糰■ 200300400600600 Do 300 400 Goo 60 TUn一10。B。nd Time Un a 10 corda o1o0200300405。o7oo 100200304005000700日00100 Time Unit·1 Second TUnN1sc。nd 01002003004005o6o70o8009001000 010020030。405060700B0。901000 Time Unh·.1 :幽N山M 0020030040。Bo007080901000 0100200 05o6007o80op0o1000 THme Uni- 0.01 second un·0.o1 Second 11w.E. Leland, M.S. Taqqu, w. Willinger: and D. v. wilson, On the self-similar nature of ethernet traffic (extended version), IEEE/ACM Trans. Networking, vol. 2, no. 1, pp. 1-15, Feb. 1994
[1] W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, “On the self-similar nature of ethernet traffic (extended version),” IEEE/ACM Trans. Networking, vol. 2, no. 1, pp. 1–15, Feb. 1994. 11
An lRD Process a a process, X=L, t=1, 2,3, with mean m and variance oz Autocovariance function, Y(k=EL(- m(xtk-mI, decays slower than exponential IID-Independent and identically distributed MMPP- Markoy modulated Poisson process LRD Poisson MMPP k
k LRD MMPP IID Poisson 0 IID – Independent and Identically Distributed MMPP – Markov Modulated Poisson Process A process, X={Xt , t=1,2,…}, with mean m and variance σ 2 . Autocovariance function, γ(k) = E[(Xt -m)(Xt+k -m)], decays slower than exponential. 12
An lRD Process a a process, X=L, t=1, 2, 3, with mean m and variance o2 Autocovariance function, r(k=EL(X-m(Xt+k-ml decays slowly Autocorrelation function(ACF), P(k=r k/o, follows ∑|p(k)=∞,andp(k)~ck21-1),k→ Hurst parameter H: the measure of the degree of the Lrd 0.5<H<1> the process iS LRD The aggregate process of X with interval t Xt follows VarX(t) 2H t→
A process, X={Xt , t=1,2,…}, with mean m and variance σ 2 . Autocovariance function, γ(k) = E[(Xt -m)(Xt+k -m)], decays slowly. Autocorrelation function (ACF), ρ(k) = γ(k)/σ 2 , follows Hurst parameter H : the measure of the degree of the LRD. 0.5 < H < 1 → the process is LRD The aggregate process of X with interval t, X (t) follows 13
Traffic Modelling Traffic Input process Data Sampling m Fitting the Important statistics of traffic parameters mean(m), variance(o and Hurst parameter(H) Traffic mod
… Data Data … Data Traffic Sampling Input process Traffic model Fitting the parameters 14 Important statistics of traffic: mean (m), variance (σ 2 ) and Hurst parameter (H)
Obiective LRD process>Input trafic process Single Server Queue(SSQ)> Link Overflow probability QoS LRD Queue LRD process SSO Ouput P(Q>X)? Mean(m SSO with oo buffer Variance(o Steady state Queue Size (Q Hurst parameter(H) Service rate(u)
LRD process → Input traffic process Single Server Queue (SSQ) → Link Overflow probability → QoS Mean (m) Variance (σ 2 ) Hurst parameter (H) SSQ with ∞ buffer Steady state Queue Size (Q) Service rate (μ) LRD process Output SSQ P(Q>x)? LRD Queue 15