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A general open problem in networking is: what are the fundamental limits tothe performance that is achievable with some given amount of resources? Morespecifically, if each node in the network has information about only its$1$-hop neighborhood, then what are the limits to performance? This problem isconsidered for wireless networks where each communication link has a minimumbandwidth quality-of-service (QoS) requirement. Links in the same vicinitycontend for the shared wireless medium. The conflict graph captures which pairsof links interfere with each other and depends on the MAC protocol. In IEEE802.11 MAC protocol-based networks, when communication between nodes $i$ and$j$ takes place, the neighbors of both $i$ and $j$ remain silent. This model ofinterference is called the $2$-hop interference model because the distance inthe network graph between any two links that can be simultaneously active is atleast $2$. In the admission control problem, the objective is to determine,using only localized information, whether a given set of flow rates isfeasible.  In the present work, a distributed algorithm is proposed for this problem,where each node has information only about its $1$-hop neighborhood. Theworst-case performance of the distributed algorithm, i.e. the largest factor bywhich the performance of this distributed algorithm is away from that of anoptimal, centralized algorithm, is analyzed. Lower and upper bounds on thesuboptimality of the distributed algorithm are obtained, and both bounds areshown to be tight. The exact worst-case performance is obtained for some ringtopologies. While distance-$d$ distributed algorithms have been analyzed forthe $1$-hop interference model, an open problem in the literature is to extendthese results to the $K$-hop interference model, and the present work initiatesthe generalization to the $K$-hop interference model.

Performance analysis of a distributed algorithm for admission control in wireless networks under the $2$-hop interference model