A Queueing Model and Analysis for Autonomous Vehicles on Highways

Abstract

We investigate the effects of autonomous vehicles (AVs) on highway congestion. AVs have the potential to significantly reduce highway congestion, since these vehicles are able to maintain smaller inter-vehicle gaps and travel together in larger platoons (or batches) than human-driven vehicles (HVs). Various policies have been proposed to regulate AVs on highways, yet no in-depth comparison of these policies exists. To address this shortcoming, we develop a queueing model for a multi-lane highway, and analyze two policies for a mixed fleet of HVs and AVs: the designated-lane policy (“D policy”) under which one lane is designated to AVs, and the integrated policy (“I policy”) under which AVs travel together with HVs in all lanes. Our analysis connects the service rate of the queueing system to congestion on the highway, as well as inter-vehicle gaps using a Markovian arrival process (MAP). We measure the performance of these policies using mean travel time and throughput as metrics. We show that although the I policy performs at least as well as a benchmark case with no AVs, the D policy outperforms the benchmark only when the highway is heavily congested and AVs constitute the majority of vehicles; in such a case this policy may outperform the I policy as well. These findings caution against recent industry and government proposals that the D policy should be employed at the beginning of the mass appearance of AVs. Finally, we calibrate our model to data; our numerical analysis shows that for highly congested highways, a moderate number of AVs can make substantial improvement (e.g., 22% AVs can improve throughput by 30%), and when all vehicles are AVs, throughput can be increased over 400%.