Unified fixed point analysis of IEEE 802.11(e) WLAN under saturated and unsaturated conditions

Most of analysis so far for IEEE 802.11(e) WLANs focuses on saturated condition. But it is of practical value to take into account the unsaturation case. In this paper, we extend Bianchi's Markov back-off model to unsaturated condition but analyze it using renewal-reward theorem. In this more general framework, we study the fixed point solution of the system and provide a condition to guarantee both the uniqueness and balance of the fixed point. From the fixed point analysis we find that under unsaturated condition, network parameters should be designed according to the traffic load in order to avoid short-term unfairness or multistability. Then, we study the system throughput. Furthermore, in an asymptotic regime with a large number of nodes, we provide explicit formulas for the collision probability, the aggregate attempt rate and the aggregate throughput. All of our analysis based on unsaturated condition is the generalized analysis which can be applied to saturated condition as well. We provide the validation of our analysis through ns2 simulations.