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The aviation community is currently working on the standardization of data communication systems for the future air traffic management. In this context, the International Civil Aviation Organization (ICAO) has initiated a work on standardization of an IPv6-based aeronautical telecommunications network and on future radio access technologies, respectively. In this paper, we integrate L-Band Digital Aeronautical Communications System Option 1 (L-DACS 1), which is one candidate for future radio access technologies, with realistic IPv6-based network layer functionality and analyze Deficit Round Robin (DRR) with fragmentation algorithm for the forward and return link in L-DACS 1. Our analysis mainly covers two application domains: file transfer and real-time services. We show that DRR with fragmentation scheduler provides good performance results in terms of throughput, delay, and bandwidth fairness.