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. A necessary condition for the validity of this approach in the asymptotic sense (when the number of wireless nodes tends to infinity) is the existence and uniqueness of a solution to a fixed point equation . However , it was also recently pointed out that this condition is not sufficient; in contrast, a necessary and sufficient condition is a global stability property of the associated ordinary differential equation. Such a property was established only for a specific case, namely for a homogeneous system (all nodes have the same parameters) and when the number of backoff stages is either two or infinite and with other restrictive conditions. 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. It is shown 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  .
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 .
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