A Convex Reformulation of the Robust Freeway Network Control Problem with Controlled Merging Junctions

TL;DR

This paper introduces a convex, robust optimization framework for freeway network control that accounts for uncertainties in traffic demand and fundamental diagrams, ensuring tractable and reliable traffic management.

Contribution

It develops a convex reformulation of the robust freeway network control problem with controlled merging junctions, addressing model uncertainties in a computationally feasible way.

Findings

The robust control problem can be reduced to a convex optimization under certain conditions.

The proposed approach handles uncertainties in demand and fundamental diagrams effectively.

Numerical solutions are tractable and suitable for practical traffic network management.

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.