Queue Length Stability of Maximal Greedy Schedules in Wireless Networks

Abstract— We consider wireless networks with interference constraints. The network consists of a set of links and a set of users who generate packets that traverse these links. Each user is associated with a route consisting of a sequence of links. The links are subject to the usual interference constraints: (i) if link l interferes with link k, then link k also interferes with link l, and (ii) two links that interfere with each other cannot transmit simultaneously. The interference set of a link is defined to be the set of links that interfere with the link, along with the link itself. A greedy scheduler is one which selects an arbitrary set of links to transmit subject only to the interference constraint. We use a traffic regulator at each link along the route of each flow which shapes the traffic of the flow. We prove that the network is queue-length stable under any maximal greedy scheduling policy provided that the total arrival rate in the interference set of each link is less than one.

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