Asymptotic Stability Region of Slotted Aloha

摘要: We analyze the stability of standard, buffered, slotted-Aloha systems. Specifically, we consider a set $N$ users, each equipped with an infinite buffer. Packets arrive into user $i$ 's buffer according to some stationary ergodic Markovian process intensity $\lambda_{i}$ . At beginning slot, if has packets in its buffer, it attempts transmit packet fixed probability $p_{i}$ over shared resource/channel. The transmission is successful only when no other use channel. such systems been open since their very first analysis 1979 by Tsybakov and Mikhailov. In this paper, propose approximate condition that provably exact number users grows large. provide theoretical evidence numerical experiments explain why proposed extremely accurate even for restricted (even two or three).