### Mixed autonomy in ride-sharing networks

Q. Wei, R. Pedarsani, S. Coogan

*IEEE Transactions on Network Control Systems*, 2020

#### Abstract

We consider ride-sharing networks served by human-driven vehicles (HVs) and autonomous vehicles (AVs). We propose a model for ride-sharing in this mixed autonomy setting for a multi-location network in which a ride-sharing platform sets prices for riders, compensation for drivers of HVs, and operates AVs for a fixed price in order to maximize profits. We consider three vehicle-to-rider assignment possibilities: HV priority assignment (rides are assigned to HVs first); AV priority assignment (rides are assigned to AVs first); weighted priority assignment (rides are assigned in proportion to the number of available HVs and AVs). Next, for each of these priority assignments, we establish a nonconvex optimization problem characterizing the optimal profits for a network operating at a steady-state equilibrium and provide a convex problem which we show to have the same optimal profits, allowing for efficient computation of equilibria. We find that, surprisingly, all three priority schemes result in the same maximum profits for the platform because, at an optimal equilibrium for any priority assignment, all vehicles are assigned a ride and thus the choice of priority assignment does not affect the platform's optimal profit. We then consider the family of star-to-complete networks. For this family, we consider the ratio of AVs to HVs that will be deployed by the platform in order to maximize profits for various operating costs of AVs. We show that when the cost of operating AVs is high, the platform will not deploy them in its fleet, and when the cost is low, the platform will use only AVs; in some cases, there is a regime for which the platform will choose to mix HVs and AVs in order to maximize its profit, while in other cases, the platform will use only HVs or only AVs. We fully characterize these thresholds analytically and demonstrate our results on an example.