Wireless Multihop Networks with Stealing: Large Buffer Asymptotics via the Ray Method
Fabrice M. Guillemin, Charles Knessl, Johan S. H. van Leeuwaarden · SIAM Journal on Applied Mathematics · 2011
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.