In recent years, a tremendous number of multimedia applications have come into widespread use in Internet environments. In multimedia communications, data, video and voice are transmitted through high speed networks. Their common transmission characteristics must satisfy the requirements of quality of service (QoS). For instance, low delay, bounded blocking rate and high throughput are fundamental factors influencing QoS. There exist many scheduling disciplines designed to guarantee QoS. In QoS guarantees, delay and loss are the main factors determining system performance. In voice transmission over the Internet (VoIP), latency is the most sensitive issue. In this paper, we focus on optimal system delay calculations based on proper bandwidth allocations. We address the problems related to the total system delay required for optimization and present a blocking probability estimation based on the large deviation principle (by LDP). More bandwidth can decrease the value of the delay, but more system resources will be exhausted. Less bandwidth may cause traffic to become congested. Schemes improve the performance when congestion occurs is not intelligent. Therefore searching for an efficient scheme to achieve optimal bandwidth allocation based on the minimum delay before congestion occurs is an important research goal. We use the Lagrange multiplier methods to achieve the optimal delay control in this paper. The system resources are dynamically adjusted according to different bandwidth requirements. Our contribution to the optimal delay is bounded as a function of the ratio of the input stream rate to the service rate, and a quick calculation for estimating the blocking probability accompanied by effective bandwidth calculations under some constraints is also provided. It is proved that a unique optimal solution exists. The technology presented here can be used by resource managers to design gateways for Internet environments.