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A learning-automata-based protocol for WDM passive star networks, which is capable of operating efficiently under bursty and correlated traffic, is introduced. According to the proposed protocol, the stations which grant permission to transmit at each time slot, are selected by means of learning automata. The choice probabilities of the selected stations are updated by taking into account the network feedback information. The probability updating scheme is designed in such a way, that the number of idle slots tends to be minimized, while the bandwidth of each wavelength Is allocated to the stations according to their needs.