A mixed behaviour equilibrium model with mode choice and its application to the endogenous demand of automated vehicles

This study develops a mixed behavioural equilibrium model with explicit consideration of mode choice (MBE-MC) in a transportation system where fully automated vehicles (AV) coexist with conventional human-driven vehicles (HV). For the mode choice, travellers select among three options, following a logit modal split: driving their private HV, or taking an AV mobility service provided by either a firm or the government. For the route choice, the HV drivers follow the random utility maximisation principle while central agents route the AV passengers following the Cournot Nash (firm agent) or Social Optimal (government agent) principles. We consider two types of travel costs (i.e. travel time and monetary travel cost) to characterise the new features (e.g. expanded link capacity and reduced value of time) of the mixed AV–HV transportation system. We model the MBE-MC problem in a combined mode–route choice framework and formulate it as a route-based variational inequality (VI) problem. We show the equivalence between the VI formulation and the MBE-MC problem, and the existence of a solution to the MBE-MC problem. Then, we modify a partial linearisation algorithm for solving the proposed model. Numerical results validate the equilibrium conditions and show the efficacy of the new model in capturing the features of the mixed AV–HV transportation system. The impact patterns of different parameters on (1) the network performance in terms of AV share and system cost and (2) on the solution efficiency are analysed.