Delivery of broadcast messages among vehicles for safety purposes, which is known as one of the key ingredients of Intelligent Transportation Systems (ITS), requires an efficient Medium Access Control (MAC) that provides low average delay and high reliability. To this end, a Geo-Location Based Access (GLOC) for vehicles has been proposed for Vehicle-to-Vehicle (V2V) communications, aiming at maximizing the distance of co-channel transmitters while preserving a low latency when accessing the resources. In this paper we analyze, with the aid of stochastic geometry, the delivery of periodic and non-periodic broadcast messages with GLOC, taking into account path loss and fading as well as the random locations of transmitting vehicles. Analytical results include the average interference, average Binary Rate (BR), capture probability, i.e., the probability of successful message transmission, and Energy Efficiency (EE). Mathematical analysis reveals interesting insights about the system performance, which are validated thought extensive Monte Carlo simulations. In particular, it is shown that the capture probability is an increasing function with exponential dependence with respect to the transmit power and it is demonstrated that an arbitrary high capture probability can be achieved, as long as the number of access resources is high enough. Finally, to facilitate the system-level design of GLOC, the optimum transmit power is derived, which leads to a maximal EE subject to a given constraint in the capture probability.