## Adversarial contention resolution for simple channels (2005)

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Venue: | In: 17th Annual Symposium on Parallelism in Algorithms and Architectures |

Citations: | 32 - 1 self |

### BibTeX

@INPROCEEDINGS{Bender05adversarialcontention,

author = {Michael A. Bender and Bradley C. Kuszmaul},

title = {Adversarial contention resolution for simple channels},

booktitle = {In: 17th Annual Symposium on Parallelism in Algorithms and Architectures},

year = {2005},

pages = {325--332},

publisher = {ACM Press}

}

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### Abstract

This paper analyzes the worst-case performance of randomized backoff on simple multiple-access channels. Most previous analysis of backoff has assumed a statistical arrival model. For batched arrivals, in which all n packets arrive at time 0, we show the following tight high-probability bounds. Randomized binary exponential backoff has makespan Θ(nlgn), and more generally, for any constant r, r-exponential backoff has makespan Θ(nlog lgr n). Quadratic backoff has makespan Θ((n/lg n) 3/2), and more generally, for r> 1, r-polynomial backoff has makespan Θ((n/lg n) 1+1/r). Thus, for batched inputs, both exponential and polynomial backoff are highly sensitive to backoff constants. We exhibit a monotone superpolynomial subexponential backoff algorithm, called loglog-iterated backoff, that achieves makespan Θ(nlg lgn/lg lglgn). We provide a matching lower bound showing that this strategy is optimal among all monotone backoff algorithms. Of independent interest is that this lower bound was proved with a delay sequence argument. In the adversarial-queuing model, we present the following stability and instability results for exponential backoff and loglogiterated backoff. Given a (λ,T)-stream, in which at most n = λT packets arrive in any interval of size T, exponential backoff is stable for arrival rates of λ = O(1/lgn) and unstable for arrival rates of λ = Ω(lglgn/lg n); loglog-iterated backoff is stable for arrival rates of λ = O(1/(lg lgnlgn)) and unstable for arrival rates of λ = Ω(1/lg n). Our instability results show that bursty input is close to being worst-case for exponential backoff and variants and that even small bursts can create instabilities in the channel.