  This paper presents a modified proportional fairness (PF) criterion suitable
for mitigating the \textit{rate anomaly} problem of multirate IEEE 802.11
Wireless LANs employing the mandatory Distributed Coordination Function (DCF)
option. Compared to the widely adopted assumption of saturated network, the
proposed criterion can be applied to general networks whereby the contending
stations are characterized by specific packet arrival rates, $\lambda_s$, and
transmission rates $R_d^{s}$.
  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 of the ones available with the
classical PF criterion. Put simply, each station is allocated a throughput that
depends on a suitable normalization of its packet rate, which, to some extent,
measures the frequency by which the station tries to gain access to the
channel. Simulation results are presented for some sample scenarios, confirming
the effectiveness of the proposed criterion.
