DocumentCode :
1523944
Title :
Asymptotic Stability Region of Slotted Aloha
Author :
Bordenave, Charles ; McDonald, David ; Proutiere, Alexandre
Author_Institution :
CNRS and the Department of Mathematics, Toulouse University, France
Volume :
58
Issue :
9
fYear :
2012
Firstpage :
5841
Lastpage :
5855
Abstract :
We analyze the stability of standard, buffered, slotted-Aloha systems. Specifically, we consider a set of N users, each equipped with an infinite buffer. Packets arrive into user i \´s buffer according to some stationary ergodic Markovian process of intensity \\lambda _{i} . At the beginning of each slot, if user i has packets in its buffer, it attempts to transmit a packet with fixed probability p_{i} over a shared resource/channel. The transmission is successful only when no other user attempts to use the channel. The stability of such systems has been open since their very first analysis in 1979 by Tsybakov and Mikhailov. In this paper, we propose an approximate stability condition that is provably exact when the number of users N grows large. We provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users (even two or three).
Keywords :
Approximation methods; Asymptotic stability; Atmospheric measurements; Markov processes; Numerical stability; Stability criteria; Aloha; mean-field asymptotics; random multiple access; stability;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2012.2201333
Filename :
6204337
Link To Document :
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