An application with guaranteed service only cares about whether or not the network can satisfy its performance requirement, such as end-to-end delay. However, the network wants to achieve the high utilization and performance guarantee simultaneously. If the end-to-end delay provided by the network can be allocated properly to each switching node, then the network resources can get a better utilization. Conventionally, the delay is allocated equally to each switching node along the path that the connections pass through, referred to as equal (EQ) allocation policy. The advantage of this policy is easy to implement. However, we can not understand how this policy will affect the network utilization. In this paper, we will prove the EQ policy has good performance in excess bandwidth. We proposed an allocation scheme called MaxMin allocation to improve network utilization. With the excess bandwidth as the performance index, we have showed that MaxMin policy is an optimal scheme. In addition, we use the MaxMin allocation policy as the benchmark to compare with EQ policy, and we find the distinction of the performance between the EQ and MaxMin policy is tiny.