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In this study, the authors propose a cross-layer resource allocation scheme for push to talk (PTT) service over orthogonal frequency division multiple access (OFDMA)-based networks. In our modelling, the authors consider two traffic types: streaming traffic, which requires a maximum guaranteed average delay and elastic traffic with flexible rate requirements. PTT traffic is also considered as a streaming traffic with more flexible delay requirements comparing to conventional streaming traffic. The authors consider queue state information as well as channel state information in a cross-layer framework to maximise the total transmission rate of the elastic users, while average delay constraint for streaming users, and maximum transmission power constraint are satisfied. An algorithm is then proposed based on dual decomposition method to obtain the subcarrier assignment and power allocation for each user. Using simulations, the authors then evaluate the impact of the streaming PTT traffic and other system parameters on the total rate of elastic users.