The standard IEEE 802.3x is introduced to manage XON/XOFF flow control mechanism in full duplex gigabit Ethernet. In a IEEE 802.3x network, a downstream station can send XOFF messages to upstream stations to stop them from sending data until a specified time slot has passed or the downstream station receives a XON message. The development of efficient XON/XOFF flow control mechanism is still an active research topic. This paper describes FLORAX, a IEEE 802.3x XON/XOFF control scheme with proposed modifications. It introduces a hop-by-hop backpressure control based on flow rate in order to fully utilize the performance of large scale LANs. The control strategy of FLORAX is based on applying backpressure depending on the bandwidth of the flows, where flow is defined to be a source-destination MAC address pair. FLORAX allows the use of Service Level Agreement (SLA) for quality of service. FLORAX is fair in the sense that it distributes the bandwidth among flows during congestion. The simulation study is performed to compare the performance of earlier approaches with the FLORAX Experiment results demonstrate that FLORAX achieves fair bandwidth distribution for the duration of transmission, efficient use of link bandwidth, and reduction in packet loss.