Multiuser Multiple-Access System: Stability and Metastability

A model of random multi-access system with an ALOHA-type protocol is analyzed when the number $N$ of users is large and the system is overloaded. In the limit as $N\to\infty$, the behavior of the system is described by a nonrandom dynamical system. We give a condition for the dynamical system to have an attractive fixed point and outline cases of several fixed points. The presence of several fixed points indicates that the finite system may exhibit a metastability phenomenon.