One of the key ingredients of Intelligent Transportation Systems (ITS) is delivery of broadcast status messages among vehicles for safety purposes. This requires an efficient Medium Access Control (MAC) that provides low average delay and high reliability. To this end, Carrier Sense Multiple Access (CSMA) has been commonly proposed for Vehicle Ad Hoc Networks (VANETs). Nevertheless, the hidden-node problem can jeopardize the reliability of CSMA, whereas the latency when accessing the channel can be unbounded. To overcome these limitations, resource allocation based on the geo-location of the vehicles can be applied in VANETs. For example, a distributed location based access (DLOC) algorithm has been proposed such that vehicles access orthogonal resource blocks based on their position, aiming at maximizing the distance of co-channel transmitters. In this paper we propose a stochastic geometry approach to analyze DLOC taking into account path loss and fading as well as the random location of transmitting vehicles. Analytical results include the average interference, average binary rate and capture probability, i.e. probability of successful message transmission. It is shown that increasing the number of RBs increases reliability but there is a trade off between reliability and average BR.
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