Ramp metering is proved to be an effective strategy for reducing or avoiding freeway traffic congestion. As a result, huge amount of research has been conducted on synthesizing effective ramp metering controls. In the previous works, freeway is assumed to be a deterministic system which is in contrast with the intrinsic stochastic nature and behavior of freeways. Our work focuses on bridging this gap, and we propose a framework for freeway ramp metering in a probabilistic setting. Our algorithm finds onramp flows in a freeway network while treating exogenous vehicular arrivals as random variables with known distributions, allowing for the network arrivals to conform with their stochastic nature. We use sampling techniques in a model predictive control setup to formulate a tractable approximation of our stochastic optimization. Furthermore, we demonstrate how to relax the non-linear constraints of our optimization to create a linear program with an augmented set of constraints. We prove that the solution of our linear program formulation is the same as the solution of the original mixed-integer formulation. We showcase the results of our algorithm on an exemplar freeway network and introduce multiple interesting future research directions that are important and can be pursued solely in a stochastic framework.

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