  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.
