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We consider a class of inhomogeneous Markovian queueing models with batch arrivals and group services. Bounds on the truncation errors in weak ergodic case are obtained. Two concrete queueing models are studied as examples.
The paper describes statistical approach to the analysis of traffic of information flows. Stochas-tic structure of traffic process can be modelled by finite probability mixtures, e.g., mixtures of gamma distributions. The approach is demonstrated on real data from the official website of the Russian Academy of Sciences.
We consider M t /M t /S-type queueing model with group services. Bounds on the rate of convergence for the queue-length process are obtained. Ordinary M t /M t /S queue and M t /M t /S type queueing model with group services are studied as examples.
A coordinate-wise modification of the grid method for separation of mixtures is proposed in the problem of the dynamical monitoring of the stochastic structure of information flows.
We investigate a class of exponentially weakly ergodic inhomogeneous birth and death processes. We consider special transformations of the reduced intensity matrix of the process and obtain uniform (in time) error bounds of truncations. Our approach also guarantees that we can find limiting characteristics approximately with an arbitrarily fixed error. As… (More)
We describe an algorithm to forecast financial risks using parametrized models of normal variance-mean mixtures. The proposed method takes a set of vectors as the input, containing a fixed number of the distribution parameters – the final result of the modified two-step grid-based decomposition algorithm applied to a moving time window. In this article we… (More)
In the paper, we discuss the transformation of the asymptotic expansion for the distribution of a statistic admitting Edgeworth expansion if the sample size is replaced by a random variable.We demonstrate that all those statistics that are regarded as asymptotically normal in the classical sense, become asymptotically Laplace or Student if the sample size… (More)