  Consider a multihop wireless network serving multiple flows in which wireless
link interference constraints are described by a link interference graph. For
such a network, we design routing-scheduling policies that maximize the
end-to-end timely throughput of the network. Timely throughput of a flow $f$ is
defined as the average rate at which packets of flow $f$ reach their
destination node $d_f$ within their deadline.
  Our policy has several surprising characteristics. Firstly, we show that the
optimal routing-scheduling decision for an individual packet that is present at
a wireless node $i\in V$ is solely a function of its location, and "age". Thus,
a wireless node $i$ does not require the knowledge of the "global" network
state in order to maximize the timely throughput. We notice that in comparison,
under the backpressure routing policy, a node $i$ requires only the knowledge
of its neighbours queue lengths in order to guarantee maximal stability, and
hence is decentralized. The key difference arises due to the fact that in our
set-up the packets loose their utility once their "age" has crossed their
deadline, thus making the task of optimizing timely throughput much more
challenging than that of ensuring network stability. Of course, due to this key
difference, the decision process involved in maximizing the timely throughput
is also much more complex than that involved in ensuring network-wide queue
stabilization. In view of this, our results are somewhat surprising.
