  We provide a simple and accurate analytical model for multi-cell
infrastructure IEEE 802.11 WLANs. Our model applies if the cell radius, $R$, is
much smaller than the carrier sensing range, $R_{cs}$. We argue that, the
condition $R_{cs} >> R$ is likely to hold in a dense deployment of Access
Points (APs) where, for every client or station (STA), there is an AP very
close to the STA such that the STA can associate with the AP at a high physical
rate. We develop a scalable cell level model for such WLANs with saturated AP
and STA queues as well as for TCP-controlled long file downloads. The accuracy
of our model is demonstrated by comparison with ns-2 simulations. We also
demonstrate how our analytical model could be applied in conjunction with a
Learning Automata (LA) algorithm for optimal channel assignment. Based on the
insights provided by our analytical model, we propose a simple decentralized
algorithm which provides static channel assignments that are Nash equilibria in
pure strategies for the objective of maximizing normalized network throughput.
Our channel assignment algorithm requires neither any explicit knowledge of the
topology nor any message passing, and provides assignments in only as many
steps as there are channels. In contrast to prior work, our approach to channel
assignment is based on the throughput metric.
