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This paper proposes a novel algorithm based on the existing deficit round robin (DRR) to provide relative differentiated delay service such that it is possible to support real time applications over the Internet. In our algorithm, a method based on the fluid-flow traffic model is first presented to compute the service rate for each priority traffic flow. The sending quantum that is proportional to the service rate is then determined, and a time varying deficit round-robin algorithm is provided to send the packets to the next router. Our algorithm only requires minor changes to the infrastructure of the current Internet. Thus, it is a very possible choice to upgrade the best effort service of the current Internet.