基于高阶累积量的流量率网络层析成像
Traffic Rate Network Tomography with Higher-Order Cumulants
摘要：
网络断层扫描的目的是从链路流量测量中估计源-目的地流量速率。这个逆问题是由Vardi在1996年提出的，用于在确定性和随机路由机制下运行的网络上的泊松流量。在本文中，我们扩展Vardi的二阶矩匹配速率估计方法高阶累积量匹配的目标，增加列秩的映射，从而提高速率估计精度。我们开发了一套系统的线性累积量匹配方程，并表示他们的Khatri-Rao产品complexly。最小二乘估计和迭代最小I-散度估计被认为是。我们开发了一个上界的均方误差（MSE）在最小二乘率估计的经验累积量。我们证明了NSFnet补充Vardi的方法与三阶经验累积量减少其平均归一化MSE相对于理论最小值的二阶矩匹配方法约12%-18%。当Vardi的二阶矩匹配方法是基于理论而不是经验矩时，可以获得最小的MSE。
英文摘要：
Network tomography aims at estimating source-destination traffic rates from link traffic measurements. This inverse problem was formulated by Vardi in 1996 for Poisson traffic over networks operating under deterministic as well as random routing regimes. In this paper we expand Vardi's second-order moment matching rate estimation approach to higher-order cumulant matching with the goal of increasing the column rank of the mapping and consequently improving the rate estimation accuracy. We develop a systematic set of linear cumulant matching equations and express them compactly in terms of the Khatri-Rao product. Both least squares estimation and iterative minimum I-divergence estimation are considered. We develop an upper bound on the mean squared error (MSE) in least squares rate estimation from empirical cumulants. We demonstrate for the NSFnet that supplementing Vardi's approach with third-order empirical cumulant reduces its averaged normalized MSE relative to the theoretical minimum of the second-order moment matching approach by about 12%-18%. This minimum MSE is obtained when Vardi's second-order moment matching approach is based on the theoretical rather than the empirical moments.
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