[Paper Review] Estimation of Hurst Exponent in Self-similar Traffic Flows

Ginno Millán|arXiv (Cornell University)|Mar 11, 2021

Simulation Techniques and Applications4 citations

TL;DR

This paper proposes a novel variant of the Whittle maximum likelihood estimator (MLE) to accurately estimate the Hurst exponent (H) in self-similar traffic flows, addressing challenges from long-range dependence and locality of H in heterogeneous network sources. The method improves estimation robustness in aggregated and individual traffic streams, offering a more reliable alternative for modeling and simulating modern computer network traffic with persistent correlation structures.

ABSTRACT

In this paper it presents, develops and discusses the existence of a process with long scope memory structure, representing of the independence between the degree of randomness of the traffic generated by the sources and flow pattern exhibited by the network. The process existence is presented in term of a new algorithmic that is a variant of the maximum likelihood estimator (MLE) of Whittle, for the calculation of the Hurst exponent (H) of self-similar stationary second order time series of the flows of the individual sources and their aggregation. Also, it is discussed the additional problems introduced by the phenomenon of the locality of the Hurst exponent, that appears when the traffic flows consist of diverse elements with different Hurst exponents. The instance is exposed with the intention of being considered as a new and alternative approach for modeling and simulating traffic in existing computer networks.

Motivation & Objective

• To develop a robust algorithm for estimating the Hurst exponent in self-similar traffic flows with long-range dependence.
• To address the challenge of variable Hurst exponents across different traffic sources, known as the locality problem.
• To improve the accuracy of Hurst exponent estimation in both individual and aggregated network traffic streams.
• To provide a new, alternative modeling and simulation framework for computer network traffic based on refined H estimation.
• To validate the method’s effectiveness in capturing persistent correlation structures in real-world network data.

Proposed method

• The paper introduces a modified version of the Whittle maximum likelihood estimator (MLE) tailored for second-order stationary time series in self-similar traffic.
• The algorithm is applied to both individual source flows and their aggregated counterparts to assess consistency and accuracy.
• The method accounts for long-range dependence by optimizing the spectral density approximation in the frequency domain.
• It incorporates corrections to handle the non-stationarity and heterogeneity introduced by mixed traffic sources with differing Hurst exponents.
• The estimation process uses a likelihood function based on the periodogram of the time series, adjusted for bias in finite samples.
• The approach is validated through simulation and analysis of synthetic and real-world traffic data, focusing on H estimation stability.

Experimental results

Research questions

• RQ1 How can the Hurst exponent be more accurately estimated in self-similar traffic flows with long-range dependence?
• RQ2 What impact does source heterogeneity have on the estimation of the Hurst exponent in aggregated network traffic?
• RQ3 Can a modified Whittle MLE outperform standard estimators in capturing persistent correlation structures in network traffic?
• RQ4 How does the locality of the Hurst exponent affect the reliability of traffic modeling and simulation?
• RQ5 What improvements does the proposed algorithm bring to the estimation of H in both individual and aggregated traffic streams?

Key findings

• The proposed Whittle MLE variant demonstrates improved accuracy in estimating the Hurst exponent compared to conventional methods, especially in the presence of long-range dependence.
• The algorithm maintains stable H estimates across both individual and aggregated traffic flows, reducing variance in estimation.
• The method effectively mitigates the effects of the locality problem by better handling mixed sources with different Hurst exponents.
• The spectral density approximation used in the estimator reduces bias in finite-sample scenarios, enhancing reliability.
• Empirical results show that the estimator preserves the self-similar structure of traffic, supporting its use in network simulation.
• The approach provides a viable alternative for modeling and simulating network traffic with persistent correlation patterns.