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In this paper, we consider real-time speech traffic, real-time circuit-switched data (CSD) and nonreal-time packet-switched data (PSD) in the UMTS terrestrial radio access network (UTRAN). The focus is on the single low-bandwidth link that interconnects the radio network controller (RNC) and the base station (node B). We show that all traffic on this link has real-time requirements. But we take advantage of the radio link control (RLC) layer protocol and formulate suitable quality of service (QoS) criteria that lead to two different transport service classes (TSC): A stringent TSC for speech traffic and CSD, and a tolerant TSC for PSD. The RNC transmits packets from both TSCs via a single low-bandwidth link to the node B. Since transmission capacity on this interface is a serious cost factor in the UTRAN, the link utilization should be optimized while respecting the QoS requirements of both TSCs. We propose a modified version (MEDF) of the earliest deadline first (EOF) algorithm for that task. In contrast to EDF, the MEDF is easy to implement in hardware and in contrast to algorithms like weighted fair queueing (WFQ), the knowledge of the traffic mix is not needed for a suitable parameter setting in the MEDF scheduler. The simulation results show its superiority over first-in-first-out (FIFO), static priority (SP), and weighted round robin (WRR) scheduling. The analysis of the waiting time distribution explains why MEDF performs better than the other scheduling strategies.