Data Transfer among international switchboard network in generally as Service of Digital Network (ISDN) are very important to be considered in the design process. This study aim at identifying the nature and mechanism of the Time Delay which immensely affects data transfer and later on identifying networks characteristics, through implementing the Mathematical Model to calculate Time- Delay caused by the control channel on the subscriber line in case of primary signing in PRI into the (ISDN).Queuing System (QS) model was introduced in order to examine time characteristics of PRI.