For a bufferless statistical multiplexer allocating link bandwidth to a single class of connections with generally distributed call holding times, we study model-based call admission control (CAC) policies that map the number of calls in progress (state variable) to the admission decision (control variable). By formulating the CAC problem as a linear programming, establishing a convexity result, and applying the complementary slackness condition, we analytically prove that a randomized threshold CAC policy minimizes the call blocking probability subject to a packet loss quality-of-service requirement.