Doubly randomized protocols for a random multiple access channel with “success–nonsuccess” feedback

We consider a model of a decentralized multiple access system with a nonstandard binary feedback where the empty and collision situations cannot be distinguished. We show that, like in the case of a ternary feedback, for any input rate $\lambda<e^{-1}$ there exists a “doubly randomized” adaptive transmission protocol which stabilizes the behavior of the system. We discuss also a number of related problems and formulate some hypotheses.