An Intelligent Transportation System (ITS), which implements information collection services and information support services for rapidly moving vehicles, requires a special-purpose communication system such as the Radio Frequency Dedicated Short Range Communication (RF-DSRC) system. Before Road Side Equipment (RSE) and On-Board Equipment (OBE) are able to communicate with RF-DSRC, OBE must first request Link Initialization Access using the Activation Channel (ACTC) in an allocated Activation Slot (ACTS) through the Slotted ALOHA protocol. Even though Link Initialization Access is an important element in choosing the performance of a communication system, adapting RF-DSRC characteristics through an optimal mathematic modeling study of Link Initialization Access is not enough. Thus, in this paper we propose novel mathematical modeling of Link Initialization Access of RF-DSRC. Activation Probability is used to prevent overload communication by trying to access. In addition, RSE that sets up Activation Probability provides OBEs the ability to prepare Link Initialization Access. We hypothesize that mathematical modeling of Link Initialization Access should consider Activation Probability in terms of the more adaptive characteristics of RF-DSRC in order to prevent a decline in performance communication by delaying Link Initialization Access. So, in this paper we analyzed Link Initialization Access success probability considering Activation Probability. It will be based on the decided scope of Activation Probability by setting RSE.