Shengkun Xie

Study of Packet Traffic Fluctuations Near Phase Transition Point from Free Flow to Congestion in Data Network Model

Phase transition phenomena between non-congested and congested phases in packet traffic have been observed in many packet switching networks (PSNs). Using the PSN model we investigate the nature of fluctuations in number of packets in transit from their source to their destination, when the mean flow density into the PSN model is close to the phase transition point. A meaningful parameter of PSN behaviour near this critical point is the Hurst exponent that when larger than 0.5 is revealing of a long memory process, i.e. a fractional Brownian motion. In this paper we have used Hurst exponents and long range dependence to analyse PSN model behaviour. We have found that the DFA analysis and several methods for estimating the Hurst exponent suggest the presence of a long memory process for the PSN model using adaptive routing. However, we have not observed this in the case of static routing for the same type of incoming traffic. Thus, the packet traffic is more correlated in PSN model with adaptive routing than the static one. We present our finding, outline the work underway and discuss its expansion.

A comparative study of noise effect on wavelet based de-noising methods

Complexity of noisy engineering or biological data often involves non-stationarity, non-gaussianity, long memory, self-similarity, multi-scale structure, etc. In application of wavelet based statistical methods to analyze these types of data it is of importance to know how the choice of wavelet basis function and the noise level contained in the signals affect the performance of a de-noising method applied to a set of multivariate noisy signals. In this paper, we study the performance of three wavelets based de-noising methods: wavelet thresholding, multivariate wavelet de-noising method and multi-scale principal component analysis (PCA), which are important wavelet based de-noising methods. We investigate the robustness of these methods to different types and levels of noise added to a set of known signals. We study the noise effect on de-noising performance using a set of signals with known structure for different types and levels of the added noise.

Impact of source load and routing on QoS of packets delivery

Abstract We study how the number of packets in transit (NPT), that is an aggregate measure of a network quality of service (QoS) performance, is affected by routing algorithm coupled with volume of incoming traffic. We use our simulation model that is an abstraction of the Network Layer of the OSI Reference Model. We consider a static routing and two different types of dynamic routings and different volumes of incoming traffic in the network free flow state. Our study shows that the efficiency of performance of a routing changes with the volume of incoming traffic among the considered routings.

Feature extraction via dynamic PCA for epilepsy diagnosis and epileptic seizure detection

Feature extraction is an important technique for complex, multivariate data containing various attributes. In this paper, we propose new detection schemes to help diagnosing epilepsy and detecting the onset of epileptic seizures. These schemes are based on the dynamic principle component analysis (PCA) approach and on partially extracted features. We propose a detection performance measure for evaluation of performance of the detection schemes. We also introduce a method for determining the threshold of the PC classifier using the normalized partial energy sequence of the extracted features of the training data set. We use partially extracted features to act as a classifier to help diagnosing epilepsy and detecting the onset of epileptic seizures. A publicly available EEG database is employed to evaluate our detection schemes. Our study shows that the proposed detection schemes are very promising in assisting diagnosis of epilepsy and for epileptic seizure detection.

Number of packets in transit as a function of source load and routing

We study how network performance in delivering packets to their destinations is affected by routing algorithm coupled with volume of incoming traffic. We focus our study on the number of packets in transit (NPT) that is an aggregate measure of a network quality of service (QoS) performance. The NPT network performance indicator measures directly the number of packets in the network on their routes to their destinations. We carry out our study using a time-discrete simulation model that is an abstraction of the Network Layer of the ISO OSI Reference Model. This model focuses on packets and their routing. We consider a static routing and two different types of dynamic routings and different volumes of incoming traffic in the network free flow state. Our study shows that the efficiency of performance of a routing measured as an average value of the NPT time series and as a variability of this series, changes with the volume of incoming traffic among the considered routings. Thus, depending on the volume of incoming traffic it is preferable to use one type of routing over the other ones if the objective is to maintain the lowest number of packets in transit and their variability, i.e. the highest QoS network performance.

