The Impact of Autonomous Vehicles on Ride-Hailing Platforms with Strategic Human Drivers

TL;DR

This work considers a ride-hailing platform that operates a mixed fleet of autonomous vehicles (AVs) and conventional vehicles (CVs), where AVs are fully controlled by the platform and CVs are operated by self-interested human drivers, and proposes three numerical algorithms to solve OPT, a non-convex problem in the platform decision parameters.

Abstract

Motivated by the rapid development of autonomous vehicle technology, this work focuses on the challenges of introducing them in ride-hailing platforms with conventional strategic human drivers. We consider a ride-hailing platform that operates a mixed fleet of autonomous vehicles (AVs) and conventional vehicles (CVs), where AVs are fully controlled by the platform and CVs are operated by self-interested human drivers. Each vehicle is modelled as a Markov Decision Process that maximizes long-run average reward by choosing its repositioning actions. The behavior of the CVs corresponds to a large game where agents interact through resource constraints that result in queuing delays. In our fluid model, drivers may wait in queues in the different regions when the supply of drivers tends to exceed the service demand by customers. Our primary objective is to optimize the mixed AV-CV system so that the total profit of the platform generated by AVs and CVs is maximized. To achieve that, we formulate this problem as a bi-level optimization problem OPT where the platform moves first by controlling the actions of the AVs and the demand revealed to CVs, and then the CVs react to the revealed demand by forming an equilibrium that can be characterized by the solution of a convex optimization problem. We prove several interesting structural properties of the optimal solution and analyze simple heuristics such as AV-first where we solve for the optimal dispatch of AVs without taking into account the subsequent reaction of the CVs. We propose three numerical algorithms to solve OPT which is a non-convex problem in the platform decision parameters. We evaluate their performance and use them to show some interesting trends in the optimal AV-CV fleet dimensioning when supply is exogenous and endogenous.

Figures (6)

• Figure 1: A two-region ride-hailing network where all customers have the same destination region 1. The demand rate is $b_{11}=b_{21}=b$ (black arrows), $b_{12}=b_{22}=0$, and the trip time of any origin-destination pair is $\tau$, implying the same payment per trip. Vehicles need repositioning from region 1 to region 2 (blue dashed arrow) to serve demand $b_{21}$ and spend an additional time $\tau$.
• Figure 2: The platform profit value against the demand revealed to CVs for the two-region network in Fig \ref{['fig:figureL2']} with customer payment per unit travel time $p=1$, driving cost rate $c=0.1$ and commission rate $R=0.5$.
• Figure 3: A two-region network with four customer routes: two within-region routes $1\to 1$, $2\to 2$ and two cross-region routes $1\to 2$, $2\to 1$. The demand rates and travel times are specified as $\{b_{11}=1, b_{12}=1, b_{21}=2, b_{22}=1\}$ and $\{\tau_{11}=1, \tau_{12}=2, \tau_{21}=2, \tau_{22}=1\}$ for each route. We assume the cross-region demands are imbalanced (i.e., $b_{21} > b_{12}$) and the traveling time of the cross-region route is greater than the within-region route.
• Figure 4: Compare the analytically derived optimal platform profit against the results obtained by the AV-first policy, gradient-descent, bundle method and genetic algorithms. Test the performance for various AV fleet sizes $M$, across two levels of CV supply (low CV supply $N=5$ and high CV supply $N=10$). Observations: 1. All three proposed algorithms attain near-optimal performance. 2. The maximum performance loss of AV-first is $10\%$ for this simulation (i.e., when $M=1$ and $N=10$). 3. For a given fleet size of AVs, a higher platform profit is achieved with a larger fleet size of CVs.
• Figure 5: Computed platform profits of the $2\times2$ grid network in Table \ref{['tab:diffinitial']} against AV fleet size $M$. Observation: 1. The marginal value of adding AVs is not monotonically decreasing, e.g. at $M=2$ and $M=8$. 2. The marginal values depend a lot on which algorithm is implemented.

Theorems & Definitions (21)

• Definition 1: CV equilibrium
• Corollary 1
• Proposition 1: CV equilibrium characterization
• Proposition 2
• Proposition 3
• Definition 2: Mixed-fleet equilibrium
• Proposition 4
• Lemma 1
• Corollary 2
• Definition 3: Bi-level optimization