In some embodiments, an apparatus includes a flow control module configured to receive a first data packet from an output queue of a stage of a multi-stage switch at a first rate when an available capacity of the output queue crosses a first threshold. The flow control module is configured to receive a second data packet from the output queue of the stage of the multi-stage switch at a second rate when the available capacity of the output queue crosses a second threshold. The flow control module configured to send a flow control signal to an edge device of the multi-stage switch from which the first data packet or the second data packet entered the multi-stage switch.