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

02/21/2019

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by   Avery Miller, et al.

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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(k d^1/k) space suffice, where d is the number of distinct destinations and k= 1/ρ; and we show that Ω(1/k d^1/k) 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.