Karim Mohammed Rezaul

A Comparison of Methods for Estimating the Tail Index of Heavy-tailed Internet 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. In this paper, we describe some of the most useful mechanisms for estimating the tail index, particularly for distributions having the power law observed in different contexts in the Internet.

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.

BPTraSha: A Novel Algorithm for Shaping Bursty Nature of Internet Traffic

Various researchers have reported that traffic measurements demonstrate considerable burstiness on several time scales, with properties of self-similarity. Also, the rapid development of technologies has widened the scope of network and Internet applications and, in turn, increased traffic. 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 introduce a novel algorithm for traffic shaping, which can smooth out the traffic burstiness. We name it the Bursty Packet Traffic Shaper (BPTraSha). 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 traffics bursty nature can be modified before it is transmitted over the core network (Internet).

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, Higuchis 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.

An Approach for Characterising Heavy-Tailed Internet Traffic Based on EDF Statistics

In this research, statistical analyses of Web traffic were carried out based on the Empirical Distribution Function (EDF) test. Several probability distributions, such as Pareto (simple), extreme value, Weibull (three parameters), exponential, logistic and Pareto (generalized) have been chosen to fit the experimental traffic data (traces), which show an analytical indication of traffic behaviour. The issues of traffic characterisation and performance shown by these models are discussed in terms of the heavy tailedness and fitness of the curves. The aim of the research is to find a suitable analytical, method which can characterise the Web traffic.

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

This paper examines the process of customizing Particle sensors for use in a home energy monitoring project. Our developments affected sensor hardware, sensor software and data capture. The developed sensors have been deployed in two homes in the UK. We examine the issues in using 3rd party toolkits to undertake research and suggest design and process enhancements to better assist with the deployment of sensors in homes.