— We consider multi-hop wireless networks serving multiple flows in which only packets that meet hard end-to-end deadline constraints are useful, i.e., if a packet is not delivered to its destination node by its deadline, it is dropped from the network. We design decentralized scheduling policies for such multi-hop networks that attain the maximum throughput of useful packets. The resulting policy is decentralized in the sense that in order to make a transmission decision, a node only needs to know the “time-till-deadline” of the packets that are currently present at that node, and not the state of the entire network. The key to obtaining an easy-to-implement and highly decentralized policy is to replace the hard constraint on the number of simultaneous packet transmissions that can take place on the outgoing links of a node, by a timeaverage constraint on the number of transmissions. The policy thus obtained is guaranteed to provide maximum throughput. Analysis can be extended ...