# New Insights from a Fixed Point Analysis of a Single Cell IEEE 802.11 Wireless Network

##
A. Kumar

### Indian Insitute of Science, Bangalore, INDIA

### Résumé:

We study a fixed point formalisation of the well known
analysis of Bianchi. We provide a significant simplification and
generalisation of the analysis. In this more general framework, the
fixed point solution and performance measures resulting from it are
studied. Uniqueness of the fixed point is established. Simple and
general throughput formulas are provided. It is shown that the
throughput of any flow will be bounded by the one with the smallest
transmission rate. In an asymptotic regime, explicit formulas for the
collision probability, the aggregate attempt rate and the aggregate
throughput are provided.