Macroscopic Framework for Mixed HDV‐AV Traffic Flow with Coupled Curbside Reservoir Dynamics Under Remote‐Valet Empty‐Mile Repositioning

ABSTRACT

Remote‐valet operations send Autonomous Vehicles (AVs) empty to remote parking sites after passenger drop‐off, introducing a continuous stream of remote‐valet vehicles into the urban network through empty‐mile repositioning. The interactions among remote‐valet vehicle flow, Human‐Driven Vehicles (HDVs), and curbside activity remain largely unexplored in macroscopic traffic theory. This paper introduces the Remote‐Valet Mixed‐Class Macroscopic Activity and Roadside Parking (RV‐MARP) framework, a continuum model that couples mixed HDV‐AV traffic flow, finite‐capacity curb activity, and empty‐mile repositioning to capture the multisource feedback governing urban traffic flow under active curb operations. A linear stability analysis is performed to characterize the conditions under which spatially uniform traffic flow remains stable. The analysis shows that remote‐valet operations destabilize traffic through increased effective density arising from lane occupancy and behavioral drag induced by interactions with remote‐valet vehicles. The resulting neutral stability condition is obtained when the combined destabilizing feedbacks associated with effective density, curb, and remote‐valet interactions are exactly balanced by the stabilizing effects of viscosity and velocity relaxation. This yields stability criteria unique to corridors with curb activity and remote‐valet vehicle flow. Numerical simulations demonstrate that the remote‐valet absorption rate governs the spatial distribution of remote‐valet vehicles, while higher AV penetration improves throughput despite generating proportionally larger empty‐mile repositioning demand. The findings reveal a fundamental trade‐off in which gains in curb management efficiency may be offset by the destabilizing effects of uncontrolled remote‐valet vehicle flow, highlighting the need for coordinated curb management policies and autonomous vehicle operations.