# Computer Sciences

## On a Total Resource Amounts at the System with Parallel Service and MMPP Arrivals

In this paper, we consider a resource system with an unlimited resources and servers number, with parallel customers servicing, arriving at the system according to the MMPP. Using a combination of multidimensional dynamic screening methods and asymptotic analysis, it is proved that the joint asymptotic probability distribution of the total resource amounts converges to a bi-dimensional Gaussian distribution under conditions of increasing intensity of MMPP. The parameters of the asymptotic probability distribution are found.

## Heterogeneous Queueing System MR(S)/M(S)/∞ with Service Parameters Depending on the State of the Underlying Markov Chain

Data streams in information and communication systems include integrated heterogeneous streams, containing voice, text data and video. Since the service of different information units takes different time depending on their format, used protocols and so on, it is proposed to model such data transmission processes using heterogeneous queueing systems with services depending on the parameters of the incoming stream. In the paper, an infinite-server heterogeneous queueing system is considered.

## Performance Analysis of Elastic Traffic with Minimum Bit Rate Guarantee Transmission in Wireless Network under Network Slicing

Future mobile networks are expected to support a significant number of applications and services. With limited network bandwidth, the usual allocation of resources leads to inefficient use of radio access networks. A possible solution is network slicing technology designed to distribute resources between virtual mobile operators. The aim of this work is to study and evaluate the performance indicators of such a network using the example of a file download service with a minimum guaranteed data transfer rate.

## Ternary Discrete Wavelet Basis

The discrete version and the basic construction of the ternary multiresolution analysis are given, similar to the binary model case of the Haar multiresolution analysis. Based on the constructed basis, an algorithm similar to the fast Haar transformation is proposed. Typical calculation examples are provided.

## An Analysis Method of Open Queueing Networks with a Degradable Structure and Instantaneous Repair Times of Systems

An unreliable open queueing network with Poisson arrivals is considered. For each queueing system the service and failures times are exponentially distributed random variables. The failures of systems lead to changes in the structure of the network and corresponding changes in the performance measures of the queueing network. It is assumed that the times between changes in the network structure are sufficient for the steady-state regime. The main measure of the quality for the network at each structure constancy interval is the average response time.

## Markov Chain States Classification in a Tandem Model with a Cyclic Service Algorithm with Prolongation

There is a limited list of papers about crossroads tandems. Usually the following service algorithms are under consideration: a cyclic algorithm with fixed duration, a cyclic algorithm with a loop a cyclic algorithm with regime changes etc. To construct a formal mathematical model of queuing systems nets and crossroads tandems in particular a descriptive approach is usually used. Using this approach input flows and service algorithms are set at the level of content, service duration distribution is known and set via a particular customer service distribution function.

## Survival Rate of Model Populations Depending on the Strategy of Energy Exchange Between the Organisms

The paper addresses the influence of the energy exchange strategy between the organisms of a population in a gradually changing environment on the survival rate of this population. At the first stage of computational experiments, a “boundary” region is determined in the space of two parameters (mutation rate and energy supply rate), within which the survival of populations with zero energy exchange is ambiguous (lies in the interval from 5 to 95%).

## Комплексный контроль ресурсов сложных человекомашинных систем

Исследуется природа возникновения аварийных ситуаций и катастроф в сложных человекомашинных системах. В целях комплексной оценки и прогнозирования аварийных ситуаций предлагается рассматривать ресурс системы в виде набора показателей, включающего человеческие ресурсы и ресурсы машин. Прогнозирование аварий предлагается осуществлять с проверкой логических условий безопасности, которые объединяют разнородные ресурсы системы.

## The Effectiveness Analysis of Several Parallel Algorithms Based on Simulated Annealing Method of Global Optimization Problem Solving

This article presents the results of the development of a parallel computing system and testing its capabilities applied to solving scientific and educational problems. Three parallel variants of the simulated annealing algorithm are proposed and implemented for multiextreme criterion function of two variables with explicit constraints. The reliability and performance of parallel versions of the algorithm, depending on their parameters and the number of working nodes in parallel computing system, is investigated.

## On the Error of Approximation by Means of Scenario Trees with Depth 1

Let¤n denote the set of scenario trees with depth 1 and n scenarios. LetX = (0 · x1 < . . . < xn · 1) and let¤n(X) denote the set of all scenario trees of depth 1 with the scenarios X = (0 · x1 < . . . < xn · 1). Let G be a probability distribution defined on [0, 1] and H be a subset of measurable functions defined on [0, 1]. Let dH,X(G) = inf ˜G∈¤n(X) dH(G, ˜ G) and dH(G) = inf ˜G∈¤n dH(G, ˜ G), where dH(G, ˜ G) := suph∈H ¯¯¯ R h dG − R h d˜G ¯¯¯ .