Throughput Optimal Decentralized Scheduling of Multi-Hop Networks with   End-to-End Deadline Constraints: Unreliable Links
  We consider unreliable multi-hop networks serving multiple flows in which packets not delivered to their destination nodes by their deadlines are dropped. We address the design of policies for routing and scheduling packets that optimize any specified weighted average of the throughputs of the flows. We provide a new approach which directly yields an optimal distributed scheduling policy that attains any desired maximal timely-throughput vector under average-power constraints on the nodes. It pursues a novel intrinsically stochastic decomposition of the Lagrangian of the constrained network-wide MDP rather than of the fluid model. All decisions regarding a packet's transmission scheduling, transmit power level, and routing, are completely distributed, based solely on the age of the packet, not requiring any knowledge of network state or queue lengths at any of the nodes. Global coordination is achieved through a tractably computable "price" for transmission energy. This price is different from that used to derive the backpressure policy where price corresponds to queue lengths. A quantifiably near-optimal policy is provided if nodes have peak-power constraints. 
Rahul Singh and P. R. Kumar
cs.NI cs.SY math.OC