Application of Nonlinear Approximation Methods to Network Fault Estimation Problems

Abstract

In the contemporary communication systems based on the Internet, the problem asking how to detect where the network failures have occurred is different from the problem asking how to predict numerically how often the network failures occur, because the former problem which is called the network fault detection problem and the latter problem which is called the network fault estimation problem are investigated with the network skills based on the statistical methods and the network skills based on the mathematical methods, respectively. Since it is one thing to locate the network failures on the network segments and quite another to predict them beforehand. Therefore it is important to apply not only statistical methods but also mathematical ones to the solutions to these problems. In this paper, we discuss the problem asking what kinds of network skills based on mathematics the network fault estimation systems should be equipped with, for the purpose of predicting the occurrence of the network failures. Exactly speaking, it is shown that application of nonlinear approximation methods to these problems enables us to estimate numerically the degree indicating how often the network failures occur without looking up in the data consisting of the SNMP traps stored in the SNMP managers.

Keywords

• monotone decreasing step function
• Taylor expansion
• Lagrange remainder term
• network fault estimation

References

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