基于涡量耗散的路由：超密集网络中无环传输的流体动力学框架
Vorticity Dissipation Based Routing: A Fluid-Kinetic Framework for Loop-Free Transport in Ultra-Dense Networks
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中文总结 AI 辅助
本文提出基于涡量耗散的路由（VDR）框架，利用亥姆霍兹-霍奇分解解耦业务通量，通过涡量耗散实现无环传输，可抑制转发环路、降低延迟并具备良好扩展性。
中文摘要 AI 辅助
超密集无线网络中的离散路由协议受信令开销和瞬态路由环路的限制，这会降低无线资源效率。尽管连续建模提供了一种可扩展的替代方案，但现有的标量密度方法缺乏表征这些拓扑异常所需的向量几何结构。本文引入一种基于流体动力学的框架——基于涡量耗散的路由（VDR），利用亥姆霍兹-霍奇分解。我们证明宏观业务通量可正交解耦为需求驱动的无旋分量和代表路由涡量的环路诱导的螺线管分量。基于这一见解，我们将网络涡量定义为量化拓扑低效性的宏观指标。路由优化被表述为在熵函数上的梯度流，得到涡量耗散方程作为控制动力学定律。李雅普诺夫稳定性分析证明该机制确保全局熵的单调衰减，趋向渐近无环平衡。数值结果验证，VDR可抑制已实现的转发环路，降低端到端延迟，保持鲁棒的分组交付，并在固定区域密集化下呈现近线性缩放，同时明确考虑依赖网格的泊松求解器成本。
英文摘要
Discrete routing protocols in ultra-dense wireless networks are constrained by signaling overhead and transient routing loops that degrade radio-resource efficiency. While continuum modeling provides a scalable alternative, existing scalar density approaches lack the vector geometric structure required to characterize these topological anomalies. This paper introduces a fluid-kinetic framework, vorticity dissipation-based routing (VDR), utilizing the Helmholtz-Hodge decomposition. We demonstrate that the macroscopic traffic flux can be orthogonally decoupled into a demand-driven irrotational component and a loop-induced solenoidal component representing routing vorticity. Building on this insight, we define network vorticity as a macroscopic metric to quantify topological inefficiency. Routing optimization is formulated as a gradient flow on an enstrophy functional, yielding a vorticity dissipation equation as the governing dynamic law. Lyapunov stability analysis proves that this mechanism ensures the monotonic decay of global enstrophy toward an asymptotically loop-free equilibrium. Numerical results validate that VDR suppresses realized forwarding loops, reduces end-to-end delay, maintains robust packet delivery, and exhibits near-linear scaling under fixed-area densification while explicitly accounting for the grid-dependent Poisson-solver cost.
