits to suppress shock waves

When freeway traffic is dense, shock waves may appear. These shock waves result in longer travel times and in sudden large variations in the speeds of the vehicles, which could lead to unsafe situations. Dynamic speed limits can be used to eliminate or at least to reduce the effects of shock waves. However, coordination of the variable speed limits is necessary in order to prevent the occurrence of new shock waves and/or a negative impact on the traffic flows in other locations. In this paper, we present a model predictive control approach to optimally coordinate variable speed limits for freeway traffic with the aim of suppressing shock waves. First, we optimize continuous valued speed limits, such that the total travel time is minimal. Next, we include a safety constraint that prevents drivers from encountering speed limit drops larger than, e.g., 10 km/h. Furthermore, to get a better correspondence between the computed and applied control signals, we also consider discrete speed limits. We illustrate our approach with a benchmark problem.