In this paper, we propose an optimization method for the broadcast rate in vehicle-to-vehicle (V2V) broadcast communications at an intersection on the basis of theoretical analysis. We consider a model in which locations of vehicles are modeled separately as queuing and running segments and derive key performance metrics of V2V broadcast communications via a stochastic geometry approach. Since these theoretical expressions are mathematically intractable, we developed closed-form approximate formulae for them. Using them, we optimize the broadcast rate such that the mean number of successful receivers per unit time is maximized. Because of the closed form approximation, the optimal rate can be used as a guideline for a real-time control-method, which is not achieved through time-consuming simulations. We evaluated our method through numerical examples and demonstrated the effectiveness of our method.