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

TL;DR

This paper introduces a heterogeneity-aware mean field game framework for LEO satellite-assisted V2X networks, providing a principled method to select agent types that balances heterogeneity representation and approximation accuracy.

Contribution

It derives an explicit type-selection law and scalable equilibrium solver, enabling efficient large-scale network optimization with theoretical and empirical validation.

Findings

Optimal number of agent types scales as N^{1/3} for 1D models.

The proposed method achieves 2.3x faster convergence and significant delay and throughput improvements.

The solver complexity is independent of fleet size, suitable for large deployments.

Abstract

Coordinating mixed fleets of massive vehicles under stringent delay constraints is a central scalability bottleneck in next-generation mobile computing networks, especially when passenger cars, freight trucks, and autonomous vehicles share the same radio and multi-access edge computing (MEC) infrastructure. Heterogeneous mean field games (HMFG) are a principled framework for this setting, but a fundamental design question remains open: how many agent types should be used for a fleet of size $N$? The difficulty is a two-sided trade-off that existing theory does not resolve: using more types improves heterogeneity representation, but it reduces per-class sample size and weakens the mean-field approximation accuracy. This paper resolves that trade-off through an explicit $\varepsilon$-Nash error decomposition, a closed-form type-selection law, a heterogeneity-aware equilibrium solver, and a robust extension to time-varying LEO backhaul dynamics. For the 1D queue state space, the optimal type count satisfies $K^*(N)=\Theta(N^{1/3})$; for the joint queue-channel model ($d=2$), the scaling becomes $K^*(N)=\Theta(N^{1/5})$ with logarithmic correction. The unified formula $K^*(N)=\Theta(N^{\alpha/(\alpha+\beta)})$ provides dimension-dependent design guidance, reducing type granularity to a principled, set-once system parameter rather than a per-deployment tuning burden. Experiments validate the 1D scaling law with empirical slope $0.334 \pm 0.004$, achieve $2.3\times$ faster PDHG convergence at $K=5$, and deliver up to $29.5\%$ lower delay and $60\%$ higher throughput than homogeneous baselines. Unlike model-free DRL methods whose training complexity scales with the state-action space, the proposed HMFG solver has per-iteration complexity $O(K^2 N_q N_t)$ independent of fleet size $N$, making it suitable for large-scale mobile edge computing deployment.