Solving a Multi-Class Traffic Assignment Model with Mixed Modes

In comparison to conventional human-driven vehicles (HVs), connected and automated vehicles (CAVs) provide benefits (e.g., reducing travel time and improving safety). However, before the period of fully CAVs appears, there will be a situation in which both HVs and CAVs are present, and the traffic flow pattern may differ from that of a single class (e.g., HV or CAV). In this study, we developed a multi-class traffic assignment problem (TAP) for a transportation network that explicitly considered mixed modes (e.g., HV and CAV). As a link's travel time is dependent on the degree of mixed flows, each mode required an asymmetric interaction cost function. For TAP, the multi-class user equilibrium (UE) model was used for the route choice model. A route-based variational inequality (VI) formulation was used to represent the multi-class TAP and solve it using the gradient projection (GP) algorithm. It has been demonstrated that the GP algorithm is an effective route-based solution for solving the single-class user equilibrium (UE) problem. However, it has rarely been applied to solving asymmetric UE problems. In this study, the single-class GP algorithm was extended to solve the multi-class TAP. The numerical results indicated the model's efficacy in capturing the features of the proposed TAP utilizing a set of simple networks and real transportation networks. Additionally, it demonstrated the computational effectiveness of the GP algorithm in solving the multi-class TAP.