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Providing the desired call blocking probability (CBP) to not only new but also existing calls has been a challenge for wireless mobile network service providers. To satisfy different requirements for new and handoff CBP, several call admission control (CAC) schemes have been proposed in the literature. Exact analysis of these schemes using 2D Markov chains is computationally intensive. Therefore, computationally efficient methods to analyze these systems using 1D Markov chain models have been considered. The "traditional" approach assumes that channel holding time for new and handoff calls have equal mean values. While the "normalized" approach relaxes this assumption, it is accurate only for the new call bounding CAC scheme. In this paper, we reevaluate the analytical methods for CBP probabilities for several widely known CAC schemes under more general assumptions by providing an easy to implement method. The numerical results show that when the average values of channel holding times for new and handoff calls are different the proposed approach gives more accurate results when compared with the traditional and normalized methods based on 1D Markov chain modeling, while keeping the computational complexity low.