Traffic Divergence Theory: An Analysis Formalism for Dynamic Networks
Matin Macktoobian, Zhan Shu, Qing Zhao
TL;DR
The paper introduces Traffic Divergence Theory (TD), a flow-based formalism for modeling dynamic networks by partitioning traffic into node divergences $\nabla_{u}$, link divergences $\nabla_{u,v}$, and route divergences $\nabla_{\Omega}$. A central concept is maximal traffic distribution, defined by $\Delta_{u,v}=1$ for neighboring pairs, with a localized condition and a spatial–temporal coupling captured by the TD rates $\square_{u}$ and $\boxplus_{u}$. The authors derive spatial and temporal dynamics, establish node-link-route correspondences, and validate the framework on datacenter throughput and robot ad-hoc network planning through simulations. Overall, TD provides a scalable, locality-aware tool for analyzing congestion, routing, and energy-aware design in heterogeneous networks.
Abstract
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic divergence, which captures the flow (im)balance of network nodes and links. It features various analytical probes to investigate both spatial and temporal traffic dynamics. In particular, the maximal traffic distribution in a network can be characterized by spatial traffic divergence rate, which reveals the relative difference among node traffic divergence. To illustrate the usefulness, we apply the theory to two network-driven problems: throughput estimation of data center networks and power-optimized communication planning for robot networks, and show the merits of the proposed theory through simulations.