Universal model for collective access patterns in the Internet traffic dynamics: A superstatistical approach

Abstract

We suggest a universal phenomenological description for the collective access patterns in the Internet traffic dynamics both at local and wide area network levels that takes into account erratic fluctuations imposed by cooperative user behaviour. Our description is based on the superstatistical approach and leads to the q-exponential inter-session time and session size distributions that are also in perfect agreement with empirical observations. The validity of the proposed description is confirmed explicitly by the analysis of complete 10-day traffic traces from the WIDE backbone link and from the local campus area network downlink from the Internet Service Provider. Remarkably, the same functional forms have been observed in the historic access patterns from single WWW servers. The suggested approach effectively accounts for the complex interplay of both "calm" and "bursty" user access patterns within a single-model setting. It also provides average sojourn time estimates with reasonable accuracy, as indicated by the queuing system performance simulation, this way largely overcoming the failure of Poisson modelling of the Internet traffic dynamics.

Superstatistical model of bacterial DNA architecture

“…In recent years, the same functional form of the distribution have been numerously observed in the dynamical and structural characteristics of several very different complex systems (see, e.g. refs 29 , 35 , 36 , 37 , 38 and references therein).…”

Video-based marker-free tracking and multi-scale analysis of mouse locomotor activity and behavioral aspects in an open field arena: A perspective approach to the quantification of complex gait disturbances associated with Alzheimer's disease

“…The latter could be potentially resolved by considering a two-level cascade model, with the first level representing the animal walking trajectory (e.g., at the body midpoint), and the second level representing animal body part movements relative to the body midpoint. The above scenario can be represented by the so-called superstatistical models (Beck and Cohen, 2003 ; Beck et al, 2005 ) that have been recently applied in the context of various natural complex systems ranging from climate and weather to information flow dynamics, as well as DNA and protein structures (Bogachev et al, 2016 , 2017 ; Tamazian et al, 2016 ; Markelov et al, 2017 ; Itto and Beck, 2021 ; Schäfer et al, 2021 ).…”

“…The latter implies that partial correlations represent a more appropriate quantity for the reconstruction of the complex animal behavior patterns from multi-scale movement analysis data. Indeed, the most intuitive way to simulate the animal movement patterns would follow a somewhat hierarchical algorithm, starting with the reconstruction of the overall animal walking pattern on large scales, further complemented by specific gait characteristics at smaller scales, as it is commonly done in the framework of superstatistical models (Beck and Cohen, 2003 ; Beck et al, 2005 ; Bogachev et al, 2016 , 2017 ; Tamazian et al, 2016 ; Markelov et al, 2017 ; Itto and Beck, 2021 ; Schäfer et al, 2021 ). A somewhat similar approach could be potentially based on the multi-scale partial cross-correlation data, which contains essential information about the relative movement characteristics of the animal body parts, while remaining invariant to particular trajectories traveled by the animals during tests, due to the detrending features of the algorithm.…”

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“…It should be noted that the proposed approach is intended to be used for small sample sizes, when no statistic alone is capable of high precision and high trueness. With the increasing sample size, all statistics should converge to the same risk of being in error and present other alternatives, such as the superstatistical approach [40]. In the same context, each of the drawings included in the sample are supposed to be independent.…”