We analyzed and improved a collision avoidance strategy, which was supported by Long Term Evolution-Vehicle (LTE-V)-based Vehicle-to-Vehicle (V2V) communication, for automated vehicles. This work was completed in two steps. In the first step, we analyzed the probability distribution of message transmission time, which was conditional on transmission distance and vehicle density. Our analysis revealed that transmission time exhibited a near-linear increase with distance and density. We also quantified the trade-off between high/low resource reselection probabilities to improve the setting of media access parameters. In the second step, we studied the required safety distance in accordance with the response time, i.e., the transmission time, derived on the basis of a novel concept of Responsibility-Sensitive Safety (RSS). We improved the strategy by considering the uncertainty of response time and its dependence on vehicle distance and density. We performed theoretical analysis and numerical testing to illustrate the effectiveness of the improved robust RSS strategy. Our results enhance the practicability of building driverless highways with special lanes reserved for the exclusive use of LTE-V vehicles.