Heterogeneous Mean Field Game Framework for LEO Satellite-Assisted V2X Networks
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| Format: | Preprint |
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2026
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| _version_ | 1866917385312665600 |
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| author | Sun, Kangkang Li, Jianhua Chen, Xiuzhen Chen, Mingzhe Guo, Minyi |
| author_facet | Sun, Kangkang Li, Jianhua Chen, Xiuzhen Chen, Mingzhe Guo, Minyi |
| contents | 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 $K^*(N)=Θ(N^{1/3})$; for the joint queue-channel model ($d=2$), the scaling becomes $K^*(N)=Θ(N^{1/5})$ with logarithmic correction. The unified formula $K^*(N)=Θ(N^{α/(α+β)})$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Heterogeneous Mean Field Game Framework for LEO Satellite-Assisted V2X Networks Sun, Kangkang Li, Jianhua Chen, Xiuzhen Chen, Mingzhe Guo, Minyi Computer Science and Game Theory C.2.1; C.2.2; C.2.4 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 $K^*(N)=Θ(N^{1/3})$; for the joint queue-channel model ($d=2$), the scaling becomes $K^*(N)=Θ(N^{1/5})$ with logarithmic correction. The unified formula $K^*(N)=Θ(N^{α/(α+β)})$ 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. |
| title | Heterogeneous Mean Field Game Framework for LEO Satellite-Assisted V2X Networks |
| topic | Computer Science and Game Theory C.2.1; C.2.2; C.2.4 |
| url | https://arxiv.org/abs/2604.00621 |