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 …

We introduce a general non-Gaussian, self-similar, stochastic process called the fractional
Lévy motion (fLm). We formally expand the family of traditional fractal network traffic models …

The result provided in this paper helps complete a unified picture of the scaling behavior in
heavy-tailed stochastic models for transmission of packet traffic on high-speed …

Long-range dependence has been recently asserted to be an important characteristic in
modeling telecommunications traffic. Inspired by the integral relationship between the …

We provide an overview of some of the research of the last ten years involving computer
network data traffic. We describe the original Ethernet data study which suggested that …

The usual concept of asymptotic independence, as discussed in the context of extreme
value theory, requires the distribution of the coordinatewise sample maxima under suitable …

Recent Bellcore studies have shown that high-speed data traffic exhibits “long-range
dependence”, characterized by H> 0.5, where H is the Hurst parameter of the traffic. In the …

After measurements on a LAN at Bellcore, it is known that data traffic is extremely variable
on timescales ranging from milliseconds to days. The traffic behaves quite different from …

We state and prove the following key mathematical result in self-similar traffic modeling: the
superposition of many ON/OFF sources (also known as packet trains) with strictly alternating …

We study the heavy traffic regime of a multiplexer driven by correlated inputs, namely the
M∨ GI∨∞ input processes of Cox. We distinguish between M∨ GI∨∞ processes with …