The on-demand multicast [1] is a novel scheme to reduce the video delivery cost for the streaming video applications. Unlike the conventional multicast, this scheme enables the transmission of the multicast data to multiple recipients at distinct times. This property is important for the streaming video applications since the users usually access the video program at different times. To deliver the same multicast data to the recipients at distinct times, the on-demand multicast scheme temporarily caches a sliding window of the incoming stream on a router (or a proxy) and then forwards it on different links at distinct times to generate time variant outgoing streams. By carefully scheduling the departure time on each router's outgoing streams, a video stream can be distributed to the recipients at their expected times. Based on this scheme, this paper presents three routing algorithms on an asymmetric transmission network model, such as cable systems and ADSL systems. The simulation results indicate that our algorithm offers an outstanding performance in reducing the number of multicast streams and the network bandwidth. In addition, our simulation results are valuable to plan the system resources when deploying the video-on-demand systems.