Multiclass dynamic system optimum solution for mixed traffic of human-driven and automated vehicles considering physical queues

•Develop a multi-class system optimum dynamic traffic assignment for mixed human-driven (HVs) and automated vehicles (AVs).•Demonstrate that the proposed method can predict the spatiotemporal dynamics of the class-specific density.•Demonstrate how the initial penetration of AVs affects the total system travel time and the distribution of the physical queues in congested networks.•Show how the link capacity is dynamically allocated to different vehicle classes in order to optimize the total system travel time. Dynamic traffic assignment (DTA) is an important method in the long term transportation planning and management processes. However, in most existing system optimum dynamic traffic assignment (SO-DTA), no side constraints are used to describe the dynamic link capacities in a network which is shared by multiple vehicle types. Our motivation is based on the possibility for dynamic system optimum (DSO) to have multiple solutions, which differ in where queues are formed and dissipated in the network. To this end, this paper proposes a novel DSO formulation for the multi-class DTA problem containing both human driven and automated vehicles in single origin-destination networks. The proposed method uses the concept of link based approach to develop a multi-class DTA model that equally distributes the total physical queues over the links while considering explicitly the variations in capacity and backward wave speeds due to class proportions. In the model, the DSO is formulated as an optimization problem considering linear vehicle composition constraints representing the dynamics of the link capacities. Numerical examples are set up to provide some insights into the effects of automated vehicles on the queue distribution as well as the total system travel times.