In vehicular ad-hoc networks (VANETs) beaconing is one of the core communication modes, which is designed to advertise the presence of a car to its neighborhood. For practical applications the delivery of beacons containing the speed, the direction and the position of a car should be organized both timely and successfully. IEEE 802.11p is the most recent developing international standard, which specifies the physical (PHY) and the medium access control (MAC) protocols for car-to-car and car-to-infrastructure communication and is expected to lay the foundation for safety-related and infotainment applications in future VANETs. In previous works, it has been shown that the requirements of safety-related applications for the mean beacon transmission delay could be met for typical cases, but the corresponding probability of a successful beacon reception does not attain the required threshold. In this paper, we present a novel analytical method based on Markov chain for car-to-car communication analysis and investigate the influence of the beacon generation rate on the probability of a successful beacon reception in an IEEE 802.11p-based network.