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Although several routing algorithms for LEO satellite networks have been proposed in the literature, the issue of providing guaranteed end-to-end delay bound QoS for with good throughput has not been solved. The motivation to design such an algorithm is based on the fact that LEO satellite networks are likely to play an important role in the future Internet. In this paper, weighted fair queuing (WFQ) is introduced into the LEO satellite system with the aim of providing end-to-end delay guarantees. High performance satellite routing (HPSR), which is able to provide a guaranteed end-to-end delay bound for LEO satellite networks with high throughput, is put forward. Unlike previously reported algorithms, HPSR applies a route computation algorithm which takes statistical multiplexing among connections into consideration, and which is able to obtain good system throughput. Through simulations on an Iridium-like constellation, the proposed approach is shown to achieve a guaranteed end-to-end delay bound with higher throughput as compared to a previously reported routing scheme.