An Ordinary Differential Equation Framework for Stability Analysis of Networks with Finite Buffers

TL;DR

This paper introduces an ODE-based framework to analyze the stability of networks with finite buffers, revealing how buffer limitations impact network stability and proposing conditions for stabilization.

Contribution

It develops a novel ODE model for buffered network dynamics and extends stability conditions from single-commodity to multi-commodity systems with buffer sharing.

Findings

Finite buffers can destabilize networks even in simple topologies.

The proposed ODE framework characterizes stabilizing policies for buffered networks.

Extended stability conditions apply to multi-commodity systems with buffer coupling.

Abstract

We consider the problem of network stability in finite-buffer systems. We observe that finite buffer may affect stability even in simplest network structure, and we propose an ordinary differential equation (ODE) model to capture the queuing dynamics and analyze the stability in buffered communication networks with general topology. For single-commodity systems, we propose a sufficient condition, which follows the fundamental idea of backpressure, for local transmission policies to stabilize the networks based on ODE stability theory. We further extend the condition to multi-commodity systems, with an additional restriction on the coupling level between different commodities, which can model networks with per-commodity buffers and shared buffers. The framework characterizes a set of policies that can stabilize buffered networks, and is useful for analyzing the effect of finite buffers on network stability.