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We present queue length based fair queueing (QLFQ), a scheme to approximate fair bandwidth allocation without per-flow state. Edge routers divide each flow into a set of layers using a linear encoding scheme and insert an appropriate label into each packet header. Core routers maintain a dropping threshold according to the current queue length at each router; packets with a label greater than the threshold are dropped. We have evaluated QLFQ together with CSFQ (core-stateless fair queueing) and RFQ (rainbow fair queueing) with several different configurations and traffic sources. The simulation results show that QLFQ is able to achieve approximately fair bandwidth sharing in all of these scenarios. The performance of QLFQ is comparable to that of CSFQ, and it performs much better than RFQ. The simulations also show that in an environment with bursty traffic sources, QLFQ provides much better fairness than CSFQ.