An abstract model for aggregated connectionless traffic, based on the fractional Brownian motion, is presented. Insight into parameters obtained by relating to an equivalent burst model. Results a corresponding storage process are The buffer occupancy distribution approximated Weibull distribution. compared with publicly available samples of real Ethernet traffic. degree short-term predictability traffic studied through exact formula conditional variance future value given past....

The Radon±Nikodym derivative between a centred fractional Brownian motion Z and the same process with constant drift is derived by ®nding an integral transformation which changes to independent increments.A representation of through standard on ®nite interval given.The maximum-likelihood estimator some other applications are presented.

This study was designed to investigate the relative accident risk of different road weather conditions and combinations conditions. The applied a recently developed method which is based on notion Palm probability, originating in theory random point processes, this case corresponds picking vehicle from traffic. consists calculating distribution comparing it with same as seen by accidents. condition affects statistically, when these two distributions differ. included all police reported...

Random (pseudo)graphs G N with the following structure are studied: first, independent and identically distributed capacities Λ i drawn for vertices = 1, …, ; then, each pair of ( , j ) is connected, independently other pairs, E edges, where has distribution Poisson(Λ / ∑ k =1 ). The main result paper that when P(Λ 1 > x) ≥ x −τ+1 τ ∈ (2, 3), asymptotically almost surely, a giant component, distance between two randomly selected component less than (2 + o ))(log log )/(-log (τ − 2)). It...

Integration with respect to the fractional Brownian motion Z Hurst parameter is discussed. The predictor represented as an integral Z, solving a weakly singular equation for prediction weight function.

When variable-bit-rate sources are multiplexed in an asynchronous transfer mode (ATM) network, there arise queues with a particular form of correlated arrival process. Such analyzed by exploiting result expressing the distribution work system G/G/1 queue originally derived V.E. Benes (1963). A simple alternative demonstration this is and extended to case fluid input systems. The applied first where process superposition periodic (the Sigma D/sub i//D/1 queue), then variable-input-rate...

We search for methods or tools to detect whether the 1-dimensional marginal distribution of traffic increments aggregate TCP-traffic satisfy hypothesis approximate normality. Gaussian approximation requires a high level aggregation in both "vertical" (source aggregation) and "horizontal" (time scale) directions. discuss these different concepts first separately, with an example from real data traffic, show how rule out cases where will not be sufficient. is then quantified square linear...

Abstract In this paper, performance formulae for a queue serving Gaussian traffic are presented. The main technique employed is motivated by general form of Schilder's theorem, the large deviation result processes. Most probable paths leading to given buffer occupancy identified. Special attention case where sample pams die process smooth. approximations compared with known analytical results or means simulation. appear be surprisingly accurate.

Random (pseudo)graphs G N with the following structure are studied: first, independent and identically distributed capacities Λ i drawn for vertices = 1, …, ; then, each pair of ( , j ) is connected, independently other pairs, E edges, where has distribution Poisson(Λ / ∑ k =1 ). The main result paper that when P(Λ 1 > x) ≥ x −τ+1 τ ∈ (2, 3), asymptotically almost surely, a giant component, distance between two randomly selected component less than (2 + o ))(log log )/(-log (τ − 2))....

In this paper we study the size of largest clique ω( G ( n , α)) in a random graph α) on vertices which has power-law degree distribution with exponent α. We show that, for ‘flat’ sequences α > 2, high probability, is constant size, while, heavy tail distribution, when 0 < grows as power . Moreover, that natural simple algorithm probability finds large (1 − o (1))ω( polynomial time.

We give two sets of conditions for the association a system's component life lengths. The are dynamic in sense that they based on evaluating, at any given time t, effect failure would have future behaviour. Of basic importance is concept “weakened by failures” introduced paper. Mathematically paper martingales case jump processes, or marked point processes.

This paper studies the limits of a spatial random field generated by uniformly scattered sets, as density λ sets grows to infinity and mean volume ρ tends zero. Assuming that distribution has regularly varying tail with infinite variance, we show centered renormalized can have three different limits, depending on relative speed at which are scaled. If much faster than shrinks, limit is Gaussian long-range dependence, while in opposite case, independently second moments. In special...

Integration with respect to the fractional Brownian motion Z Hurst parameter is discussed. The predictor represented as an integral Z, solving a weakly singular equation for prediction weight function.

We introduce a general transformation of hazard rates and discuss the corresponding change life length distribution. Minimal repair transformations are shown to be special cases this framework which builds on results concerning likelihood ratios for point processes, in particular Girsanov theorem processes. then study role available information consequent definition “state” distributions. By using notion F-minimal repair, where F stands identifies state considered device, we show that “black...

In various fields, such as teletraffic and economics, measured time series have been reported to adhere multifractal scaling. Classical cascading measures possess scaling, but their increments form a nonstationary process. To overcome this problem, we introduce construction of random based on iterative multiplication stationary stochastic processes, special T -martingales. We study the ℒ 2 -convergence, nondegeneracy, continuity limit Establishing power law for its moments, obtain formula...