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WDM broadcast-and-select star networks using fixed lasers and tunable optical filters are favored by the current state-of-the-art in technology over the other WDM star architectural forms. However networks of this architectural form suffer from low efficiency when the offered traffic is bursty. Under bursty traffic conditions, it is probable that some wavelengths are idle, while some other wavelengths are overloaded. Therefore, the overall network performance is degraded. In this paper a new MAC protocol which is capable of operating efficiently under bursty traffic conditions is introduced. According to the proposed protocol an array of tunable wavelength converters is placed at the network hub in order to uniformly distribute the incoming packets to the available wavelengths. In this way, the load is balanced between the wavelengths and consequently, the network performance is improved. The performance of the proposed protocol is studied via analytical and simulation results which indicate that a WDM star network operating under this protocol achieves a high throughput-delay performance under both bursty and non-bursty traffic conditions.