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

Abstract

We consider the Adversarial Queuing Theory (AQT) model, where packet arrivals are subject to a maximum average rate 0 ≤ ρ ≤ 1 and burstiness σ ≤ 0. 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(ℓ d1/ℓ + σ) space suffice, where d is the number of distinct destinations and ℓ=⌋1/ρ⌊ and we show that Ω(1 over ℓ d1/ℓ + σ) space is necessary. For directed trees, we describe an algorithm whose buffer space requirement is at most 1 + d' + σ where d' is the maximum number of destinations on any root-leaf path.