  The problem of reducing the age-of-information has been extensively studied
in the single-hop networks. In this paper, we minimize the age-of-information
in general multihop networks. If the packet transmission times over the network
links are exponentially distributed, we prove that a preemptive Last Generated
First Served (LGFS) policy results in smaller age processes at all nodes of the
network (in a stochastic ordering sense) than any other causal policy. In
addition, for arbitrary general distributions of packet transmission times, the
non-preemptive LGFS policy is shown to minimize the age processes at all nodes
of the network among all non-preemptive work-conserving policies (again in a
stochastic ordering sense). It is surprising that such simple policies can
achieve optimality of the joint distribution of the age processes at all nodes
even under arbitrary network topologies, as well as arbitrary packet generation
and arrival times. These optimality results not only hold for the age
processes, but also for any non-decreasing functional of the age processes.
