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This paper introduces a frame-based round-robin arbitration scheme with explicit feedback control (FRE) for combined input-crosspoint buffered packet switches. We consider a CICB switch with fixed-length packets, called cells. The proposed scheme dynamically sets the frame size according to the amount of cell accumulation at the input queues. We study FRE when applied to a continuous system. We transport the FRE concept into a discrete system as an arbitration scheme for a packet switch, and study the switching performance. We combine FRE, which is used as the input arbitration scheme, with other round-robin based schemes, used as output arbitration schemes. The resulting combined schemes provide high throughput under several admissible traffic patterns when used in a switch with one-cell crosspoint buffers and no speedup.