In the EDD connection admission control scheme, a connection is established if its allowable end-to-end delay is larger than or equal to the worst-case end-to-end delay, and the timing of assignment of the difference (called a delay margin) between the two delays is an important issue. In conventional assignment methods, the assignment is performed when the connection establishment request is accepted. In this paper, we propose a new assignment method in which the assignment is not performed when the connection establishment request is accepted, and is performed when it is necessary to establish a connection in the future. Simulation results show that the maximum number of established connections by the proposed method is roughly equal to or up to 1.30 times as large as those by conventional ones.