# Computer Sciences

## 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.

## 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.