AP Association in a IEEE 802.11 WLAN

The IEEE 802.11x protocol is currently the standard for wireless LANs (WLANs). It has been widely deployed in airports, coffee shops and homes. Users scan the wireless channel in order to find the access point (AP) which shows the highest signal strength and associate to it. User throughput in each AP is determined by the number of other users as well as the physical rate being used. In particular, it has also been observed that all the users connected to the same AP receive the same throughput. Resorting to non-cooperative game theory is quite suitable to model the way users compete selfishly for limited resources. Devising an optimal AP selection scheme depends on the existence of Nash equilibriums for the present game. In this paper, we prove that the model at hand is an ordinal potential game, known to have at least one PNE. Furthermore, we prove that an algorithm based on replicator dynamics converges to the PNEs of our game. Finally, to quantify the efficiency loss of the distributed game approach, known as the price of anarchy, we compare its performance against a centralized approach where resource allocation is made in a way that satisfies all mobile users. It turns out that even though the distributed game results are sub-optimal, the acceptable discrepancy between the two sets of results and the inherent adaptability of the decentralized approach makes it really promising.