Many traffic-related applications require the nodes in a vehicular ad-hoc network (VANET) to periodically broadcast their state information. As measurements campaigns or simulations to evaluate the reliability of packet transmission are slow and scenario-specific, we present an analytic performance assessment tool that accounts for the spatial statistics of the nodes on a road, in a scenario of crossing roads and fast fading. Based on stochastic geometry, our tool is able to capture a static two-dimensional road geometry and the effect of interference due to node clustering in the vicinity of an intersection. Numerical results reveal how packet transmission is affected as the receiver gets closer to the intersection.