Packets received by a network switch device from upstream network devices, coupled to respective ones of a plurality of ports of the network switch device, are temporarily stored in an internal memory of the network switch device. In response to detecting a first congestion state in the internal memory, the network switch device transmits a first flow control message via a first subset of ports, without transmitting the flow control message via any port not included in the first subset of ports, to cause upstream network devices in a first subset of upstream network devices to temporarily suspend transmission of packets to the network switch device. The network switch device alternates between causing different subsets of the network devices to temporarily suspend transmission of packets to the network switch device, while continuing to monitor congestion in the internal memory of the network switch device.