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Router mechanisms designed to achieve fair bandwidth allocations, like fair queuing, have many desirable properties for congestion control in the Internet. However, such mechanisms usually need to maintain state, manage buffers, and/or perform packet scheduling on a per flow basis, and this complexity may prevent them from being cost effectively implemented and widely deployed. In this paper, architecture is proposed that significantly reduces this implementation complexity yet still achieves approximately fair bandwidth allocations. We apply this approach to routers, and we distinguish between edge routers and core routers. Edge routers maintain per flow state whereas core routers maintain no per flow state; they use FIFO packet scheduling augmented by a probabilistic dropping algorithm that uses the packet labels and an estimate of the aggregate traffic at the router. The scheme used here is core-stateless fair queuing and the simulations and analysis on the performance of this approach is presented.