Additive Increase Multiplicative Decrease (AIMD) window adjustment mechanism has been embedded in TCP in order to regulate the transmission rate in modern communication networks. In recent years, the AIMD (1,0.5) traffic regulation mechanism along with possibly additional enhancements, such as false timeout detection and explicit notification, has been considered in the carriers with Optical Burst Switching (OBS) as the underlying transmission technology. This paper introduces a novel rate control mechanism based on Generalized AIMD (α,β), called Burst AIMD (BAIMD), for tuning the rate control parameters (α, β) at each sender. BAIMD is designed to improve throughput while maintaining friendliness with co-existing AIMD (1,0.5) flows, and is characterized in the following two folds: (1) no burst window is required in the TCP sender's level; (2) no explicit notifications are required. The above characteristics make the proposed scheme distinguished from all the past reported counterparts by minimizing the signalling efforts and control complexity. The simulation result shows that BAIMD can solidly outperform the past reported AIMD-based (1,0.5) rate control schemes under a wide range of traffic loads. We also suggest that BAIMD rate control mechanism may serve as a better choice than AIMD (1,0.5) in the bufferless OBS networks due to its dynamic and flexible (α,β) parameter pair.