A Novel Proportional Fairness Criterion for Throughput Allocation in   Multirate IEEE 802.11
  This paper focuses on multirate IEEE 802.11 Wireless LAN employing the mandatory Distributed Coordination Function (DCF) option. Its aim is threefold. Upon starting from the multi-dimensional Markovian state transition model proposed by Malone \textit{et.al.} for characterizing the behavior of the IEEE 802.11 protocol at the Medium Access Control layer, it presents an extension accounting for packet transmission failures due to channel errors. Second, it establishes the conditions under which a network constituted by $N$ stations, each station transmitting with its own bit rate, $R^{(s)}_d$, and packet rate, $\lambda_s$, can be assumed loaded. Finally, it proposes a modified Proportional Fairness (PF) criterion, suitable for mitigating the \textit{rate anomaly} problem of multirate loaded IEEE 802.11 Wireless LANs, employing the mandatory DCF option. Compared to the widely adopted assumption of saturated network, the proposed fairness criterion can be applied to general loaded networks.   The throughput allocation resulting from the proposed algorithm is able to greatly increase the aggregate throughput of the DCF, while ensuring fairness levels among the stations of the same order as the ones guaranteed by the classical PF criterion.   Simulation results are presented for some sample scenarios, confirming the effectiveness of the proposed criterion for optimized throughput allocation. 
M. Laddomada, F. Mesiti, M. Mondin, and F. Daneshgaran