Stability analysis of static Poisson networks

The stable packet arrival rate region of the discrete-time slotted ALOHA network with the sources distributed as a static Poisson point process is investigated here. The problem is a generalization and extension of interacting queues problem, in which the physical layer is abstracted. Employing tools from queueing theory as well as point process theory, we obtain sufficient conditions and necessary conditions for stability by the concept of dominance. Numerical results show that the gap between sufficient conditions and necessary conditions is small, and the results also reveal how these conditions vary with system parameters.