Modeling of Autocorrelation Functions Using Weighted Non- linear least squares
Altyeb Altaher Altyeb, Iman A. Abumaaly, Sami Mohamed Sharif · arXiv (Cornell University) · 2006
Abstract Because autocorrelation functions play an important role in stochastic processes and can be used to model the traffic data practically, it is significant to study how to find a function that best fits the autocorrelation sequence of a real-traffic trace. This paper presents a asymptotic model for autocorrelation functions using Weighted non-linear least squares. Keywords : traffic modeling, long-range dependence, autocorrelation functions 1. INTRODUCTION Recent researches have shown that the behaviors of the traffic on LAN and WAN are well modeled by second-order self-similar processes with long-range dependence (LRD) [ 1][6]. Second-order self-similar processes are classified into two classes [l][6]. One is exactly second-order self-similar model and the other asymptotically second-order self-similar model. [1] pointed out that exactly second-order self-similar model is not enough to model real trafic. Hence, asymptotically second- order self-similar processes are considered in the paper. Throughout the paper, the term LRD processes means second-order self-similar processes unless otherwise stated. LRD processes are defined by autocorrelation functions (ACFs). As ACFs can be used to study queuing systems [9], it is significant to study how to find a function that best fits the autocorrelation sequence of a real-traffic trace (target ACF). Because the ACFs of LRD processes are characterized by a single parameter H [6], the estimation of H is paid attention to [l][6], [5][4]. However, for a specific traffic trace, the various estimation methods might yield different values of H's substantially for the same trace as remarked in [4]. This makes it difficult to model traffic with ACFs. Thus, an optimal representation of ACFs of LRD processes is well worth discussing. Mathematically, optimally modeling ACFs of real-traffic traces can be abstracted as follows. For a given r indicating a target ACF of a real traffic, find a function of a LRD process which best fits it in the sense of F(e) = min, where e = (