With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing

TL;DR

This paper analyzes buffer space requirements in adversarial queuing models, revealing how space scales with traffic rate, burstiness, and destination count, providing both bounds and algorithms for efficient routing.

Contribution

It characterizes the space-bandwidth tradeoffs in routing under adversarial traffic, offering tight bounds and an algorithm for buffer management in directed trees.

Findings

O(k d^{1/k}) space suffices for general paths

Omega(1/k d^{1/k}) space is necessary

Buffer algorithm for directed trees with space at most 1 + d' + sigma

Abstract

We consider the Adversarial Queuing Theory (AQT) model, where packet arrivals are subject to a maximum average rate $0\le\rho\le1$ and burstiness $\sigma\ge0$. In this model, we analyze the size of buffers required to avoid overflows in the basic case of a path. Our main results characterize the space required by the average rate and the number of distinct destinations: we show that $O(k d^{1/k})$ space suffice, where $d$ is the number of distinct destinations and $k=\lfloor 1/\rho \rfloor$; and we show that $\Omega(\frac 1 k d^{1/k})$ space is necessary. For directed trees, we describe an algorithm whose buffer space requirement is at most $1 + d' + \sigma$ where $d'$ is the maximum number of destinations on any root-leaf path.