In this paper the 6×6 fundamental matrix of a linear six- dimensional system with arbitrary piecewise-constant parameters isobtained in the analytical form in elementary functions for the firsttime. To write this matrix the new sign-functionF(i,j)qis introducedand described here. This function determines the order of interactionof eigen-oscillations of intervals with constant parameters in a result-ing equivalent oscillation. The fundamentally new concept of equivalentoscillations for six-dimensional systems is introduced for the first timetoo. The stability problem of these systems is considered and the stabil-ity conditions are obtained in the analytical form in original parametersof a linear six-dimensional system. The results obtained allow solving anumber of problems in mechanics, electrical engineering, communicationsystems, optoelectronics, automatic control theory and information the-ory. It can be, for example, the problems of determining the stability ofdynamical systems, the problems of synthesizing dynamical systems ofvarious nature, etc В работе впервые получена фундаментальная матрица 6 × 6 линейной шестимерной системы с произвольными кусочно-постоянными параметрами в аналитическом виде в элементарных функциях. Для записи этой матрицы здесь вводится и описывается новая знаковая функция F (i, j) q. Эта функция определяет порядок взаимодействия собственных колебаний интервалов с постоянными параметрами в результирующем эквивалентном колебании. Впервые вводится принципиально новое понятие эквивалентных колебаний для шестимерных систем. Рассмотрена проблема устойчивости этих систем и получены условия устойчивости в аналитическом виде в исходных параметрах линейной шестимерной системы. Полученные результаты позволяют решать ряд задач механики, электротехники, систем связи, оптоэлектроники, теории автоматического управления и теории информации. Это могут быть, например, задачи определения устойчивости динамических систем, задачи синтеза динамических систем различной природы и т. д.

The paper is dedicated to the design problem of a wireless communication network. The problem of base stations optimal placement along a linear section subject to control with end-to-end delay limited is formulated. The goal is to maximize the coverage area that comes to under the control of multiple deployed base stations while respecting technological conditions and budget constraints. In the paper, the features of the technological statement are analyzed. The formulation of the problem in the form of integer linear programming is proposed. When forming a mathematical model, a queuing network model with a Poisson arrival process is used.

The article discusses a multiphase queuing system with a recurrent incoming flow, storage units of unlimited capacity, and recurrent service times at its nodes. To analyze and evaluate the main parameters of the performance of this network, a new approach is presented, which consists in combining simulation with data mining methods. This approach is universal in nature, and its area of application is not limited to studies of tandem networks only, but, on the contrary, extends to any other networks of arbitrary topology, as well as to queuing systems with various combinations of its main components. To assess the quality of the characteristics obtained, namely the average end-to-end delay, a comparative analysis is carried out with the known approximate results obtained in earlier works.

In the light of the proliferation of the Internet of Things (IoT), the device-to-device (D2D) communication is becoming a promising technology and a key enabler for enhancing the energy efficiency of the wireless network environment and reducing the traffic latency between user equipments (UEs) within their communication range. This papers considers one simplified analytical framework for modeling of communication offloading scenario within the D2D communications underlying cellular network, in which a UE generates a session toward another UE in the same cell. The model aims to improve the system capacity and energy-efficiency by offloading cellular traffic onto D2D communications, when the source and destination UEs are proximate enough to satisfy their QoS requirements.

The problem of sensitivity of a redundant system’s probability characteristics to shapes of the input distributions is considered. In some previous works, closed-form representations have been obtained for stationary characteristics of hot-standby redundant systems with exponential lifetime distribution of their elements and general distribution of their repair time. In the current paper we carry out the sensitivity analysis of a k-out-of −n :F system with the help of a simulation approach. Comparison of analytic and simulation results is presented.