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A time-domain wavelength interleaved network (TWIN) (Widjaja, I. et al., IEEE Commun. Mag., vol.41, 2003) is an optical network with an ultrafast tunable laser and a fixed receiver at each node. We consider the problem of scheduling bursts of data in a TWIN. Due to the high data rates employed on the optical links, the burst transmissions typically last for very short times compared with the round trip propagation times between source-destination pairs. A good schedule should ensure that: 1) there are no transmit/receive conflicts; 2) propagation delays are observed; 3) throughput is maximized (schedule length is minimized). We formulate the scheduling problem with periodic demand as a generalization of the well-known crossbar switch scheduling. We prove that even in the presence of propagation delays, there exist a class of computationally viable scheduling algorithms which asymptotically achieve the maximum throughput obtainable without propagation delays. We also show that any schedule can be rearranged to achieve a factor-two approximation of the maximum throughput even without asymptotic limits. However, the delay/throughput performance of these schedules is limited in practice. We consequently propose a scheduling algorithm that exhibits near optimal (on average within ∼7% of optimum) delay/throughput performance in realistic network examples.