# Computer Sciences

## 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%).

## About closed queuing networks with variable number of queues

Consider a closed queueing network with the possibility of breakdowns at each server. When a breakdown occurs at one server, all customers there are transferred in queue with operational server immediately, and the server is then sent for repair. Steady- state probability of the queue sizes is obtained, and is shown to have a product form solution.

## Some interval problems of the theory of discrete linear systems

Artificial neural networks can be used effectively for a quite general class of problems. Still there exists no formal foundation of some important constructions used in the theory. In this paper an

attempt is undertaken to formalize some concepts of neuroinformatics and consider their properties from the point of view of applied universal algebra. It is proposed to treat neural networks as heterogeneous algebras which has made it possible to prove for them basic results similar to algebraic theorems on homomorphisms and congruences.

## Modeling the Dynamics of Massless Charge Carries is Two-Dimensional System

The paper presents the results obtained in the process of developing a system for simulating the generation of massless charge carriers with a photon-like spectrum by an external electric field for two-dimensional media. The basis of the system is a physical model of the process, built in the formalism of a kinetic equation for an adequate quantum-field theory. It does not use simplifying assumptions, including expansions in some small parameters (perturbation theory). In this sense, the model used is accurate.

## The Study of the Statistical Characteristics of the Text Based on the Graph Model of the Linguistic Corpus

The article is devoted to the study of the statistical characteristics of the text, which are calculated on the basis of the graph model of the text from the linguistic corpus. The introduction describes

## Construction of All Minimal Edge Extensions of the Graph with Isomorphism Rejection

In 1993 Frank Harary and John P. Hayes proposed a graph model for investigating edge fault tolerance of discrete systems. The technical system is mapped to a graph. The elements of the system correspond to the vertices of the graph, and links between the elements correspond to edges or arcs of the graph. Failure of a system element refers to the removal of the corresponding vertex from the system graph along with all its edges. The formalization of a fault tolerant system implementation is the extension of the graph.

## Geometrical images of finite state machines

In this work a new way of defining finite state machines (FSM) is being suggested. The discrete word geometry is built for that purpose, in which machine image is expressed as a set of lines. The methods of synthesis and analysis of geometrical images of FSMs and their features are researched. The new way of defining the FSMs allows analyzing the machine's behavior, excluding the exhausting recursive procedure of defining the initial fragments of machine functioning.

## Algebraic properties of recurrent neural networks of discrete time

Artificial neural networks can be used effectively for a quite general class of problems. Still there exists no formal foundation of some important constructions used in the theory. In this paper an attempt is undertaken to formalize some concepts of neuroinformatics and consider their properties from the point of view of applied universal algebra. It is proposed to treat neural networks as heterogeneous algebras which has made it possible to prove for them basic results similar to algebraic theorems on homomorphisms and congruences.