Vorticity Dissipation Based Routing: A Fluid-Kinetic Framework for Loop-Free Transport in Ultra-Dense Networks

2026-08-20

AI Summary

本文提出基于涡度耗散的路由方法，利用流体动力学框架解决超密集网络中的环路问题，提高无线资源效率。

Abstract

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.

Problem

• ultra-dense networks
• routing loops
• signaling overhead
• topological anomalies
• radio-resource efficiency

Innovation

• vorticity dissipation-based routing (VDR)
• Helmholtz-Hodge decomposition
• gradient flow optimization
• loop-free equilibrium
• topological inefficiency