CoLoRaDe: A Novel Algorithm for Controlling Long-Range Dependent Network Traffic

Long-range dependence characteristics have been observed in many natural or physical phenomena. In particular, a significant impact on data network performance has been shown in several papers. Congested Internet situations, where TCP/IP buffers start to fill, show long-range dependent (LRD) self-similar chaotic behaviour. The exponential growth of the number of servers, as well as the number of users, causes the performance of the Internet to be problematic since the LRD traffic has a significant impact on the buffer requirements. The Internet is a large-scale, wide-area network for which the importance of measurement and analysis of traffic is vital. The intensity of the long-range dependence (LRD) of communications network traffic can be measured using the Hurst parameter. A variety of techniques (such as R/S analysis, aggregated variance-time analysis, periodogram analysis, Whittle estimator, Higuchi's method, wavelet-based estimator, absolute moment method, etc.) exist for estimating Hurst exponent but the accuracy of the estimation is still a complicated and controversial issue. Earlier research (Rezaul et al., 2006) introduced a novel estimator called the Hurst exponent from the autocorrelation function (HEAF) and it was shown why lag 2 in HEAF (i.e. HEAF (2)) is considered when estimating LRD of network traffic. HEAF estimates H by a process which is simple, quick and reliable. In this research we extend these concepts by introducing a novel algorithm for controlling the long-range dependence of network traffic, named CoLoRaDe which is shown to reduce the LRD of packet sequences at the router buffer

Managing the Bursty Nature of Packet Traffic using the BPTraSha Algorithm

The rapid development of network technologies has widened the scope of Internet applications and, in turn, increased both Internet traffic and the need for its accurate measurement, modelling and control. Various researchers have reported that traffic measurements demonstrate considerable burstiness on several time scales, with properties of self-similarity. The self-similar nature of this data traffic may exhibit spikiness and burstiness on large scales with such behaviour being caused by strong dependence characteristics in data: that is, large values tend to come in clusters and clusters of clusters and so on. Several studies have shown that TCP, the dominant network (Internet) transport protocol, contributes to the propagation of self-similarity. Bursty traffic can affect the Quality of Service of all traffic on the network by introducing inconsistent latency. It is easier to manage the workloads under less bursty (i.e. smoother) conditions. In this paper, we examine the use of a novel algorithm, the Bursty Packet Traffic Shaper (BPTraSha), for traffic shaping, which can smooth out the traffic burstiness. Experimental results show that this approach allows significant traffic control by smoothing the incoming traffic. BPTraSha can be implemented on the distribution router buffer so that the traffic’s bursty nature can be modified before it is transmitted over the core network

A Survey of Performance Evaluation and Control for Self-Similar Network Traffic

This paper surveys techniques for the recognition and treatment of self-similar network or internetwork traffic. Various researchers have reported traffic measurements that demonstrate considerable burstiness on a range of time scales with properties of self-similarity. Rapid technological development has widened the scope of network and Internet applications and, in turn, increased traffic volume. The exponential growth of the number of servers, as well as the number of users, causes Internet performance to be problematic as a result of the significant impact that long-range dependent traffic has on buffer requirements. Consequently, accurate and reliable measurement, analysis and control of Internet traffic are vital. The most significant techniques for performance evaluation include theoretical analysis, simulation, and empirical study based on measurement. In this research, we discuss existing and recent developments in performance evaluation and control tools used in network traffic engineering

Coherent states of the Poincaré group, related frames and transforms

We construct here families of coherent states for the full Poincare group, for representations corresponding to mass $m>0$ and arbitrary integral or half-integral spin. Each family of coherent states is defined by an affine section in the group and constitutes a frame. The sections, in their turn, are determined by particular velocity vector fields, the latter always appearing in dual pairs. We discretize the coherent states of Poincare group in 1-space and 1-time dimensions and show that they form a discrete frame, develop a transform, similar to a windowed Fourier transform, which we call the relativistic windowed Fourier transform. We also obtain a reconstruction formula. Finally, we perform numerical computations. We evaluate the discrete frame operator numerically and present it graphically for different sections and windows. We also reconstruct some functions, compare reconstructed functions with the original ones graphically. We compare the reconstruction scheme of the relativistic windowed Fourier transform with that of the standard windowed Fourier transform

Towards Finding Efficient Tools for Measuring the Tail Index and Intensity of Long-range Dependent Network Traffic

