Packets that are to be transmitted via a plurality of egress interfaces of a network device are stored in a memory of the network device. The packets are stored in a plurality of queues that respectively correspond to the egress interfaces. The network device determines a set of queues, from among the plurality of queues, for which packet dropping is enabled. The network device determines whether a utilization level of the memory meets a threshold. In response to determining that the utilization level of the memory meets the threshold: the network device randomly or pseudorandomly selects a first queue from the set of queues for which packet dropping is enabled, dequeues a first packet from the selected first queue, and deletes the first packet that was dequeued from the selected first queue.