Жалейко Е.В. HEAVY NETWORK TRAFFIC MODELING AND SIMULATION USING STABLE FARIMA PROCESSES

HEAVY NETWORK TRAFFIC MODELING AND SIMULATION USING STABLE FARIMA PROCESSES

F.C. Harmantzis , D. Hatzinakos

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Источник: http://teletraffic.ru/public/pdf/Harmantzis_Heavy%20Network%20Traffic_2003.pdf

Abstract. Fractionally autoregressive integrated moving average (FARIMA) processes have been proposed for network traffic modeling. In this paper we focus on the generalization of those processes, considering heavy-tailed (Stable) innovations. The resulted linear Stable FARIMA model captures the short and long range dependences as well as the heavy-tailed behavior of the network traffic. The contribution is an integrated procedure of fitting Stable FARIMA parameters to real data and generating artificial data series. We reduce the complexity of the problem, considering a three-step algorithm for parameter estimation and system identification. We finally test the accuracy of our algorithm and we apply it to a real network data series.

Introduction. It has been suggested that Internet traffic is far too complicated to be modeled using the techniques developed for telephone networks or computer systems. More specifically, there is increasing evidence of the so-called self-similar (or fractal) and heavy-tailed nature of data traffic. Self-similarity manifests itself usually through the display of persistence or long range dependence (LRD).

As a consequence, a large number of traffic models have been proposed in order to successfully characterize the nature of the traffic in networks today. The reason is that fractality and heavy-tailness have serious implications for analysis, design, and control of computer networks. In contrast, traditional schemes, typically Markovian in nature, which have been (and currently are) extensively used, may lead to substantial underestimation of Quality of Service (QoS) metrics such as delay and blocking.

Unfortunately, the proposed self-similar models, such as the ones based on Fractional Brownian Motion (FBM) and Linear Fractional Stable Motion (LFSM), cannot be used to describe the short range Dependences (SRD). For example, it is known that the Variable Bit Rate (VBR) video frame sizes exhibit both short and long range dependences and their distribution is non-Gaussian. Therefore, models are required to describe both short and long memories, as well as heavy-tailed marginal distribution simultaneously.

In this paper, we recommend the fractional autoregressive integrated moving average (FARIMA) process with Stable innovations as a unified approach to characterize real network traffic. Although there have been several attempts to model real traffic using ARMA and FARIMA processes, e.g., to the authors knowledge, this is the first systematic effort to fit a FARIMA process with Stable innovations to real data. The main contribution of our work is in designing the overall process of calibrating such a model, using identification algorithms and parameter estimation methods suitable for Stable and self-similar processes. We also test the accuracy of the algorithm and we apply it to real and simulated data series.

In more detail, the contributions and organization of the paper are as follows: Section 2 is the background section: we review basic definitions, describe the Stable FARIMA process and refer to related work in the literature. In Section 3 we provide a novel procedure to fit a FARIMA process with Stable innovations to real traffic data. The procedure is based on a three-step identification algorithm. In Section 4 we describe a method to generate artificially a Stable FARIMA process with given parameters. We also present simulation experiments and numerical results, in order to test the performance of the proposed algorithm. Finally, in the Conclusions we summarize the main observations and contributions of our work.

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