Throughput Optimal Decentralized Scheduling of Multihop Networks With End-to-End Deadline Constraints: Unreliable Links

We consider multihop networks serving multiple flows in which packets have hard deadlines. Packets not delivered to their destinations by their deadlines are of no value. The throughput of packets delivered within their deadlines is called the timely throughput. We address the design of packet scheduling, transmit power control, and routing policies that maximize any specified weighted average of the timely throughputs of the multiple flows. We determine a tractable linear program (LP) whose solution yields an optimal routing, scheduling, and power control policy, when nodes have average-power constraints. The optimal policy is fully decentralized, with decisions regarding any packet's transmission scheduling, transmit power level, and routing, based solely on the age and location of that packet. No knowledge of states of any other packets in the network is needed. This resolves a fundamental obstacle that arises whenever one attempts to optimally schedule networks. The number of variables in the LP is bounded by the product of the square of the number of nodes, the number of flows, the maximum relative deadline, and the number of transmit power levels. This solution is obtained from decomposition of the Lagrangian of the constrained Markov decision process describing the complete network state. Global coordination is achieved through a price for energy usage paid by a packet each time that its transmission is attempted at a node. It is fundamentally different from the decomposition of the fluid model used to derive the backpressure policy, which is throughput optimal when packets have no deadlines, where prices are related to queue lengths. If nodes instead have peak-power constraints, then a decentralized policy obtained by simple truncation is near optimal as link capacities increase in a proportional way.