A Unifying Graph-Coloring Approach for Intersection Control in a Connected and Automated Vehicle Environment

Abstract

This paper investigates intersection control in a fully connected and automated vehicle (CAV) environment, which aims to coordinate in real-time conflicting traffic movements under safety and kinodynamic constraints to maximize intersection throughput or minimize traffic delay. Given the problem's NP-hardness, we leverage graph coloring techniques to devise a control approach that can be viewed as an approximation algorithm for the intersection control problem. We prove that our algorithm provides a polynomial-time approximation scheme (PTAS) for the throughput maximization problem at an intersection with a sufficiently large footprint. Furthermore, with stationary, admissible vehicle arrivals, our scheme ensures the delay each vehicle experiences is less than a constant that linearly depends on the number of lanes and the inverse of the approximation algorithm's precision factor.

Our scheme is unifying in the sense that it includes, as a special case, the traditional signal control for manually driven vehicles and several previously introduced signal-free schemes for automated vehicles. Our optimized control, however, outperforms the other methods substantially. In particular, we prove that in a $R$-way intersection where the number of lanes for each through/turning movement is proportionate to its associated demand, our scheme multiplies the throughput of the intersection by the factor $\frac{R}{2}$ over an optimal signal-based control. Additionally, our scheme is robust in handling a set of vehicles of heterogeneous size and accommodating online variations in safety measures, such as the effect of weather and environmental conditions on the minimum safety gap between vehicles. Its optimality guarantee will not be compromised when addressing these issues.

Keywords: Intersection control; connected and automated vehicles; graph coloring; approximation algorithm; traffic signal control; signal-free control.