A Macroscopic Continuum Framework for Urban Traffic With Dynamic Curbside Parking Activity

Abstract

Urban traffic performance is strongly shaped by interactions between moving vehicles and curbside activities such as parking maneuvers, deliveries, and ride-hailing pickups. These interactions modify effective capacity and driver behavior in ways not captured by conventional macroscopic traffic models. This study introduces the macroscopic activity and roadside parking (MARP) model, a continuum framework that couples vehicle motion with parking and rejoining dynamics through mass exchange, obstruction-dependent equilibrium velocity, and nonlocal blockage effects. Linear stability analysis establishes explicit threshold conditions under which curb occupancy and temporary obstructions destabilize the flow, while weakly nonlinear analysis reduces the governing system to a Korteweg–de Vries (KdV)–Burgers equation that characterizes the evolution of stop-and-go waves near the instability boundary. Numerical simulations demonstrate that the model reproduces key qualitative features of urban traffic dynamics, including smooth capacity recovery under parking bans, congestion waves triggered by double parking, and oscillatory bottlenecks arising from spatially distributed pickup demand. The results show that curb activity acts as a dynamic source of localized and distributed perturbations, capable of reshaping traffic flow while maintaining system-level stability under certain conditions. The proposed model provides a basis for evaluating corridor-level impacts of curb management strategies within a consistent macroscopic setting.