In this paper, we present an opportunistic packet scheduling algorithm to support both real-time (RT) and non-real-time (NRT) services in mobile broadband wireless access (MBWA) systems. Our design objective is to determine the maximum number of RT and NRT users with respect to the overall service revenue while satisfying individual QoS requirements, e.g., the maximum allowable packet loss rate for RT traffic and the minimum reserved bit rate for NRT traffic. As opposed to a typical priority queueing-based scheduling scheme in which RT users are always served a prior to NRT users while NRT users are served with the remaining resource, the proposed scheme takes the urgency of the RT service into account only when their head-of-line (HOL) packet delays exceed a given threshold. The delay threshold-based scheduling scheme allows for leveraging the multi-user diversity of NRT users, eventually maximizing the overall system throughput. By evaluating the proposed approach in an orthogonal frequency division multiple access/frequency division duplex (OFDMA/FDD)-based mobile access system, it is shown that the overall system throughput can be significantly improved in terms of the number of users or total service revenue.