Fundamentals of the Backoff Process in 802.11: Dichotomy of the Aggregation

Details Fundamentals of the Backoff Process in 802.11: Dichotomy of the Aggregation Fundamentals of the Backoff Process in 802.11: Dichotomy of the Aggregation

2009-04-27

arxiv.org/abs/0904.4155v5

Computer Science

Networking and Internet Architecture

15 pages, 4 figures; An abstract version of this paper was presented at ACM SIGMETRICS Workshop on MAthematical performance Mo

Scientific paper

This paper discovers fundamental principles of the backoff process that governs the performance of IEEE 802.11. A simplistic principle founded upon regular variation theory is that the backoff time has a truncated Pareto-type tail distribution with an exponent of $(\log \gamma)/\log m$ ($m$ is the multiplicative factor and $\gamma$ is the collision probability). This reveals that the per-node backoff process is heavy-tailed in the strict sense for $\gamma>1/m^2$, and paves the way for the following unifying result. The state-of-the-art theory on the superposition of the heavy-tailed processes is applied to establish a dichotomy exhibited by the aggregate backoff process, putting emphasis on the importance of time-scale on which we view the backoff processes. While the aggregation on normal time-scales leads to a Poisson process, it is approximated by a new limiting process possessing long-range dependence (LRD) on coarse time-scales. This dichotomy turns out to be instrumental in formulating short-term fairness, extending existing formulas to arbitrary population, and to elucidate the absence of LRD in practical situations. A refined wavelet analysis is conducted to strengthen this argument.

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