Self-similarity and long-range dependence in teletraffic
MUSP'09 Proceedings of the 9th WSEAS international conference on Multimedia systems & signal processing
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The stationary processes of waiting times {W n } n = 1,2,驴 in a GI/G/1 queue and queue sizes at successive departure epochs {Q n}n = 1,2,驴 in an M/G/1 queue are long-range dependent when 3 S S is the moment index of the independent identically distributed (i.i.d.) sequence of service times. When the tail of the service time is regularly varying at infinity the stationary long-range dependent process {W n } has Hurst index 陆(5驴驴 S ), i.e. $${\rm sup} \left\{h : {\rm lim sup}_{n\to\infty}\, \frac{{\rm var}(W_1+\cdots+W_n)}{n^{2h}} = \infty \right\} = \frac{5-\kappa_S} {2}\,.$$ If this assumption does not hold but the sequence of serial correlation coefficients {驴 n } of the stationary process {W n } behaves asymptotically as cn 驴驴 for some finite positive c and 驴 驴 (0,1), where 驴 = 驴 S 驴 3, then {W n } has Hurst index 陆(5驴驴 S ). If this condition also holds for the sequence of serial correlation coefficients {r n } of the stationary process {Q n } then it also has Hurst index 陆(5驴 S )