Volume 218, Nº 3 (2016)

The concept of getting services and applications at “any time” and at “any place” requires the corresponding development of cellular networks, namely in LTE networks. At present, there is a lack of quality of service related recommendations describing various popular services, e.g., video conferencing. The problem is to find the optimal bit rate values for this service while not affecting the background lower priority services. In this paper we propose an instrument for solving this problem. First, we obtain mathematical model in the form of a queueing system with multicast highpriority traffic and unicast background traffic. The admission control assumes the adaptive bit rate change of multicast traffic and unicast traffic interruption. Second, we obtain the recursive algorithm for calculating mean bit rate and other performance measures. Third, we study the problem of optimizing mean bit rate.

One of the most popular experimental techniques for investigation of brain activity is the so-called method of evoked potentials: the subject repeatedly makes some movements (by his/her finger), whereas brain activity and some auxiliary signals are recorded for further analysis. The key problem is the detection of points in the myogram that correspond to the beginning of the movements. The more precisely the points are detected, the more successfully the magnetoencephalogram is processed aiming at the identification of sensors that are closest to the activity areas.

This paper proposes a statistical approach to this problem based on mixtures models that uses a specially modified method of moving separation of mixtures of probability distributions (MSMmethod) to detect the start points of the finger’s movements. We demonstrate the correctness of the new procedure and its advantages as compared with the method based on the notion of the myogram window variance.

In this paper, product representations are obtained for random variables with theWeibull distribution in terms of random variables with normal, exponential and stable distributions yielding scale mixture representations for the corresponding distributions. Main attention is paid to the case where the shape parameter γ of theWeibull distribution belongs to the interval (0, 1]. The case of small values of γ is of special interest, since the Weibull distributions with such parameters occupy an intermediate position between distributions with exponentially decreasing tails (e.g., exponential and gamma-distributions) and heavy-tailed distributions with Zipf–Pareto power-type decrease of tails. As a by-product result of the representation of the Weibull distribution with γ ∈ (0, 1) in the form of a mixed exponential distribution, the explicit representation of the moments of symmetric or one-sided strictly stable distributions are obtained. It is demonstrated that if γ ∈ (0, 1], then the Weibull distribution is a mixed half-normal law, and hence, it can be limiting for maximal random sums of independent random variables with finite variances. It is also demonstrated that the symmetric two-sided Weibull distribution with γ ∈ (0, 1] is a scale mixture of normal laws. Necessary and sufficient conditions are proved for the convergence of the distributions of extremal random sums of independent random variables with finite variances and of the distributions of the absolute values of these random sums to the Weibull distribution as well as of those of random sums themselves to the symmetric two-sided Weibull distribution. These results can serve as theoretical grounds for the application of the Weibull distribution as an asymptotic approximation for statistical regularities observed in the scheme of stopped random walks used, say, to describe the evolution of stock prices and financial indexes. Also, necessary and sufficient conditions are proved for the convergence of the distributions of more general regular statistics constructed from samples with random sizes to the symmetric two-sided Weibull distribution.

In the paper the multichannel stochastic networks are considered. A non-homogeneous Poisson input flow of calls arrives at each node. An approximate method of investigation of the service process in heavy traffic is developed. For the multichannel Markovian networks the limit process is represented as a multidimensional diffusion.

In this paper, we propose robust numerical methods for finding the maximum likelihood estimation of the generalized inverse Gaussian distribution. A comparative analysis of the existing algorithms and the results of numerical experiments are presented. Special attention is paid to reproducibility of the tests.