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This paper presents a comprehensive study of contention-resolution schemes in a multiwavelength optical packet-switched network. This investigation aims to provide a unified study of a network of optical routers, which include contention resolution in wavelength, time, and space dimensions. Specifically, we show: 1) how to accommodate all three dimensions of contention resolution in an integrated optical router; 2) how the performance of the three dimensions compare with one another; and 3) how various combinational schemes can be designed and how they perform. With the representative architectures and network topologies studied in this paper, the simulation experiment results capture the characteristics of different contention-resolution schemes, and they quantify the upper-bound average offered transmitter load for these schemes. The combinational contention resolution schemes are shown to effectively resolve packet contention and achieve good network performance under light to intermediate load.