<title>Use of alpha-stable self-similar stochastic processes for modeling traffic in broadband networks</title>

Fractional lévy motion and its application to network traffic modeling

“…The rate of decay in (29) is at most an algebraic function of the buffer size, and is in accordance of the results reported in [5], and [8].…”

“…Our approach is different of the ones used in the literature, i.e., [2], [5], [8], [11], since we use the power series expansion of the probability distribution function of the fLm. …”

“…So, in continuous time, the cumulative traffic (or arrival) process At, that is the amount of total load (in bits, say) produced by a source in the time interval 0; t ; t 0 , can be modeled by At = mt + m 1= L ;H t; (14) where m 0 is the mean input rate, is the scale factor, and L ;H t is the fLm process defined by (5).…”

“…In [6], a comparison study of the queuing performance of the fGn and the noise induced by the LFSM is presented, and in [7] admission control issues are addressed. Consequently, similar models based on other self-similar -stable processes with stationary increments, e.g., -stable Levy motion, log-fractional stable motion, have tried to address the problem of self-similarity and heavy-tails at the same time [2], [5], [11]. For more information about these non-Gaussian processes see [23].…”

Nonlinear Least lp-Norm Filters for Nonlinear Autoregressive α-Stable Processes

“…Since Mandelbrot's work on financial time series analysis [29], α-stable distributions have found applications in econometrics, telecommunications (e.g., [30]), radar signal processing (e.g., [49]), teletraffic analysis (e.g., [14]), audio restoration (e.g., [25]), and recently in image processing (e.g., [26]). In particular, linear parametric models with SαS innovations have been extensively studied [6,35].…”