An exact convex relaxation of the freeway network control problem with controlled merging junctions

Abstract

In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging flows are controlled, there exist tight convex relaxations of the corresponding optimization problem. However, model uncertainty, in particular regarding the fundamental diagram and predictions of future traffic demand, can be a problem in practice. This uncertainty poses a challenge to control approaches that pursue a model-and optimization-based strategy. In this work, we propose a robust counterpart to the FNC problem, where we introduce uncertainty sets for both the fundamental diagram and future, external traffic demands and seek to optimize the system operation, minimizing the worst-case cost. For a network with controlled merging junctions, and assuming that certain technical conditions on the uncertainty sets are satisfied, we show that the robust counterpart of the FNC problem can be reduced to a convex, finite-dimensional and deterministic optimization problem, whose numerical solution is tractable.

Data-Driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

“…Literature Review: Several congestion control schemes have been proposed in the literature with the goal of mitigating congestion, such as ramp metering control [1], [2], lane assignment [3], [4], optimal control [5], [6], logicbased control [7] and many other innovative control strategies [8]- [10]. More recently, variable speed limits have been proposed as an effective congestion control mechanism in transportation [11]- [14].…”