Fair, Real-Time Control of a Traffic Signal

Abstract

Information on the vehicles approaching an intersection is used to control the traffic signal in order to reduce delay fairly. Two fairness mechanisms, min-max fairness and proportional fairness, are defined. Min-max fairness minimizes the maximum delay of vehicles, and is fair from the perspective of the vehicles, and proportional fairness minimizes the delays of vehicles controlled by a phase of the traffic signal, and is fair from the perspective of the traffic signal. These fairness mechanisms are compared with an earlier mechanism that minimizes the average delay and with fixed cycle traffic signals. The comparisons for a range of arrival rates, and for both balanced and unbalanced loads on the approaches to the signal, are performed. All of the real-time mechanisms are similar at low to moderate loads, and provide a significant improvement over the fixed traffic signal. This is expected because vehicles don’t wait at a red light when there are no vehicles passing through the intersection. As the load increases: Minimum delay control has a significantly smaller delay than fixed control, but treats some vehicles extremely unfairly; the average delay of min-max fairness may be slightly greater than fixed control, but the individual vehicles are treated much more fairly; and, proportional fairness reduces the average delay close to that of minimum delay control, and treats the individual vehicles almost as fairly as min-max fairness. Based upon this study, proportional fairness is recommended to control traffic signals.