In this paper, we first propose an analytical model of WLANs (Wireless LANs) with an arbitrary backoff distribution and AIFS (Arbitration Inter-Frame Space). From the analysis, we show that the achievable bandwidth is determined by the mean of backoff distribution regardless of the shape of the backoff distribution. We compare the effectiveness of four parameters on channel access differentiation, namely, the mean of backoff distribution, CWmin (Initial Contention Window), the number of backoff stages, and AIFS. Numerical results show that the mean of backoff distribution provides weighted fair channel access most accurately. Second, based on the proposed analytic frame work, we develop three schemes for the uplink/downlink bandwidth differentiation in order to achieve weighted fairness between uplink and downlink transmissions. Note that IEEE 802.11 is known to have unfairness between uplink and downlink accesses. Each scheme is characterized according to the corresponding channel access rule. The simulation results show that the proposed schemes achieve high system throughput while accurately differentiating bandwidth allocation.