The Age of Information in Multihop Networks
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The problem of minimizing the age-of-information has been extensively studied in single-hop networks. In this paper, we minimize the age of a single information flow in multihop networks. If the packet transmission times over the network links are exponentially distributed, we prove that a preemptive Last-Generated, First-Serve (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 distributions of packet transmission times, the non-preemptive LGFS policy is shown to minimize the age processes at all nodes among all non-preemptive work-conserving policies (again in a stochastic ordering sense). Interestingly, these 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. Finally, we investigate the class of New-Better-than-Used (NBU) packet transmission time distributions and show that the non-preemptive LGFS policy is within a constant age gap from the optimum average age, and that the gap is independent of system parameters.
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