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 congestion in the internal memory of the network switch device, a flow control engine triggers, during respective timeslots of a timing schedule and while the flow control engine continues to monitor congestion in the internal memory of the network switch device, transmission of respective flow control messages via different subsets of ports, among the plurality of ports, to control flow of packets from different subsets of upstream network device, among the plurality of upstream network devices, to the network switch device so that flow control is distributed over time among upstream network devices of the plurality of upstream network devices.