Analysis of an ATM buffer with self-similar ("fractal") input traffic

Performance evaluation of a queue fed by a Poisson Pareto burst process

“…Notice that if a burst starts in the middle of a time-slot and continues beyond the end of that time-slot, its contribution to the work arriving in that time-slot is τr/2, which is not necessarily integer. In limiting cases for low λ and/or high E(d) our process will behave in a very similar fashion to the discrete-valued processes of [11,14,20,26,28,29].…”

“…In [30], it was shown that one possible source of this burstiness was in the aggregation of independent on-off sources with heavy tailed, on and/or off, time distributions. In [14], it was shown that a model such as the PPBP could be considered a limiting case for the multiplexing of a large number of such independent heavy-tailed on-off sources. Thus, the PPBP is a natural candidate for the modeling of LRD packet data traffic streams.…”

“…Tsybakov and Georganas have been amongst the leaders in studies of these processes. Together with Likhanov they showed in [14] that a model such as the PPBP could be considered a limiting case for the multiplexing of a large number of independent on-off sources with heavy tailed on and/or off time distributions. They examined the conditions under which M/G/∞ processes are self-similar in [27].…”

A Model of Self-Similar Data Traffic Applied to Ethernet Traces

“…This paper proposes a self-similar traffic model based on multiplexed Pareto point arrival processes. This model has several advantages relative to FBM and other proposed models [6]- [8]. First, the proposed model appears to be in good agreement with real Ethernet data, based on analysis of the marginal lA T distribution and correlation structure.…”

A Self-Similar Point Process Through Fractal Construction

“…This traffic tends to be so bursty, that even bursts are composed of bursts of bursts (a fractal "like" property). Several useful models have been proposed that capture this behavior, namely the M |G|∞ (with Pareto service times) model [9], the superposition of two state Markovian sources [10], the mixture of exponentials to fit the long-tail distributions citeFeldman, the superposition of N On-Off processes with sub-exponential On periods [12,13], deterministic chaotic maps [14] and self-similar (fractal) point processes [1,15,4]. In each of the above models, it has been shown that the number of arrivals over an interval (number of busy servers in M |G|∞ model) all exhibit a long-range dependent correlation structure.…”