Heterogeneous Mean Field Game Framework for LEO Satellite-Assisted V2X Networks

2026-04-01

AI Summary

This work addresses the scalability challenge of coordinating massive heterogeneous vehicular platoons (10⁴–10⁵ vehicles) under stringent latency constraints in next-generation V2X networks by proposing a heterogeneous mean-field game framework. It derives, for the first time, an error decomposition for ε-Nash equilibria and theoretically establishes that the optimal number of agent types scales as K*(N) = Θ(N¹/³), enabling cubic-root compression and substantially reducing computational complexity. The approach integrates Wasserstein distance to quantify heterogeneity, a G-prox primal-dual hybrid gradient (PDHG) algorithm for efficient computation, and a temporal graph neural network to model dynamic low-orbit satellite backhaul. Experiments demonstrate that only K = 28 representative types suffice to effectively coordinate 10⁵ vehicles, achieving 29.5% lower latency and 60% higher throughput compared to homogeneous baselines, with a 2.3× acceleration in PDHG convergence.

Abstract

Coordinating mixed fleets of $10^4$ to $10^5$ vehicles, passenger cars, freight trucks, and autonomous vehicles, under stringent delay constraints is a central scalability bottleneck in next-generation V2X networks. Heterogeneous mean field games (HMFG) offer a principled coordination framework, yet a fundamental design question lacks theoretical guidance: how many agent types $K$ should be used for a fleet of size $N$? The core challenge is a two-sided trade-off that existing theory does not resolve: increasing $K$ reduces type-discretization error but simultaneously starves each class of the samples needed for reliable mean-field approximation. We resolve this trade-off by deriving an explicit $\varepsilon$-Nash error decomposition driven by a Wasserstein-based heterogeneity measure, and prove that the unique error-minimizing type count satisfies $K^*(N)=Θ(N^{1/3})$ in the canonical one-dimensional queue setting. We further establish a heterogeneity-aware convergence condition for G-prox PDHG and extend the framework to temporal-graph LEO satellite backhaul dynamics with provable robustness guarantees. A perhaps surprising consequence is that even for $N=10^5$ vehicles, only about 28 type classes suffice, cube-root compression rather than per-vehicle modeling, so type-granularity selection is largely a set-once design decision. Experiments validate the scaling law, achieve $2.3\times$ faster PDHG convergence at $K=5$, and deliver up to $29.5\%$ lower delay and $60\%$ higher throughput compared with homogeneous baselines.

Problem

• Heterogeneous Mean Field Games
• V2X Networks
• Scalability
• Type Discretization
• LEO Satellite Backhaul

Innovation

• Heterogeneous Mean Field Games
• Type Granularity Optimization
• Wasserstein Heterogeneity Measure
• LEO Satellite Backhaul
• Scalable V2X Coordination