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With increase in time-critical applications over the Internet, the need for differentiating services has become a major endeavor in research communities. One promising paradigm proposed to support such traffic diversity in the next-generation Internet is optical burst switching (OBS). In the literature, two simple but efficient approaches namely, threshold and wavelength-based techniques have been investigated under the resource allocation-based QoS management scheme as solutions to overcome the bandwidth requirement in the backbone. However, to the best of our knowledge, the wavelength-based technique has not been analytically studied for any arbitrary number of service classes. In this paper, we generalize the wavelength-based technique to support any number of classes. Firstly, we present a novel mathematical model for the wavelength-based technique for real-time and non-real-time service classes. The proposed model is then extended to support any arbitrary number of classes. Simulations conducted at the switch level validate the model.