The Robotaxi Placement Problem: Minimizing Expected ETA for Stochastic Demand

2026-05-15

AI Summary

This study addresses the problem of deploying $k$ autonomous taxis under stochastic passenger demand to minimize expected waiting time, formalized as the stochastic $k$-facility location problem ($k$-RP) in metric spaces. The work proposes the first theoretical framework for this problem: a 2-approximation randomized algorithm for general metric spaces, accompanied by a matching lower bound proving the approximation ratio is tight; and an exact polynomial-time dynamic programming algorithm for tree metrics. The approach integrates random sampling, gap-preserving reductions, and variance reduction techniques to effectively lower expected matching costs. Experiments on real-world ride-hailing data demonstrate that the proposed variance-reduction deployment strategy achieves performance close to computationally expensive exact solutions while significantly reducing passenger waiting times.

Abstract

Autonomous ride-hailing platforms must strategically position idle robotaxis to minimize the wait times of prospective riders. We formalize this as the \emph{robotaxi placement problem} ($k$-RP). Given a finite metric space and a demand distribution over its points, the goal is to position $k$ robotaxis to minimize the expected total distance in a perfect matching between the robotaxis and $k$ random riders. We present several theoretical results for this stochastic optimization problem. First, we observe that sampling robotaxi locations independently according to the demand distribution yields a randomized $2$-approximation algorithm. Second, we present an explicit inapproximability bound via a novel gap-preserving reduction from the maximum coverage problem. Furthermore, while it is not even clear whether the exact expected cost of a placement can be computed efficiently on general metrics, we design an exact polynomial-time dynamic programming algorithm for $k$-RP in tree metrics by decoupling the stochastic matching dependencies. Finally, empirical evaluations on real-world ride-hailing data reveal that a variance-reduced random placement strategy is highly effective in practice, yielding expected wait times that are very close to those obtained by computationally heavy exact algorithms for the uniform capacitated $k$-median problem.

Problem

• Robotaxi placement
• stochastic demand
• expected ETA
• ride-hailing
• stochastic optimization

Innovation

• robotaxi placement
• stochastic optimization
• approximation algorithm
• dynamic programming
• tree metrics