Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control

• A two-stage on-line signal control strategy is proposed based on linear decision rules.
• The signal control method utilizes both historical and real-time traffic information.
• A distributionally robust optimization ensures the on-line performance of the controls.
• All computations are performed off line, making on-line operation efficient and reliable.
• A case study shows significant improvement of the on-line control over fixed signal plans.

We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data-driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic.