A Markovian Traffic Equilibrium Model for Ride-Hailing

2026-04-23

AI Summary

This study addresses the dynamic decision-making of vacant and occupied ride-hailing vehicles in urban road networks, endogenously capturing inter-vehicle competition for passenger demand and link-level traffic congestion. The authors propose a Markov traffic equilibrium model in which drivers’ order-acceptance and routing choices are formulated as an infinite-horizon semi-Markov decision process aimed at maximizing discounted rewards, with equilibrium characterized via a fixed-point system. A key innovation lies in jointly incorporating drivers’ forward-looking behavior and link congestion within a unified equilibrium framework, demonstrating that omitting either factor leads to substantial biases in policy evaluation. The model’s validity is empirically verified on real-world road networks using a relaxed fixed-point iteration algorithm combined with network equilibrium analysis, proving convergence under certain network structures and quantifying the evaluation errors induced by conventional simplifying assumptions.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Game Theory and Economic Paradigms: Equilibrium
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We develop a Markovian traffic equilibrium model for ride-hailing in which vehicles, whether empty or hired, make sequential order-acceptance and link-choice decisions over a traffic network to maximize total discounted return in an infinite-horizon semi-Markov decision process. The model endogenizes both competition among empty vehicles for passenger demand and traffic congestion arising from road usage at the link level. We characterize equilibrium as the solution to a fixed-point system, establish its existence, and develop relaxed fixed-point iteration algorithms for equilibrium computation, with convergence results for specialized network structures. Computational experiments on realistic networks demonstrate the model's practical value for transportation planning. Ablation analyses reveal that ignoring either traffic congestion or drivers' forward-looking behavior can lead to potentially substantial biases in policy evaluation.

Problem

• ride-hailing
• traffic equilibrium
• congestion
• forward-looking behavior
• Markov decision process

Innovation

• Markovian traffic equilibrium
• ride-hailing
• semi-Markov decision process
• endogenous congestion
• fixed-point iteration