In this paper, we study the trade-off between the aggregate MAC flow throughput and the fairness in IEEE 802.11 based wireless mesh networks (WMNs) that utilize scheduling on top of the CSMA/CA access scheme. We use a toy WMN topology to allow us to understand easily this trade-off and propose an analytical model to study the interaction between contending links in this topology. Based on this model, we formulate the bandwidth scheduling problem as an aggregate MAC flow throughput maximization problem subject to the fairness requirements dictated by the scheduler. This study is dictated by the need to understand the limits of such scheduling algorithms which have proliferated in recent years to balance the throughput and fairness of WMNs without modifying the CSMA/CA protocol or the binary exponential backoff due to the non-programmability of the MAC and backoff procedure in modern commercial Wi-Fi chipset. As an example, we evaluate our previously proposed bandwidth scheduling mechanism -the so-called distributed fair MAC scheduler (DFMS) to validate our model on one hand and demonstrate the efficiency of our scheduler on the other.