Capacity Drop as a Phase Transition: An Analytical Model via Stochastic Disturbance Propagation

Understanding and mitigating capacity drop is crucial for efficient transportation systems, yet an explicit link from microscopic interactions to this macroscopic phenomenon remains unclear. Drawing on phase transition and critical phenomena theory, this study models the capacity drop as a collective response to speed disturbances that originate from microscopic stochastic interactions and propagate across the platoon at critical density. Specifically, by inducing speed disturbances into the equilibrium traffic, we first develop the response function of mean flow under disturbances. To quantify the effective range of disturbance propagation, we introduce the correlation length, defined as the distance over which the correlation between disturbances remains significant before decaying. With the maximum correlation length indicating the critical density, we thus derive the capacity drop as the response function of the mean flow within this length. Building on this formulation, we propose an analytical model for capacity drop considering the effects of disturbance propagation, based on the equilibrium traffic flow model―the leader-follower conditional distribution based stochastic traffic model (LFCD-STM) developed in our previous work. The proposed capacity drop model is validated using Zen and I-24 MOTION datasets, demonstrating satisfactory performance with all relative errors in flow rates and critical density below 5%. Overall, this work provides a foundational understanding and analytical modeling of capacity drop from the perspective of speed disturbance propagation, offering valuable insights that help develop traffic management strategies and guide the advancement of connected and automated vehicle technologies.