In this letter, we propose a spatio-temporal analytical framework to comprehensively assess the performance of a statistical priority-based multiple access (SPMA) network. By combining tools from stochastic geometry with queueing theory, we characterize both the macroscopic interference distribution of the spatially interacting priority queues, and the microscopic temporal evolution of each priority queue. The proposed analytical framework allows to derive the analytical expressions of burst success probability, medium access probability (MAP), and packet success probability, and evaluate the impacts of key system parameters on a stable SPMA network. The advantage of SPMA is further highlighted by compared with the traditional CSMA scheme.