One embodiment of the present invention provides a switch. During operation, the switch maintains a first counter to indicate a first number of packets in a queue of the switch. The switch then determines whether a clock of the switch has reached a threshold value. If the clock reaches the threshold value, the switch starts maintaining a second counter to indicate a second number of packets in the queue that have been received after the clock has reached the threshold value. The switch continues to decrement the first counter in response to a packet leaving the queue until the first counter reaches a value of zero. When the clock reaches a maximum value supported by the clock, the switch drops a third number of packets from the queue indicated by the first counter.