Optimal toll design problems under mixed traffic flow of human-driven vehicles and connected and autonomous vehicles

Compared to human-driven vehicles (HDVs), connected and autonomous vehicles (CAVs) can drive closer to each other to enhance link capacity. Thereby, they have great potential to mitigate traffic congestion. However, the presence of HDVs in mixed traffic can significantly reduce the effects of CAVs on link capacity, especially when the proportion of HDVs is high. To address this problem, this study seeks to control the HDV flow using the autonomous vehicle/toll (AVT) lanes introduced by Liu and Song (2019). The AVT lanes grant free access to CAVs while allowing HDVs to access by paying a toll. To find the optimal toll rates for the AVT lanes to improve the network performance, first, this study proposes a multiclass traffic assignment problem with elastic demand (MTA-ED problem) to estimate the impacts of link tolls on equilibrium flows. It not only enhances behavioral realism for modeling the route choices of HDV and CAV travelers by considering their knowledge level of traffic conditions but also captures the elasticity of both HDV and CAV demand in response to the changes in the level of service induced by the tolls on AVT lanes. Thereby, it better estimate the equilibrium network flows after the tolls are deployed. Then, two categories of optimal toll design problems are formulated according to whether the solution of the HDV route flows, CAV link flows and corresponding origin?destination demand of the proposed MTA-ED problem is unique or not. To solve these optimal toll design problems, this study proposes a revised method of feasible direction. It linearizes the anonymous terms in the upper-level problem by leveraging the analytical sensitivity analysis results of the lower-level MTA-ED problem. This algorithm is globally convergent on the condition that the MTA-ED problem has a unique solution. It can also be leveraged to solve optimal toll design problems when the MTA-ED problem has multiple solutions. Numerical application found that due to disruptive effects on link capacity, using HDVs may significantly reduce the network performance such as customer surplus and total travel demand. The proposed method can assist different stakeholders to find the optimal toll rates for HDVs on AVT lanes to maximize the network performance under mixed traffic environments.