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.

Recent studies on traffic measurement analysis in the various networks (LAN, MAN, WAN) have shown that packet traffic exhibits Self-Similarity. The packet traffic represents some behavior quite different from what it has been assumed. Some papers reported that Self-Similarity degrades the network performance, such as buffer overflow and network congestion. Thus, we need new network control scheme considering Self-Similar properties. The control scheme requires high-speed calculation method of Hurst Parameter. In this paper, we propose high-speed calculation method of Hurst Parameter based on the Variance-Time Plot method, and show its performance. Furthermore, we try to apply this method to the simple network control, in order to show effectiveness of the network control with Self-Similarity.