Modelling Internet Traffic Streams with Ga/M/1/K Queuing Systems under Self-similarity

High-intensity concurrent arrivals of request packets in Internet traffic can cause dependence of event-to-event-times of the requests being served, which causes non-memoryless, modelled with heavy-tail distributions unlike common known traffics. The performance of Internet traffic can be examined using analytical models for the purpose of optimizing the system to reduce its operating costs. Therefore, our study examined a Ga/M/1/K Internet queue class (Gamma arrival processes, Ga; with memoryless-Poisson service process, M; a single server, 1, and K waiting room) and proposed specific derivations of its performance indicators. Real-life data of a corporate organisation Internet server was monitored at both peak and off-peak periods of its usage for Internet traffic data analysis. The minimum ‘0’ in the arrival process indicates self-similarity and was assessed using Hurst parameter, H, and their (standard deviation). ‘H’ > 0.5 arrival process in the peak period only, indicates self-similarity. Performance of Ga/M/1/K was compared with various queuing Internet traffic models used in existing literatures. Results showed that the value of the waiting room size for Ga/M/1/K has closest ties with true self-similar model at peak-periods usage of the Internet, which indicates possible concurrent arrival of clients' requests leading to more usage of the waiting room, but with light-tailed queue model at the off-peak periods. Therefore, the proposed Ga/M/1/K model can assist in evaluating the performance of high-intensity self-similar Internet traffic.      Keywords: Internet traffic; self-similarity; Ga/M/1/K model; gamma distributio

Perbandingan Kinerja Jaringan Internet Kampus Berdasarkan Karakteristik Trafik Self-Similarity

Internet traffic measurements performed at four locations on the campus of the University of Surabaya the Faculty of Engineering, Faculty of Business and Economics, Library and campus Ubaya Ngagel. Daily Internet traffic measurement period was conducted between the hours of 03:00 am until 23:59 pm with an average sample every 5 minutes. Internet network performance in this study were analyzed based on the characteristics of traffic self-similarity. Characteristics of Self-Similarity is expressed in the Hurst parameter (H) with a value of H (½, 1), where getting close to H = 1 then the worse the performance of its network. While the value of H parameter can be obtained using FARIMA (p, d, q) model whose relationship can be expressed H = d + ½, d is the order of FARIMA model. From the calculation and analysis of daily Internet traffic obtained that contained the smallest value of H parameter on the location of the Library. It can be concluded that the best network performance between the three other locations on campus are at the Library

Self-similar traffic and network dynamics

Copyright © 2002 IEEEOne of the most significant findings of traffic measurement studies over the last decade has been the observed self-similarity in packet network traffic. Subsequent research has focused on the origins of this self-similarity, and the network engineering significance of this phenomenon. This paper reviews what is currently known about network traffic self-similarity and its significance. We then consider a matter of current research, namely, the manner in which network dynamics (specifically, the dynamics of transmission control protocol (TCP), the predominant transport protocol used in today's Internet) can affect the observed self-similarity. To this end, we first discuss some of the pitfalls associated with applying traditional performance evaluation techniques to highly-interacting, large-scale networks such as the Internet. We then present one promising approach based on chaotic maps to capture and model the dynamics of TCP-type feedback control in such networks. Not only can appropriately chosen chaotic map models capture a range of realistic source characteristics, but by coupling these to network state equations, one can study the effects of network dynamics on the observed scaling behavior. We consider several aspects of TCP feedback, and illustrate by examples that while TCP-type feedback can modify the self-similar scaling behavior of network traffic, it neither generates it nor eliminates it.Ashok Erramilli, Matthew Roughan, Darryl Veitch and Walter Willinge

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

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

Discrete-time heavy-tailed chains, and their properties in modelling network traffic

The particular statistical properties found in network measurements, namely self-similarity and long-range dependence, cannot be ignored in modelling network and Internet traffic. Thus, despite their mathematical tractability, traditional Markov models are not appropriate for this purpose, since their memoryless nature contradicts the burstiness of transmitted packets. However, it is desirable to find a similarly tractable model which is, at the same time, rigorous at capturing the features of network traffic. This work presents the discrete-time heavy-tailed chains, a tractable approach to characterise network traffic as a superposition of discrete-time “on/off” sources. This is a particular case of the generic “on/off” heavy-tailed model, thus showing the same statistical features as the former; particularly, self-similarity and long-range dependence, when the number of aggregated sources approaches infinity. The model is then applicable to characterise a number of discrete-time communication systems, for instance ATM and Optical Packet Switching, and further derive meaningful performance met- rics, such as the average burst duration and the number of active sources in a random instant

A critical look at power law modelling of the Internet

This paper takes a critical look at the usefulness of power law models of the Internet. The twin focuses of the paper are Internet traffic and topology generation. The aim of the paper is twofold. Firstly it summarises the state of the art in power law modelling particularly giving attention to existing open research questions. Secondly it provides insight into the failings of such models and where progress needs to be made for power law research to feed through to actual improvements in network performance.Comment: To appear Computer Communication

The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena

The Internet is the most complex system ever created in human history. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This paper is a review of the complex dynamics of Internet traffic. Departing from normal treatises, we will take a view from both the network engineering and physics perspectives showing the strengths and weaknesses as well as insights of both. In addition, many less covered phenomena such as traffic oscillations, large-scale effects of worm traffic, and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex System