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The combination of boundary flow control and variable speed limit (VSL) is awidely used strategy for highway corridors to maintain safety and throughputwhen the capacity downstream is dropped. However, most proposed models assumefixed and known demand, which is not always true in reality. Following arecently proposed boundary flow and VSL control model that is based on theLax-Hopf solution to the Lighthill-Whitham-Richards (LWR) model, this paperproposes a two-stage stochastic model to tackle the uncertainties in demand.Our model assumes the demand follows a discrete distribution and the speedlimit can be chosen from a pre-defined set with reasonable values. The firststage tries to find the optimal inflow control, which is the here-and-nowdecision, by considering the speed limit control downstream, and the secondstage is to determine the optimal speed limit after observing the real demand.Those controls are coordinated by using a rolling horizon scheme. The casestudy shows the proposed model outperforms three deterministic models, whichuse the minimum, mean value and maximum of the demand as model input, undervarious scenarios. With ensuring the maximum of throughput, the proposed modelis demonstrated to be able to reduce the fluctuation of entry flow without asignificant increase in blocked vehicles.

A Two-stage Stochastic Model Considering Randomness of Demand in Variable Speed Limit and Boundary Flow Control