This paper presents a feedback control design for a coordinated ramp metering problem for two consecutive on-ramps. We design a traffic allocation scheme for ramps based on Godunov's numerical method and using a distributive model. Most of the previous work for designing feedback control for ramp metering is based on either the discretized linear methods or nonlinear methods based on the traffic ordinary differential equations (ODEs). We utilize the distributive model to construct a control condition for regulating the traffic density at critical density. Then, we design a Godunov-method-based satisfiable allocation scheme that gives us the actual control for each ramp individually. We show the stability properties of the closed-loop system and validate the effectiveness of the feedback control law by running a simulation using real traffic flow measurements with parameter estimation.
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Agarwal et al. (2015) studied this question.