Wireless multi-hop networks with stealing: Large buffer asymptotics

Wireless networks equipped with CSMA are scheduled in a fully distributed manner. A disadvantage of such distributed control in multi-hop networks is the hidden node problem that causes the effect of stealing, in which a downstream node steals the channel from an upstream node with probability p. Aziz, Starobinski and Thiran have recently shown that the N-hop model with stealing is stable only in the case N = 3 and p ∈ (0, 1]. This 3-hop model can be modeled 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.