We consider the stability of the longest-queue-first (LQF) scheduling policy in wireless networks with multihop traffic under the one-hop interference model. Although it is well known that the back-pressure (BP) algorithm achieves the maximal stability, its computational complexity is very high. In this paper, we consider LQF, a low-complexity scheduling algorithm, which has been shown to have near optimal throughput performance in many networks with single-hop traffic flows. We are interested in the performance of LQF for multihop traffic flows. In this scenario, the analysis of local-pooling factors for LQF does not carry through because of the complicated coupling between queues due to multihop traffic flows. Using fluid limit techniques, we show that LQF achieves the maximal stability for linear networks with multihop traffic and a single destination under the one-hop interference.
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