# Computer Sciences

## Method of Markovian summation for study the repeated flow in queueing tandem M|GI|∞ → GI|∞

The paper presents a mathematical model of queueing tandem M|GI|∞ → GI|∞ with feedback. The service times at the first stage are independent and identically distributed (i.i.d.) with an arbitrary distribution function B1(x). Service times at the second stage are i.i.d. with an arbitrary distribution function B2(x). The problem is to determine the probability distribution of the number of repeated customers (r-flow) during fixed time period.

## Heavy outgoing call asymptotics for MMPP|M|1 retrial queue with two way communication and multiple types of outgoing calls

In this paper, we consider a single server retrial queue MMPP|M|1 with two way communication and multiple types of outgoing calls. Calls received by the system occupy the device for operating, if it is free, or are sent to orbit, where they make a random delay before the next attempt to occupy the device. The duration of the delay has an exponential distribution. The main issue of this model is an existence of various types of outgoing calls in the system. The intensity of outgoing calls is different for different types of outgoing calls.

## Output process of the M|GI|1 is an asymptotical renewal process

Most of the studies on models with retrials are devoted to the research of the number of applications in the system or in the source of repeated calls using asymptotic and numerical approaches or simulation. Although one of the main characteristics that determines the quality of the communication system is the number of applications served by the system per unit of time. Information on the characteristics of the output processes is of great practical interest, since the output process of one system may be incoming to another.

## Multi-criteria approach to pair-multiple linear regression models constructing

A pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear regression model. In this case, pair-multiple regression models retain the ability to interpret the coefficients and predict the values of the explained variable.

## Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed.

## Analysis of Closed Queueing Networks with Batch Service

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy.

## Masking of Internal Nodes Faults Based on Applying of Incompletely Specified Boolean Functions

Combinational circuits (combinational parts of sequential circuits) are considered. Masking of internal nodes faults with applying sub-circuit, inputs of which are connected to the circuit inputs and outputs — to the circuit proper internal nodes, is suggested. The algorithm of deriving incompletely specified Boolean function for an internal node of the circuit based on using operations on ROBDDs is described.

## Using the Mask-RCNN Convolutional Neural Network to Automate the Construction of Two-Dimensional Solid Vertebral Models

Biomechanical modeling requires the construction of an accurate solid model of the object under study based on the data of a particular patient. This problem can be solved manually using modern software packages for medical data processing or using computer-aided design systems. This approach is used by many researchers and allows you to create accurate solid models, but is time consuming. In this regard, the automation of the construction of solid models suitable for performing biomechanical calculations is an urgent task and can be carried out using neural network technologies.

## 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.