Konstantopoulos, Takis; Lin, Si-Jian Macroscopic models for long-range dependent network traffic. (English) Zbl 0908.90131 Queueing Syst. 28, No. 1-3, 215-243 (1998). Summary: A common way to inject long-range dependence in a stochastic traffic model possessing a weak regenerative structure is to make the variance of the underlying period infinite (while keeping the mean finite). This method is supported both by physical reasoning and by experimental evidence. We exhibit the long-range dependence of such a process and, by studying its second-order properties, we asymptotically match its correlation structure to that of a fractional Brownian motion. By studying a certain distributional limit theorem associated with such a process, we explain the emergence of an extremely skewed stable Lévy motion as a macroscopic model for the aforementioned traffic. Surprisingly, long-range dependence vanishes in the limit, being “replaced” by independent increments and highly varying marginals. The marginal distribution is computed and is shown to match the one empirically obtained in practice. Results on performance of queueing systems with Lévy inputs of the aforementioned type are also reported in this paper: they are shown to be in agreement with pre-limiting models, without violating experimental queueing analysis. Cited in 24 Documents MSC: 90B22 Queues and service in operations research 60K25 Queueing theory (aspects of probability theory) Keywords:long-range dependence; Lévy processes; traffic modeling; performance evaluation; self-similarity; regular variation; stochastic traffic model; fractional Brownian motion; marginal distribution PDFBibTeX XMLCite \textit{T. Konstantopoulos} and \textit{S.-J. Lin}, Queueing Syst. 28, No. 1--3, 215--243 (1998; Zbl 0908.90131) Full Text: DOI