This paper investigates the effectiveness of using P-persistent carrier sensing multiple access (P-Persistent CSMA) on vehicular connectivity as vehicles dynamically form temporary communication networks using simulation and mathematical modelling. In the connected and autonomous environment, effective and efficient connectivity between vehicles (V2V) and between vehicles and infrastructure (V2I) is critical. The simulation was performed in MATLAB and included the investigation of the effect of vehicular density, probability value change, and increase in Backoff time, and change in data frame size. The results showed that as vehicular density, probability, and data frame size increased, throughput decreased as data traffic increased, whereas as Backoff time and probability increased, throughput increased. Furthermore, as data size increases with decreasing probability level, channel utilization improves. Based on these findings and the derived mathematical expressions, a proposed dynamic and adaptive model is presented, allowing for maximum throughput while minimizing collisions. This is accomplished by equating four mathematical expressions and substituting them using iteration to achieve a balanced and optimal level of communication channel utilization by dynamically adjusting the three main parameters under consideration as a function of increasing vehicular density (P-Persistent probability level, Backoff time, and data frame length). To achieve such dynamical and adaptive optimization, four mathematical expressions are used. The resulting model is promising and will improve the efficiency of non-adaptive conventional P-Persistent CSMA. The presented work proved to increase the effectiveness of the conventional p-persistent technique using a multi-dimensional parameter correlation, which is more effective than weighted, slotted, or adaptive P-Persistent approaches.