Effects of sampling and spatio/temporal granularity in traffic monitoring on anomaly detectability

We quantitatively evaluate how sampling and spatio/ temporal granularity in traffic monitoring affect the detectability of anomalous traffic. Those parameters also affect the monitoring burden, so network operators face a trade-off between the monitoring burden and detectability and need to know which are the optimal paramter values. We derive equations to calculate the false positive ratio and false negative ratio for given values of the sampling rate, granularity, statistics of normal traffic, and volume of anomalies to be detected. Specifically, assuming that the normal traffic has a Gaussian distribution, which is parameterized by its mean and standard deviation, we analyze how sampling and monitoring granularity change these distribution parameters. This analysis is based on observation of the backbone traffic, which exhibits spatially uncorrelated and temporally long-range dependence. Then we derive the equations for detectability. With those equations, we can answer the practical questions that arise in actual network operations: what sampling rate to set to find the given volume of anomaly, or, if the sampling is too high for actual operation, what granularity is optimal to find the anomaly for a given lower limit of sampling rate.