  Vehicular safety communications (VSCs) are known to provide relevant
contributions to avoid congestions and prevent road accidents, and more
particularly at road intersections since these areas are more prone to
accidents. In this context, one of the main impairments that affect the
performance of VSCs are interference. In this paper, we develop a tractable
framework to model cooperative transmissions in presence of interference for
VSCs at intersections. We use tools from stochastic geometry, and model
interferer vehicles locations as a Poisson point process. First, we calculate
the outage probability (OP) for a direct transmission when the received node
can be anywhere on the plan. Then, we analyze the OP performance of a
cooperative transmission scheme. The analysis takes into account two
dimensions: the decoding strategy at the receiver, and the vehicles mobility.
We derive the optimal relay position, from analytical and simulation results,
for different traffic densities and for different vehicles mobility models. We
also show that the OP does not improve after the number of infrastructure
relays reached a threshold value. Finally, we show that the OP performance of
VSCs is higher at intersections than on highways. We validated our analytical
results by Monte-Carlo simulations.
