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Optical networks have been extensively investigated in recent years to provide high capacity for the Internet traffic. Among them the optical packet-switching network deploying buffering, wavelength conversion and multipath routing could be the most suitable one. It cannot only provide high capacity transport for Internet traffic but also achieve high utilization of the network resources. However due to the packet-oriented routing and switching, such a network can result in a large amount of packets out-of-order, packet loss and/or with various delays upon arriving at end systems, causing TCP flows that comprise those packets corrupted. Large amount of corrupted flows can increase the burstiness of the Internet traffic and cause higher-layer protocol to malfunction. This paper presents a novel routing and switching method for optical IP networks-flow routing. Without using a complicate control mechanism flow routing deals with packet-flows to reduce the amount of corrupted flows. The performance of the wavelength-converted optical flow router is investigated, based on a novel analytical model. A performance metric, i.e., good-throughput, is used, measuring the ratio of the amount of packets comprised in the noncorrupted flows to total amount of packets. Comparing with optical packet-switching routers, a remarkable improvement of good-throughput can be obtained by using optical flow routers. More important, using wavelength conversion can greatly improve the good-throughput of optical flow routers.