Abstract
Wireless networks equipped with CSMA are scheduled in a fully distributed manner. A disadvantage of such distributed control in multihop networks is the hidden node problem, which causes the effect of stealing, in which a downstream node steals the channel from an upstream node with probability $p$. Aziz, Starobinski, and Thiran [IEEE/ACM Trans. Networking, to appear] have recently shown that the $N$-hop model with stealing is stable only in the case $N=3$ and $p\in(0,1]$. This 3-hop model can be represented as a random walk in the quarter plane. We derive various asymptotic expressions for the stationary large buffer probabilities of the 3-hop model that capture the effect of $p$. We mainly rely on the ray method, and we show how this method is related to the compensation approach and singularity analysis.
Original language | English |
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Pages (from-to) | 1220-1240 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 71 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2011 |