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In this paper we examine the feasibility of semi-persistent scheduling (SPS) for voice over IP (VoIP) by random access and evaluate its performance in terms of throughput of random access and traffic channels, and random access delay. We further investigate system stability issues and present methods to stabilize the system. To see the VoIP capacity gain, we show the maximum number of acceptable VoIP terminals without exceeding some front-end packet dropping (i.e., voice clipping) probability. In addition, we examine the effect of the parameter called implicit release after in the LTE standard on the system performance, which is used for silence period detection. Our performance evaluation model based on Equilibrium Point Analysis is compared to simulations.