The telecommunication industry is moving toward a converged network, which uses a single global IP based packet-switched network, which uses a single global IP based packet-switched network to carry all types of network services, the quality of service cannot be fully guaranteed [1]. One of the popular methods to guarantee the quality of service is to use resource reservation. This kind of methods, however, might cause resource underutilization because the resource requesters may not show up or, even if does, it does not fully utilize the reserved resources. In order to enhance the efficiency of resource utilization, this study proposed an efficient resource utilization concept, that is, over-admission. Over-admission, in which the admission controller may admit more traffic volume than what it can allowed. Even though over-admission is effective, it has its own problems: the admission controller may admit too excessive traffic to impair the system performance. In order to maintain system performance, it is important for the network administrators to find out the appropriate admitted amount that does not cause excessive overflow. In this thesis, an analysis model is constructed to estimate the optimal admitted traffic amount under various traffic conditions. Then, simulation is conducted to verify this model and to evaluate the performance of our proposed method. The results reveal that this analysis model can improve the efficiency of resource utilization.