Long-tail Traffic - Short-range Dependence Vs. Long-range Dependence

Short-range Dependence Vs. Long-range Dependence

Long-range and short-range dependent processes are characterised by their autocovariance functions.

In short-range dependent processes, the coupling between values at different times decreases rapidly as the time difference increases.

• The sum of the autocorrelation function over all lags is finite.
• As the lag increases, the autocorrelation function of short-range dependent processes decays quickly.

In long-range processes, the correlations at longer time scales are more significant.

• The area under the autocorrelation function summed over all lags is infinite .
• The decay of the autocorrelation function is often assumed to have the specific functional form,

where ρ(k) is the autocorrelation function at a lag k, α is a parameter in the interval (0,1) and the ~ means asymptotically proportional to as k approaches infinity.