Semi-Experiments and the Modelling of Internet Traffic - SAMSI
Semi-Experiments and the Modelling of Internet Traffic - SAMSI
Semi-Experiments and the Modelling of Internet Traffic - SAMSI
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<strong>Modelling</strong> Flows: Averages over Flows<br />
Tail <strong>of</strong> P<br />
Tail <strong>of</strong> D<br />
log( Pr[ P > k ] )<br />
0<br />
−1<br />
−2<br />
−3<br />
−4<br />
−5<br />
AUCK<br />
UNC<br />
Abilene<br />
Mel ISP<br />
−6<br />
0 1 2 3 4 5 6<br />
log( k )<br />
log( Pr[ D > x ] )<br />
0<br />
−0.2<br />
−0.4<br />
−0.6<br />
−0.8<br />
−1<br />
−1.2<br />
−1.4<br />
−1.6<br />
−1.8<br />
−2<br />
AUCK<br />
UNC<br />
Abilene<br />
Mel ISP<br />
−0.5 0 0.5 1 1.5 2 2.5<br />
log( x sec )<br />
• Slave durations to P<br />
• Heavy tail for P , use hyperbolic variable H(k; a, β)<br />
F H (k; a, β) = 1 − (ak + 1) −β ∼ 1 − Lk −β k = 1, 2, · · ·,<br />
• To match L <strong>and</strong> β <strong>and</strong> µ P , vary mixture parameter p ∈ [0, 1] for fixed (γ, a 2 ) = (2.5, 0.01):<br />
F P (k; p, a, β) = pF H (k; a 2 , γ) + (1 − p)F H (k; a, β)<br />
• Careful <strong>of</strong> power-law body, not just far tail!<br />
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