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In this paper, we exploit how to provide quality of service at the downlink in the OFDMA wireless communication systems. The OFDMA, also referred to as multiuser-OFDM, is considered as a strong candidate wireless system for the next generation mobile communications. Since there are a variety of traffic demands for real-time and non-real-time traffics in the next generation mobile communications, especially at the downlink from a base station, scheduling of such downlink traffic packets is expected to be a key function for QoS provisioning to users. One such scheduling algorithm designed not only to support multiple users simultaneously but also to offer real-time and non-real-time services to a user at the same time is the urgency and efficiency based packet scheduling (UEPS) algorithm [S. Ryu et al., 2005]. The UEPS algorithm uses the time-utility function as a scheduling urgency factor and the relative status of the current channel to the average one as an efficiency indicator of radio resource usage. The design goal to maximize throughput of non-real-time traffics with satisfying QoS requirements of real-time traffics.