In this paper, we propose router mechanisms to regulate unresponsivebest-effort traffic. By unresponsive traffic, we mean flows that do not reducetheir sending rate in response to congestion. The goal of the proposedmechanisms is to drop undeliverable packets as close to the periphery of thenetwork as possible. The key ideas of our approach are: (1) edge routers keeptrack of incoming flows and their arrival rates; (2) core routers use RED forqueue management and generate rate-limited source quenches on packet drops toadvice sources to reduce their sending rates; and (3) edge routers snoop onsource quenches passing through them and use them to control per-flowregulators. Regulators adjust their maximum sending rate using amultiplicative-decrease, additive-increase discipline. A decrease is triggeredby the arrival of a source quench; an increase is triggered byon-arrival of source quenches for a time period. We examine theimpact of these mechanisms for a variety of simulated network topologies andtraffic patterns.