Each DMA channel has two AXI read interfaces. One interface is used for reading data buffers and the other interface is used for reading buffer descriptors. The DMA implements round-robin arbitration. Arbitration is never granted to any request if the common buffer does not have enough space. This way the DMA does not put back pressure on the AXI read channel.
If there is not enough space in the common buffer, the arbiter stays parked on the requesting channel until space is available.