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A new probabilistic call admission control scheme is proposed for multiservice wireless networks. The new scheme gradually suppresses the admission rate of the new calls and of the calls of each service class (SC) supported considering their priorities independently. The scheme is examined both for a single SC and for multiple SCs under general conditions. The analysis employs Markov chain theory and yields analytical expressions for the call blocking probabilities. The proposed analytical method was validated via simulations employing different distributions for the channel holding time; the simulations demonstrated the accuracy of the proposed framework.