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Combined input-crosspoint buffered switches relax arbitration timing and provide high-performance switching for packet switches with high-speed ports. It has been shown that these switches, with one-cell crosspoint buffer and round-robin arbitration at input and output ports, provide 100% throughput under uniform traffic. However, under admissible traffic patterns with nonuniform distributions, only weight-based selection schemes are reported to provide high throughput. This paper proposes a round-robin based arbitration scheme for a combined input-crosspoint buffered packet switch. The presented scheme uses adaptable-size frames, where the frame size is determined by the received service. The resulting switch provides nearly 100% throughput for several admissible traffic patterns, including uniform and unbalanced traffic, using one-cell crosspoint buffers.