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In this paper, we propose a cross-layer resource-allocation scheme for orthogonal frequency-division multiple-access (OFDMA) systems with imperfect channel-state information (CSI). In our modeling, we consider two traffic types: 1) streaming traffic, which requires a maximum guaranteed average delay, and 2) elastic traffic with flexible rate requirements. We then consider queue-state information (QSI) and CSI in a cross-layer framework to maximize the total transmission rate of elastic users while the average delay constraint for streaming users and the maximum transmission power constraint are satisfied. We also consider the impact of imperfect CSI. An algorithm is then proposed based on the dual decomposition method to obtain the subcarrier assignment and power allocation for each user. Using simulations, we evaluate the impact of streaming traffic on the total achievable rate of elastic users for different values of the required outage probability. It is also shown by simulation that, by increasing the variance of CSI estimation, the total rate of elastic traffic is decreased.