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In this paper, we propose a variable-server queuing model to analyze the performance of an optical WDM network where connection requests arrive with differentiated SLA requirements, and they are provisioned by an appropriate protection scheme. The proposed model consists of three stages where each stage corresponds to one of these provisioning types. Each stage i scales the connection arrival rate with a coefficient αi which is related to the contribution of the corresponding provisioning scheme to the overall blocking probability. We generate various SLA classes and compare the results of our proposed analysis method to simulations under the NSFNET topology. Numerical results show that, our proposed model is able to provide a close lower bound to blocking probability, and a close upper bound for the average number of connections utilizing the wavelength channels.