Traffic Equilibrium in Mixed-Autonomy Network with Capped Customer Waiting

Abstract: This paper develops a unified modeling framework to capture the equilibrium-state interactions among ride-hailing companies, travelers, and traffic of mixed-autonomy transportation networks. Our framework integrates four interrelated sub-modules: (i) the operational behavior of representative ride-hailing Mixed-Fleet Traffic Network Companies (MiFleet TNCs) managing autonomous vehicle (AV) and human-driven vehicle (HV) fleets, (ii) traveler mode-choice decisions taking into account travel costs and waiting time, (iii) capped customer waiting times to reflect the option available to travelers not to wait for TNCs' service beyond his/her patience and to resort to existing travel modes, and (iv) a flow-dependent traffic congestion model for travel times. A key modeling feature distinguishes AVs and HVs across the pickup and service (customer-on-board) stages: AVs follow Wardrop pickup routes but may deviate during service under company coordination, whereas HVs operate in the reverse manner. The overall framework is formulated as a Nonlinear Complementarity Problem (NCP), which is equivalent to a Variational Inequality(VI) formulation based on which the existence of a variational equilibrium solution to the traffic model is established. Numerical experiments examine how AV penetration and Wardrop relaxation factors, which bound route deviation, affect company, traveler, and system performance to various degrees. The results provide actionable insights for policymakers on regulating AV adoption and company vehicle deviation behavior in modern-day traffic systems that are fast changing due to the advances in technology and information accessibility.