A Random Early Detection (RED) policer in accordance with the invention does not tail-drop arriving packets as being non-conforming. For instance, because the RED policer uses a running estimate such as an exponential weighted moving average (EWMA), for example, it allows the policer to absorb traffic bursts. The policer uses randomization in choosing which packets to drop; with this method, the probability of dropping a packet from a particular sending node is roughly proportional to the node's bandwidth share, hence the packets of different flows are fairly dropped.