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Integrated services schemes have not been used to support QoS in OBS networks, largely because of the high control overhead involved in monitoring bursts continuously at intermediate nodes. In this paper, we propose for the first time, an integrated services scheme to support elastic QoS in OBS networks. Our scheme relieves intermediate nodes of the burden of monitoring individual bursts continuously, thus largely decreasing the control overhead. We show how absolute bandwidth guarantees can be provided, and how bandwidth used by each connection can be made elastic. We demonstrate the effectiveness of our scheme using simulation studies.