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A hybrid electro-optic router is attractive, where packet buffering and table lookup are carried out in electrical domain and switching is done optically. In this paper, we propose a load-balanced optical switch (LBOS) fabric for a hybrid router. LBOS comprises N linecards connected by an N-wavelength WDM fiber ring. Each linecard i is configured to receive on channel λi. To send a packet, it can select and transmit on an idle channel based on where the packet goes. The packet remains in the optical domain all the way from input linecard to output linecard. Meanwhile, the loading in the ring network is perfectly balanced by spreading the packets for different destinations to use different wavelengths, and the packets for the same destination to use different time slots. With the pipelined operation of the LBOS, we show that LBOS can yield close-to-100% throughput performance. To address the ring-fairness problem under the inadmissible traffic patterns, an efficient throughput-fair scheduler is devised. To efficiently support multicast traffic, a simple multicast scheduler is also proposed. Finally, the linecard placement problem is investigated for further cutting down the average packet delay.