Blind maximum likelihood estimation of traffic matrices under long-range dependent traffic

Abstract

a b s t r a c tA new method, based on the maximum likelihood principle, through the numerical Expectation-Maximization algorithm, is proposed to estimate traffic matrices when traffic exhibits long-range dependence. The methods proposed so far in the literature do not account for long-range dependence. The method proposed in the present paper also provides an estimate of the Hurst parameter. Simulation results show that: (i) the estimate of the traffic matrix is more efficient than those obtained via existing techniques; (ii) the estimation error of the traffic matrix is lower for larger values of the true traffic intensity; (iii) the estimate of the Hurst parameter is slightly negatively biased.

Baselining network-wide traffic by time-frequency constrained Stable Principal Component Pursuit

“…As the OD flows in the backbone network are highly aggregated by superimposing independent traffic processes, it is appropriate to model the noise traffic by the Gaussian processes following the central limitation theory [6], [16]. For simplicity, we assume each time-series N j (1 ≤ j ≤ P) is the white Gaussian noise with variance σ 2 j > 0 in this study 3 .…”

“…The mean values {a j,0 } P j=1 of different columns satisfies the wellknown gravity model [21], and in each simulation run, their sum is fixed at the constant 10 6 . As the period of the m-th sine is T l m × ∆t 60 hours, we choose {l m } = {7, 14, 28, 56, 112}, to simulate the {24, 12, 6, 3, 1.5} hours periodical traffic patterns 6 .…”

“…The mean values {a j,0 } P j=1 of different columns satisfies the wellknown gravity model [21], and in each simulation run, their sum is fixed at the constant 10 6 . As the period of the m-th sine is T l m × ∆t 60 hours, we choose {l m } = {7, 14, 28, 56, 112}, to simulate the {24, 12, 6, 3, 1.5} hours periodical traffic patterns 6 . In addition, the amplitudes of these sine functions decay quickly as m increases by a j,m+1 = 0.5a j,m , and the phase parameters {ϕ j,m } are independently and uniformly sampled from the interval [− • The anomaly traffic matrix E. In each simulation run, the non-zero entries (each corresponds to an anomaly incident) of E takes 1% randomly chosen positions, and in each column E j (1 ≤ j ≤ P), the volume of an anomaly is fixed at 0.8a j,0 .…”

“…Compared with other traffic data such as the link loads, it has a significant advantage [6]: the OD flows are invariant under the changes of topology and routing. Thus the traffic matrix shows the true intensity of the relationships between the OD pairs, and hence is quite helpful for archiving the optimization in capacity planning and traffic engineering, and detecting the network-wide anomalies more accurately.…”

Bayesian estimation of self-similarity exponent

“…Examples include geologic [55], hydrologic [121] and finance [15,17,92,107] data; data from human sciences [53,60,64], traffic networks [32,75], turbulence [51,63], DNA sequences [10] and other data types.…”