Data-driven Variable Speed Limit Design with Performance Guarantees for Highways
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This paper studies the data-driven design of variable speed limits for highways subject to uncertainty, including unknown driver actions as well as vehicle arrivals and departures. With accessibility to sample measurements of the uncertain variables, we aim to find the set of speed limits that prevents traffic congestion and an optimum vehicle throughput with high probability. This results into the formulation of a stochastic optimization problem (P), which is intractable due to the unknown distribution of the uncertainty variables. By developing a distributionally robust optimization framework, we present an equivalent and yet tractable reformulation of (P). Further, we propose an efficient algorithm that provides suboptimal data-driven solutions and guarantees congestion-free conditions with high probability. We employ the resulting control method on a traffic simulator to illustrate the effectiveness of this approach.
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