Border Effects, Fairness, and Phase Transition in Large Wireless Networks

We characterize the fairness of decentralized medium access control protocols based on CSMA/CA, such as IEEE 802.11, in large multi-hop wireless networks. In particular, we show that the widely observed unfairness of the protocol in small network topologies does not always persist in large topologies. This unfairness is essentially due to the unfair advantage of nodes at the border of the network, which have a restricted neighborhood and thus a higher probability to access the communication channel. In large one-dimensional networks these border effects do not propagate inside the network, and nodes sufficiently far away from the border have equal access to the channel; as a result the protocol is long-term fair. In two-dimensional networks, we observe a phase transition. If the access intensity of the protocol is small, the border effects remain local and the protocol behaves similarly as in one- dimensional networks. However, if the access intensity of the protocol is large enough, the border effects persist independently of the size of the network and the protocol is strongly unfair. Finally, in situations where the protocol is long-term fair, we provide a characterization of its short-term fairness.