All-optical networks (AONs) with a broadcast-star based physical topology offer the possibility of transmission scheduling to resolve channel and receiver conflicts. This paper considers the problem of scheduling packet transmissions in a wavelength-division multiplexed (WDM) optical network with tunable transmitters and fixed-tuned receivers. The scheduling problem is complicated by tuning latency, a limited number of channels, and arbitrary traffic demands. We first analyze scheduling all-to-all packet transmissions and obtain a new lower bound for the schedule length. The lower bound is achieved by an algorithm proposed by Pieris and Sasaki (1994). We then extend the analysis to the case of arbitrary traffic demands and obtain lower bounds for the schedule length. Two constructions for scheduling algorithms are provided through list scheduling and multigraphs. The upper bounds so obtained not only provide performance guarantees with arbitrary demands, but also nearly meet the lower bound in simulations.
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