Fair Allocation of Delays in the Real-Time Control of an Autonomous Traffic Signal

Our objective is to use information on the vehicles approaching an intersection to control the traffic signal. Recent work in this area has used this information to minimize the average delay of vehicles controlled by the signal. We demonstrate that, when there are significant differences in the volume of traffic approaching from different directions, the average delay of the vehicles in the low volume directions can be much greater than those in the high volume direction. In order to treat the vehicles more fairly, we define two fairness mechanisms, min-max fairness and proportional fairness. Min-max fairness minimizes the maximum delay of vehicles, and is fair from the perspective of the vehicles, and proportional fairness minimizes the sum of the delays of vehicles controlled by a phase of the traffic signal, and is fair from the perspective of the traffic signal. We compare our fairness mechanisms with a real-time mechanism that minimizes the queue length of vehicles waiting at a traffic signal, and a fixed cycle traffic signal. We perform the comparisons for a range of arrival rates, and for both balanced and unbalanced loads on the approaches to the signal. We find that the min-max fairness mechanism treats the individual vehicles more fairly, but can significantly increase the average delay in comparison with the queue length mechanism. Proportional fairness, however, treats the vehicles as fairly as min-max fairness without significantly increasing the average delay. Based upon this study we recommend proportional fairness for the real time control of traffic signals.