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This work presents a novel optimization formulation to solve the problem of variable speed limit control on road networks modeled by the Lighthill-Whitham-Richards (LWR) partial differential equation. It also presents some mathematical rules that allow for a reduction in the size and computational time of the optimization problem. Using the analytical solutions to the LWR model, an optimization problem is formulated for the variable speed limit and ramp metering control of traffic on highway networks using the Lax-Hopf algorithm. The resulting problem, which is non-linear in the decision variables, is transformed into a Mixed Integer Linear Program. Examples are presented to show the effectiveness of the approach, including its application to a real-world highway network with multiple ramp connections. The possibility of linear relaxation of integer variables in the problem is also considered. Lastly, the method is compared to a classical Link Transmission Model formulation of the variable speed limit control problem.

This work presents a novel optimization formulation to solve the problem of variable speed limit control on road networks modeled by the Lighthill-Whitham-Richards (LWR) partial differential equation. It also presents some mathematical rules that allow for a reduction in the size and computational time of the optimization problem. Using the analytical solutions to the LWR model, an optimization problem is formulated for the variable speed limit and ramp metering control of traffic on highway networks using the Lax-Hopf algorithm. The resulting problem, which is non-linear in the decision variables, is transformed into a Mixed Integer Linear Program. Examples are presented to show the effectiveness of the approach, including its application to a real-world highway network with multiple ramp connections. The possibility of linear relaxation of integer variables in the problem is also considered. Lastly, the method is compared to a classical Link Transmission Model formulation of the variable speed limit control problem.