On the morning commute problem with mixed autonomous and human-driven traffic under stochastic bottleneck capacity

This paper investigates the impact of external uncertainty on morning commute behavior when autonomous vehicles (AVs) are introduced and interact with human-driven vehicles (HVs). We adopt the bottleneck model to study the morning commuting dynamics. In this context, we consider two potential benefits for AVs, i.e., value-of-time (VOT) compensation/reduction and capacity enhancement. We develop an extension-elimination-verification-supplement approach to simplify the equilibrium analysis process to obtain the equilibrium departure flow patterns. We find that the external uncertainty makes the equilibrium departure flow patterns more complicated than those under the deterministic setting, yielding three basic departure flow pattern types, i.e., AVs travel inside HVs, AVs travel after HVs, and HVs and AVs depart alternatively. If AVs are able to reduce VOT, their ability to improve bottleneck capacity does not qualitatively change the equilibrium departure flow patterns. Moreover, although increasing the penetration of AVs can improve the system performance to some degree, the total travel costs may not be monotonically decreasing with respect to AV penetration when AVs cannot significantly enhance bottleneck capacity. The optimal penetration rate of AVs minimizing the total travel costs is no less than 50% and the total travel costs reach the minimum in the situation with mixed HVs and AVs rather than in the 100% AV penetration if the bottleneck capacity enhancement caused by AVs is not significant enough. Furthermore, increasing the penetration of AVs may indeed increase traffic congestion when compared to that under 100% HVs if AVs cannot enhance bottleneck capacity sufficiently. To reduce total travel costs by increasing AV penetration, it is necessary to ensure that AVs can enhance bottleneck capacity sufficiently as the penetration rate of AVs increases when the adverse effects of VOT compensation on traffic congestion are dominated. When the penetration rate of AVs reaches 100%, the capacity enhancement from AVs should be sufficiently large to ensure that AVs can simultaneously improve the system performance and reduce traffic congestion.