While considerable work has addressed the optimal AoI under different circumstances in single-hop networks, the exploration of AoI in multi-hop wireless networks is rarely attempted. More importantly, the inherent relationships between AoI and throughput are yet to be explored, especially in multi-hop networks. This paper studies AoI in multi-hop wireless networks and explores its potential relationships with throughput for the very first time, particularly focusing on the impacts of flexible routes on the two metrics, i.e., AoI and throughput. By developing a rigorous mathematical model with interference, channel allocation, link scheduling, and routing path selection taken into consideration, we build the interrelation between AoI and throughput in multi-hop networks. A multi-criteria optimization problem is formulated with the goal of simultaneously minimizing AoI and maximizing network throughput. By qualitatively analyzing their relationships, we exhibit that the two metrics may conflict with each other, implying the optimal solutions for the multi-criteria problem will include a set of Pareto-optimal points rather than a single point existing in the traditional optimization problem. We resort to a novel approach by transforming the multi-criteria problem into a single objective one so as to find the weakly Pareto-optimal points iteratively, thereby allowing us to screen all Pareto-optimal points for the solution. Through formal proof, our solution is demonstrated to be able to identify all Pareto-optimal points and terminate in a finite number of iterations. We conduct the simulation evaluation to identify the optimal tradeoff points of AoI and throughput, demonstrating that one performance metric may improve at the expense of degrading the other, with the routing path found as one of the key factors in determining such a tradeoff.

中文翻译：

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提升或阻碍：路由感知多跳无线网络中的 AoI 和吞吐量相互关系

虽然大量工作已经解决了单跳网络中不同情况下的最佳 AoI，但很少尝试探索多跳无线网络中的 AoI。更重要的是，AoI 和吞吐量之间的内在关系还有待探索，尤其是在多跳网络中。本文首次研究了多跳无线网络中的 AoI，并探讨了其与吞吐量的潜在关系，特别关注灵活路由对 AoI 和吞吐量这两个指标的影响。通过开发考虑干扰、信道分配、链路调度和路由路径选择的严格数学模型，我们建立了多跳网络中 AoI 和吞吐量之间的相互关系。制定了多标准优化问题，目标是同时最小化 AoI 和最大化网络吞吐量。通过定性分析它们的关系，我们表明这两个指标可能相互冲突，这意味着多准则问题的最优解将包括一组帕累托最优点，而不是传统优化问题中存在的单个点。我们采用了一种新颖的方法，将多标准问题转化为单一目标问题，以便迭代地找到弱帕累托最优点，从而允许我们筛选所有帕累托最优点的解决方案。通过形式证明，我们的解决方案被证明能够识别所有帕累托最优点并在有限次数的迭代中终止。