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For the passive star-coupled wavelength-division multiple-access (WDMA) network, a modified accelerative preallocation WDMA (MAP-WDMA) media access control (MAC) protocol is proposed, which is based on AP-WDMA. To show the advantages of MAP-WDMA as an adequate MAC protocol for the network over AP-WDMA, the channel utilization, the channel-access delay, and the latency of MAP-WDMA are investigated and compared with those of AP-WDMA under various data traffic patterns, including uniform, quasi-uniform type, disconnected type, mesh type, and ring type data traffics, as well as the assumption that a given number of network stations is equal to that of channels, in other words, without channel sharing. As a result, the channel utilization of MAP-WDMA can be competitive with respect to that of AP-WDMA at the expense of insignificantly higher latency. Namely, if the number of network stations is small, MAP-WDMA provides better channel utilization for uniform, quasi-uniform-type, and disconnected-type data traffics at all data traffic loads, as well as for mesh and ring-type data traffics at low data traffic loads. Otherwise, MAP-WDMA only outperforms AP-WDMA for the first three data traffics at higher data traffic loads. In the aspect of channel-access delay, MAP-WDMA gives better performance than AP-WDMA, regardless of data traffic patterns and the number of network stations.