How to efficiently perform network tomography is a fundamental problem in network management and monitoring. A network tomography task usually consists of applying multiple probing experiments, e.g., across different paths or via different casts (e.g., unicast and multicast). We study how to optimize the network tomography process through online sequential decision-making. From the methodology perspective, we introduce an online probe allocation algorithm that sequentially performs network tomography based on the principles of optimal experimental design and the maximum likelihood estimation. We rigorously analyze the regret of the algorithm under the conditions that i) the optimal allocation is Lipschitz continuous in the parameters being estimated and ii) the parameter estimators satisfy a concentration property. From the application perspective, we present two case studies: a) the classical lossy packet-switched network and b) the quantum bit-flip network. We show that both cases fulfill the two theoretical conditions and provide their corresponding regrets when deploying our proposed online probe allocation algorithm. Besides case studies with theoretical guarantees, we also conduct simulations to compare our proposed algorithm with existing methods and demonstrate our algorithm's effectiveness in a broader range of scenarios. In an experiment on the Roofnet topology, our algorithm improves the estimation accuracy by 13.64% compared with the state-of-the-art baseline.

翻译：如何高效执行网络断层扫描是网络管理与监测中的一个基础性问题。网络断层扫描任务通常包含实施多种探针实验，例如跨越不同路径或通过不同的播送方式（如单播与组播）。我们研究如何通过在线序贯决策来优化网络断层扫描过程。从方法论角度，我们引入了一种在线探针分配算法，该算法基于最优实验设计和最大似然估计原理，序贯地执行网络断层扫描。我们严格分析了该算法的遗憾值，其满足两个条件：i) 最优分配关于待估参数是Lipschitz连续的；ii) 参数估计量满足集中性性质。从应用角度，我们提出了两个案例研究：a) 经典有损分组交换网络，以及b) 量子比特翻转网络。我们证明了这两种情况均满足上述两个理论条件，并给出了部署我们提出的在线探针分配算法时相应的遗憾值。除了有理论保证的案例研究外，我们还进行了仿真实验，将我们提出的算法与现有方法进行比较，并在更广泛的场景中展示了我们算法的有效性。在Roofnet拓扑结构上的实验中，与最先进的基线方法相比，我们的算法将估计精度提高了13.64%。