In urban transit network inquiry system, the optimal scheme of bus line having excessive transfers requires us to consider limiting the number of transfers when to compute the optimal scheme of bus line [1], which can come down to shortest path problem limiting the number of intermediate vertex. And support system of QoS (Quality-of-Service) is playing a more and more important role in communication network. QoS routing problem [2] is to choose transmission path meeting the requirements of QoS service to hop counts, bandwidth, latency, packet loss rate etc. and ensuring effective use of global...