  Performance evaluation of the 802.11 MAC protocol is classically based on the
decoupling assumption, which hypothesizes that the backoff processes at
different nodes are independent. This decoupling assumption results from mean
field convergence and is generally true in transient regime in the asymptotic
sense (when the number of wireless nodes tends to infinity), but, contrary to
widespread belief, may not necessarily hold in stationary regime. The issue is
often related with the existence and uniqueness of a solution to a fixed point
equation; however, it was also recently shown that this condition is not
sufficient; in contrast, a sufficient condition is a global stability property
of the associated ordinary differential equation. In this paper, we give a
simple condition that establishes the asymptotic validity of the decoupling
assumption for the homogeneous case. We also discuss the heterogeneous and the
differentiated service cases and formulate a new ordinary differential
equation. We show that the uniqueness of a solution to the associated fixed
point equation is not sufficient; we exhibit one case where the fixed point
equation has a unique solution but the decoupling assumption is not valid in
the asymptotic sense in stationary regime.
