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As the typical delay tolerant networks, the satellite networks possess the intermittent connections, the large-scale time delays and the time-varying topologies. Obviously, such features seriously affect the delivery of mission data with certain requirements on the traffic or latency. To decrease the delivery time, existing relay-based contact graph routing (CGR) method selects the earliest reachable path to forward mission data. However, this method cannot guarantee the transmission of a large amount data and wastes the rare contact opportunities. Therefore, in this paper, we focus on the transmission QoS problem of multiple missions over the satellite networks, and design a QoS support routing strategy to achieve multiple flow-maximizing paths with acceptable delivery delays. Especially, with the storage time aggregated graph (STAG), we construct an on-demand mission model to depict both the network dynamic …