Numerical Estimation of Network Traffic Failure Based on Probabilistic Approximation Methods: To what extent the network traffic failure can be predicted?

As for the modern network traffic circulation which has been realized by the Internet, it is one thing to discuss the problem asking how to detect where the network traffic failure has occurred, and quite another to discuss the problem asking how to predict and how to estimate the frequency indicating numerically how often the network traffic failure occurs, because the former problem, which is called the network traffic failure detection problem, and the latter problem, which is called the network traffic failure estimation problem, are investigated with the network skills based on the statistical methods and the network skills based on the probabilistic methods, respectively. Moreover, since it is one thing to locate the network traffic failure on the network segments and quite another to predict them beforehand, it is important for us to apply not only statistical methods but also probabilistic ones for the solutions to these problems.