Asymptotic Stabilization in the Decentralized ALOHA Algorithm. Diffusion Approximation

We consider a synchronous communication system controlled by a decentralized ALOHA algorithm. Such a system is not ergodic [1–5]. However, as the basic parameter of the algorithm is reduced, the system reveals the property of being asymptotically stable (ergodic) on increasing time intervals. The diffusion approximation on these intervals is obtained.