A stochastic dynamic network loading model for mixed traffic with autonomous and human-driven vehicles

In this study, we develop a stochastic dynamic network loading (DNL) model for the mixed traffic with autonomous vehicles (AVs) and human-driven vehicles (HVs). The source of stochasticity is the uncertainty inherent in the arrival process of the two classes of vehicular flow. The developed model captures both within-link and between-link traffic flow dependencies and evaluates the network state distribution in an analytical manner. The model has two main components, a probabilistic link model and a probabilistic node model. The link model is a stochastic formulation of the link transmission model (LTM), which captures the boundary conditions of a link and approximates the evolution of link state distribution. The node model, on the other hand, characterizes the flow transmissions across a network node. It reflects the between-link dependency by evaluating the expected transmission flow through an iterative algorithm, with an explicit consideration of the interactions between supply and demand constraints associated with a node. The developed model is validated versus replicated running of the deterministic LTM as well as microscopic traffic simulations, and the results reveal that it yields relatively accurate estimations. We also present two applications of the proposed model, including a traffic signal control problem and a class-based ramp metering problem, to demonstrate its practical value.