For the efficient use of radio resource, semi-persistent scheduling (SPS) has been adopted to reduce control overhead required for resource allocation. In this letter, for voice over Internet protocol traffic, a lower bound on blocking probability and a closed-form maximum achievable control overhead reduction ratio are derived through a novel Markov chain model. Also, the performance evaluation of SPS under various resource assignment algorithms is provided on the blocking probability and overhead reduction ratio. Analytical expressions are validated through simulations.