Many researchers have discussed the effects of heavy-tailedness in network traffic patterns and shown that Internet traffic flows exhibit characteristics of self-similarity that can be explained by the heavy-tailedness of the various distributions involved. Self-similarity and heavy-tailedness are of great importance for network capacity planning purposes in which researchers are interested in developing analytical methods for analysing traffic characteristics. Designers of computing and telecommunication systems are increasingly interested in employing heavy-tailed distributions to generate workloads for use in simulation - although simulations employing such workloads may show unusual characteristics. Congested Internet situations, where TCP/IP buffers start to fill, show long-range dependent (LRD) self-similar chaotic behaviour. Such chaotic behaviour has been found to be present in Internet traffic by many researchers. In this context, the 'Hurst exponent', H, is used as a measure of the degree of long-range dependence. Having a reliable estimator can yield a good insight into traffic behaviour and may eventually lead to improved traffic engineering. In this paper, we describe some of the most useful mechanisms for estimating the tail index of Internet traffic, particularly for distributions having the power law observed in different contexts, and also the performance of the estimators for measuring the intensity of LRD traffic in terms of their accuracy and reliability

Identifying Long-range Dependent Network Traffic through Autocorrelation Functions

For over a decade researchers have been reporting the impact of self-similar long-range dependent network traffic. Long-range dependence (LRD) is of great significance in traffic engineering problems such as measurement, queuing strategy, buffer sizing and admission and congestion control. In this research, in order to determine the existence of LRD, we apply three different robust versions of the autocorrelation function (ACF), namely weighted ACF (WACF), trimmed ACF (TACF) and variance-ratio of differences and sums, known as the D/S variance estimator (DACF), in conjunction with the sample ACF (which is moment based). Here we define the moment based ACF as MACF. In telecommunications, LRD traffic defines that a similar pattern of traffic persists for a longer span of time. Through ACF, it is possible to detect how long the traffic lasts. The aim of this research is to investigate the performance of ACF in identifying the existence of LRD traffic

TRAUMA THEORY IN MARY WOLLSTONECRAFT’S MARIA: OR, THE WRONGS OF WOMAN

Maria: or, The Wrongs of Woman, asserts and protests strenuously against the rigid laws that enslave women. The piece of work sheds light on the prevailing morality, which believes that chastity, repentance and submission should be the only virtues of women. Mary Wollstonecraft’s posthumous work is equipped with such powerful political statements. Maria’s character is nothing but a written defence against her oppressive and abusive husband’s misconducts against her. Wollstonecraft pens this feminist manifesto to denounce the numerous wrongs that are done to women. Her proclamation stands tall, demanding women’s right to be free of male oppression. In this research work, we would like to draw not only on the measurements of Maria: or, The Wrongs of Woman but also take a different path, focusing on a theme that is central to the novel and its feminist politics which has received little attention so far: trauma. The novel is a structuring of intertwined life events of suffering and ruptured relationships. We would here delve deep into the novel; the protagonist’s life events and the writer’s concerns through Trauma Theory

Identifying Long-range Dependent Network Traffic through Autocorrelation Functions

For over a decade researchers have been reporting the impact of self-similar long-range dependent network traffic. Long-range dependence (LRD) is of great significance in traffic engineering problems such as measurement, queuing strategy, buffer sizing and admission and congestion control. In this research, in order to determine the existence of LRD, we apply three different robust versions of the autocorrelation function (ACF), namely weighted ACF (WACF), trimmed ACF (TACF) and variance-ratio of differences and sums, known as the D/S variance estimator (DACF), in conjunction with the sample ACF (which is moment based). Here we define the moment based ACF as MACF. In telecommunications, LRD traffic defines that a similar pattern of traffic persists for a longer span of time. Through ACF, it is possible to detect how long the traffic lasts. The aim of this research is to investigate the performance of ACF in identifying the existence of LRD traffic

Mathematical modeling on the transmission of COVID-19 and its reproduction numbers in SAARC countries

In the middle of December 2019, a virus known as coronavirus (COVID-19) generated by severe acute respiratory syndrome corona virus 2 (SARC-CoV-2) was first detected in Wuhan, Hubei Province, China. As of the 9th of March, 2022, spread to over 212 countries, causing 429 million confirmed cases and 6 million people to lose their lives worldwide. In developing countries like the South Asian area, alarming dynamic variations in the pattern of confirmed cases and death tolls were displayed. During epidemics, accurate assessment of the characteristics that characterize infectious disease transmission is critical for optimizing control actions, planning, and adapting public health interventions. The reproductive number, or the typical number of secondary cases caused by an infected individual, can be employed to determine transmissibility. Several statistical and mathematical techniques have been presented to calculate across the duration of an epidemic. A technique is provided for calculating epidemic reproduction numbers. It is a MATLAB version of the EpiEstim package's R function estimate R, version 2.2-3. in the South Asian Association for Regional Cooperation (SAARC) countries. The three methodologies supported are 'parametric SI,' 'non-parametric SI,' and 'uncertain SI.' The present study indicated that the highest reproduction number was 12.123 and 11.861 on 5th and 14th March 2020 in India and Sri_Lanka, whereas the lowest reproduction number was the lowest was 0.300 and 0.315 in Sri_Lanka and India. The Maximum and minimum reproductive number of Bangladesh was 3.752 and 0.725. In this study, we have tried to point out the worst, best and current situation of SAARC countries