Long-term evolution (LTE)-based vehicular-to-everything (V2X) service is one of the promising technologies for supporting intelligent transportation systems (ITSs). LTE adopts a request-grant approach for allocating wireless resources. Each user follows a contention-based random access (RA) procedure to transmit its request. However, this procedure may result in unbounded delay if too many users compete for limited RA resources. Therefore, prioritized critical access in the LTE RA procedure is required to differentiate critical V2X services from noncritical ones.