Optical Burst Switching (OBS) has recently been proposed as a candidate architecture for the next generation optical Internet. Several challenging issues remain to be solved to pave the way for the OBS vision. Contention arises in OBS networks when two or more bursts are destined for the same wavelength, and a wide variety of reactive contention resolution mechanisms have been proposed in the literature. One challenging issue in OBS is proactively controlling the traffic flowing through the OBS network so that the network does not stay in a persistent state of contention, which we call the congestion avoidance problem. Another challenging issue is the need for service differentiation, which is common today in electronically switched networks via the use of advanced buffer management and scheduling mechanisms. However, such mechanisms cannot be used in OBS networks due to the limited use, or total absence, of buffering. One of the popular existing approaches to service differentiation in OBS networks is the use of larger offset times for high-priority bursts which, however, increases the delays and may adversely affect application-level performance. In this paper, we propose a feedback-based rate control protocol for the control plane of the OBS network to both address the congestion avoidance and service differentiation issues. Using this protocol, the incoming traffic is dynamically shaped at the edge of the OBS network in order to avoid potential congestion in the burst-switched core. Moreover, the traffic shaping policies for the low and high priority traffic classes are different, and it is possible using the proposed protocol to isolate high-priority and low-priority traffic almost perfectly over time scales on the order of a few round-trip times. Simulation results are reported to validate the congestion avoidance and service differentiation capabilities of the proposed architecture.