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In this study, the authors formulate the optimal radio resource allocation for OFDM-based relay networks with heterogeneous delay requirements. The authors consider streaming traffic that requires a maximum guaranteed average delay and elastic traffic with flexible rate requirements. The main objective is to maximise the total transmission rate of elastic users, while average delay constraint for streaming traffic is satisfied. In the proposed formulation we also consider transmit power constraint for the base station as well as each relay. The authors then propose an algorithm based on dual approach to find the optimum subcarrier, relay assignment and power allocation. Using simulations, the authors evaluate the impact of streaming traffic on the total rate of elastic users for different number of relays and various power constraints.