State Dependent Attempt Rate Modeling of Single Cell IEEE~802.11 WLANs with Homogeneous Nodes and Poisson Packet Arrivals

Analytical models for IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known \textit{decoupling approximation} proposed by Bianchi for modeling single cell WLANs consisting of saturated nodes. In this paper, we provide a new approach to model the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model $M$ queues (one queue per node) served by the CSMA/CA protocol as standardized in the IEEE 802.11 DCF MAC protocol. The approximation is that, when $n$ of the $M$ queues are non-empty, the transmission attempt probability of the $n$ non-empty nodes is given by the long-term transmission attempt probability of $n$ "saturated" nodes as provided by Bianchi's model. The SDAR approximation reduces a single cell WLAN with non-saturated nodes to a "coupled queue system". When packets arrive to the $M$ queues according to independent Poisson processes, we provide a Markov model for the coupled queue system with SDAR service. \textit{The main contribution of this paper is to provide an analysis of the coupled queue process by studying a lower dimensional process, and by introducing a certain conditional independence approximation}. We show that the SDAR model of contention provides an accurate model for the DCF MAC protocol in single cells, and report the simulation speed-ups thus obtained by our \textit{model-based simulation}.