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.

翻译：在严格时延约束下协调混合车队（包含\(10^4\)至\(10^5\)辆车辆、乘用车、货运卡车及自动驾驶车辆）是下一代V2X网络的核心可扩展性瓶颈。异构平均场博弈（Heterogeneous mean field games, HMFG）提供了一种原则性协调框架，但一个基础设计问题缺乏理论指导：对于规模为\(N\)的车队，应使用多少种智能体类型\(K\)？核心挑战在于现有理论未能解析的双边权衡：增加\(K\)可降低类型离散化误差，但同时导致每类样本稀缺，削弱平均场近似的可靠性。我们通过推导基于Wasserstein异质性度量的显式\(\varepsilon\)-Nash误差分解解决了这一权衡，并证明在经典一维队列场景中，唯一误差最小化的类型数量满足\(K^*(N)=Θ(N^{1/3})\)。我们进一步建立了G-prox PDHG的异质性感知收敛条件，并将框架扩展至具有可证明鲁棒性保证的时间图低轨卫星回程动力学。一个可能令人惊讶的结论是：即使对于\(N=10^5\)辆车辆，仅需约28个类型类即可——立方根压缩而非单车建模，因此类型粒度选择基本是一次性设计决策。实验验证了该缩放定律，在\(K=5\)时实现PDHG收敛速度提升2.3倍，与同构基线相比，时延降低高达29.5%，吞吐量提升60%。