Effective communication in vehicular networks depends on the scheduling of wireless channel resources. There are two types of channel resource scheduling in Release 14 of the 3GPP, i.e., (1) controlled by eNodeB and (2) a distributed scheduling carried out by every vehicle, known as Autonomous Resource Selection (ARS). The most suitable resource scheduling for vehicle safety applications is the ARS mechanism. ARS includes (a) counter selection (i.e., specifying the number of subsequent transmissions) and (b) resource reselection (specifying the reuse of the same resource after counter expiry). ARS is a decentralized approach for resource selection. Therefore, resource collisions can occur during the initial selection, where multiple vehicles might select the same resource, hence resulting in packet loss. ARS is not adaptive towards vehicle density and employs a uniform random selection probability approach for counter selection and reselection. As a result, it can prevent some vehicles from transmitting in a congested vehicular network. To this end, the paper presents Truly Autonomous Resource Selection (TARS) for vehicular networks. TARS considers resource allocation as a problem of locally detecting the selected resources at neighbor vehicles to avoid resource collisions. The paper also models the behavior of counter selection and resource block reselection on resource collisions using the Discrete Time Markov Chain (DTMC). Observation of the model is used to propose a fair policy of counter selection and resource reselection in ARS. The simulation of the proposed TARS mechanism showed better performance in terms of resource collision probability and the packet delivery ratio when compared with the LTE Mode 4 standard and with a competing approach proposed by Jianhua He et al.