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Consider a multihop wireless network serving multiple flows in which wireless interference constraints between links are described by a link-interference graph. The timely-throughput of a flow is defined as the throughput of packets of that flow that reach their destination node within a specified deadline, and the weighted timely throughput of the network is their weighted average over the flows with a given set of positive weights. The problem is particularly challenging, and has generally been open, when there is wireless interference between transmissions. We show that a modified CSMA routing-scheduling policy with an appropriate set of attempt probabilities is nearly optimal for maximizing weighted timely-throughput. This policy has the useful property that the routing-scheduling decision for an individual packet is solely a function of its location and time-to-deadline, and so a wireless node does not require knowledge of the global network state. It is easily implementable in a decentralized fashion by the nodes given the attempt probabilities. A gradient-based adaptive CSMA routing-scheduling policy to determine the optimal attempt probabilities is further provided. It moves along the gradient of the timely throughput and converges to a local maximum.

Adaptive CSMA for Decentralized Scheduling of Multi-Hop Networks With End-to-End Deadline Constraints