Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Maximizing information exchange between complex networks

We introduce the concept of generalized stochastically bounded burstiness (gSBB) for Internet traffic, the tail distribution of whose burstiness can be bounded by a decreasing function in a function class with few restrictions. This new concept extends the concept of stochastically bounded burstiness (SBB) introduced by previous researchers to a much larger extent - while the SBB model can apply to Gaussian self-similar input processes, such as fractional Brownian motion, gSBB traffic contains non-Gaussian self-similar input processes, such as /spl alpha/-stable self-similar processes, which are not SBB in general. We develop a network calculus for gSBB traffic. We characterize gSBB traffic by the distribution of its queue size. We explore the property of sums of gSBB traffic and the relation of input and output processes. We apply this calculus to a work-conserving system shared by a number of gSBB sources, to analyze the behavior of output traffic for each source and to estimate the probabilistic bounds for delays. We expect this new calculus to be of particular interest in the implementation of services with statistical qualitative guarantees.

Analysis on generalized stochastically bounded bursty traffic for communication networks

Fundamental calculus on generalized stochastically bounded bursty traffic for communication networks

The high plasma temperatures expected at reactor conditions in magnetic confinement fusion toroidal devices suggest that near-marginal operation could be a reality in future devices and reactors. By near-marginal it is meant that the plasma profiles might wander around the local critical thresholds for the onset of instabilities. Self-organized criticality (SOC) was suggested in the mid 1990s as a more proper paradigm to describe the dynamics of tokamak plasma transport in near-marginal conditions. It advocated that, near marginality, the evolution of mean profiles and fluctuations should be considered simultaneously, in contrast to the more common view of a large separation of scales existing between them. Otherwise, intrinsic features of near-marginal transport would be missed, that are of importance to understand the properties of energy confinement. In the intervening 20 years, the relevance of the idea of SOC for near-marginal transport in fusion plasmas has transitioned from an initial excessive hype to the much more realistic standing of today, which we will attempt to examine critically in this review paper. First, the main theoretical ideas behind SOC will be described. Secondly, how they might relate to the dynamics of near-marginal transport in real magnetically confined plasmas will be discussed. Next, we will review what has been learnt about SOC from various numerical studies and what it has meant for the way in which we do numerical simulation of fusion plasmas today. Then, we will discuss the experimental evidence available from the several experiments that have looked for SOC dynamics in fusion plasmas. Finally, we will conclude by identifying the various problems that still remain open to investigation in this area. Special attention will be given to the discussion of frequent misconceptions and ongoing controversies. The review also contains a description of ongoing efforts that seek effective transport models better suited than traditional equations to capture SOC dynamics. Most of these models, based on the use of fractional transport equations and related concepts, could prove useful both in reactor operation and experiment control and design.

http://iopscience.iop.org/article/10.1088/0741-3335/57/12/123002/pdf

I. Lambadatis

Papers

Fractional Lévy motion and its applocation to network traffic modeling