The backpressure scheduling algorithm for multihop wireless networks is known to be throughput optimal, but it requires each node to maintain per-destination queues. Recently, a clever generalization of processor sharing has been proposed which is also throughput optimal, but which only uses per-link queues. Here, we propose another algorithm, called Queue-Proportional Rate Allocation (QPRA), which also only uses per-link queues and allocates service rates to links in proportion to their queue lengths, and employs the Serve-In-Random-Order queueing discipline within each link. Through fluid limit techniques and using a novel Lyapunov function, we show that the QPRA algorithm achieves the maximum throughput. We demonstrate an advantage of QPRA by showing that, for the so-called primary interference model, it is able to develop a low-complexity scheduling scheme which approximates QPRA and achieves a constant fraction of the maximum throughput region, independent of network size.