Numerical Methods of Multifractal Analysis in Information Communication Systems and Networks

In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and scaling functions, and methods used in their determination by means of Wavelet Transform Modulus Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectrum are presented. A method based on multifractal data analysis at network layer level by means of WTMM is proposed for the detection of traffic anomalies in computer and telecommunication networks. The chapter also introduces WTMM as the informative indicator to exploit the distinction of fractal dimen- sions on various parts of a given dataset. A novel approach based on the use of multifractal spectrum parameters is proposed for estimating queuing performance for the generalized multifractal traffic on the input of a buffering device. It is shown that the multifractal character of traffic has significant impact on queuing performance characteristics

Determining Resilience Gains from Anomaly Detection for Event Integrity in Wireless Sensor Networks

Measurements collected in a wireless sensor network (WSN) can be maliciously compromised through several attacks, but anomaly detection algorithms may provide resilience by detecting inconsistencies in the data. Anomaly detection can identify severe threats to WSN applications, provided that there is a sufficient amount of genuine information. This article presents a novel method to calculate an assurance measure for the network by estimating the maximum number of malicious measurements that can be tolerated. In previous work, the resilience of anomaly detection to malicious measurements has been tested only against arbitrary attacks, which are not necessarily sophisticated. The novel method presented here is based on an optimization algorithm, which maximizes the attack’s chance of staying undetected while causing damage to the application, thus seeking the worst-case scenario for the anomaly detection algorithm. The algorithm is tested on a wildfire monitoring WSN to estimate the benefits of anomaly detection on the system’s resilience. The algorithm also returns the measurements that the attacker needs to synthesize, which are studied to highlight the weak spots of anomaly detection. Finally, this article presents a novel methodology that takes in input the degree of resilience required and automatically designs the deployment that satisfies such a requirement