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

TL;DR

This paper uncovers fundamental principles of the IEEE 802.11 backoff process, revealing a heavy-tailed distribution and a dichotomy in aggregate behavior depending on the time-scale, with implications for fairness and practical performance.

Contribution

It introduces a unified view of the backoff process using regular variation theory and characterizes the dichotomy in aggregate behavior across different time-scales.

Findings

Backoff time has a truncated Pareto-type tail distribution.

Aggregate backoff process exhibits Poisson behavior on normal time-scales.

On coarse time-scales, the process shows long-range dependence.

Abstract

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.