In a network of interconnected edge and core routers, where packet data flows are received at edge routers and then transmitted toward intended destinations via a path through one or more core routers, fair bandwidth sharing is achieved without per-flow state monitoring in the interior routers. Each edge router is arranged to divide each input data flow into a set of layers each having an associated level, based on rate. The division process is done without reference to the content of the flow, and can use layers of equal or unequal size. The packets in a flow are marked at an edge router with their layer level, in a globally consistent manner. Each core router maintains a layer level threshold, based upon buffer management conditions, and drops layers whose level exceeds the threshold. During congestion, the level threshold is decreased; when congestion clears, the level threshold is increased.