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.

翻译：本文研究有限缓冲区系统中的网络稳定性问题。我们观察到即使在最简单的网络结构中，有限缓冲区也可能影响稳定性，为此提出一种常微分方程（ODE）模型来捕捉排队动态，并分析具有一般拓扑结构的缓冲通信网络的稳定性。针对单商品系统，基于ODE稳定性理论，我们提出一个遵循背压基本思想的充分条件，使得局部传输策略能够稳定网络。我们进一步将该条件推广至多商品系统，并附加不同商品间耦合程度的限制条件，该框架可建模具有单商品缓冲区与共享缓冲区的网络。该框架刻画了一组能够稳定缓冲网络的策略，对分析有限缓冲区对网络稳定性的影响具有重要价值。