Features extraction via wavelet kernel PCA for data classification

The performance of a kernel-based method is usually sensitive to a choice of the values of the hyper parameters of a kernel function. In this paper, we present a novel framework of using wavelet kernels in the kernel principal component analysis (KPCA) in order to better explain the nonlinear relationships among original multivariate data. We propose to introduce dilation and translation factors into a wavelet kernel function, in order to narrow down the search for kernel parameters required to calculate the kernel matrix. We tested the hypothesis of implementing a wavelet kernel PCA (WKPCA) to extract the feature information using a set of simulated multi-scale clustered data. We show that WKPCA is an effective feature extraction method for transforming a variety of multi-dimensional clustered data into data with a higher level of linearity among the data attributes. That brings to an improvement in the accuracy of linear classifiers.

Study of number of packets in transit in a data network model near onset of congestion using functional fixed effect models

Performance of data communication networks is influenced by many factors, e.g. routing algorithms, traffic load, network connection topology. Using functional fixed effect models we study how the factors, routing cost metric, source load with various levels and their interactions affect a response metric, a network performance indicator ldquonumber of packets in transitrdquo. Our focus is on the study near phase transition point (critical point) from free flow to congested states of a packet switching network model where throughput is the highest. We characterize the critical point by the level of packets production at sources. In our model we consider different dynamic routing cost metrics (i.e., when the costs of transmission of packets from one router to another incorporate the information about how congested the routers are) and static routing cost metric (i.e., when the cost of transmission of packets from one router to another is constant over time). Our work provides insight on the selection of the most efficient strategy to deliver packets to their destinations when the network is near congestion.

Wavelet-Domain Statistics of Packet Switching Networks Near Traffic Congestion

Recent theoretical and applied works have demonstrated the appropriateness of wavelets for analysing signals containing non- stationarity, unsteadiness, self-similarity, and non-Markovity. We applied wavelets to study packet traffic in a packet switching network model, focusing on the spectral properties of packet traffic near phase transition (critical point) from free flow to congestion, and considered different dynamic & static routing metrics. We show that wavelet power spectraand variance are important estimators of the changes occurring with source load increasing from sub-critical, through critical, to super-critical and it depends on the routing algorithm.

Wavelet Spectral Analysis of Packet Traffic Near Phase Transition Point from Free Flow to Congestion in Data Network Model

We have applied wavelet statistics to study packet traffic in a data communication network model of the packet switching type. Our focus is on the study of spectral properties of packet traffic near phase transition point (critical point) from free flow to congested states of the network model. We characterize the critical point by the level of packets production at sources in the packet switching network (PSN) model. In our model we consider different dynamic routing cost metrics (i.e., when the costs of transmission of packets from one router to another incorporate the information about how congested the routers are) and static routing cost metric (i.e., when the cost of transmission of packets from one router to another is constant over time). Using wavelets we study spectral properties of number of packets in transit from their sources to their destinations in PSN model for various routing algorithms and network connection topologies when source loads are close to the critical ones. We show that the wavelet power spectra is an important estimator of the changes occurring with the increase of source load values from sub-critical, through critical to supercritical ones and it is dependent on the routing algorithm.

Detection of stationary network load increase using univariate network aggregate traffic data by dynamic PCA

Network operators are now facing bandwidth outages as well as a growing pressure to ensure good Quality of Service (QoS). An important practical issue for network service providers is to pay close attention to the load changes of network traffic, in particular, the stationary increase of load from a normal demand. Many network monitoring applications and performance analysis tools are based on the study of an aggregate measure of network traffic, e.g. number of packets in transit (NPT), which is a long-term univariate time series. To classify this type of network traffic data and detect any increase of network source load, we propose a dynamic principal component analysis (PCA) method, first to extract data features and then to detect a stationary load increase of network traffic. The proposed detection schemes are based on either the major or the minor principal components of network traffic data. To demonstrate the applications of the proposed feature extraction method and the detection schemes, we applied them to network traffic data simulated from the packet switching network (PSN) model. Additionally, we propose a combined detection scheme that uses both the major and the minor principal components. The proposed detection schemes, based on dynamic PCA, show enhanced performance in detecting an increase of network load for the simulated network traffic data. These results offer a new feature extraction method based on dynamic PCA that creates additional feature variables for event detection in a univariate time series.