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## Über dieses Buch

This book constitutes the refereed proceedings of the 19th International Conference on Distributed and Computer and Communication Networks, DCCN 2016, held in Moscow, Russia, in November 2016.

The 50 revised full papers and the 6 revised short papers presented were carefully reviewed and selected from 141 submissions. The papers cover the following topics: computer and communication networks architecture optimization; control in computer and communication networks; performance and QoS/QoE evaluation in wireless networks; analytical modeling and simulation of next-generation communications systems; queuing theory and reliability theory applications in computer networks; wireless 4G/5G networks, cm- and mm-wave radio technologies; RFID technology and its application in intellectual transportation networks; internet of things, wearables, and applications of distributed information systems; probabilistic and statistical models in information systems; mathematical modeling of high-tech systems; mathematical modeling and control problems; distributed and cloud computing systems, big data analytics.

## Inhaltsverzeichnis

### Enhanced C-RAN Architecture Supporting SDN and NFV Functionalities for D2D Communications

Future Fifth Generation (5G) cellular systems will be characterized by ultra-dense areas, where users are gradually asking for new multimedia applications and hungry-bandwidth services. Therefore, a promising solution to boost and optimize this future wireless heterogeneous networks is represented by the Cloud Radio Access Network (C-RAN) with the joint use of Software Defined Networking (SDN) and Network Function Virtualization (NFV). In such a scenario, low power base stations and device-to-device communications (D2D), involved into traditional cellular network, represented a possible solution to offload the heavy traffic of macrocells, while guaranteeing user experience as well. Nevertheless, the high centralization and the limited-capacity backhauls makes it difficult to perform centralized control plane functions on a large network scale. To address this issue, we investigate the integration of two enabling technologies for C-RAN (i.e., SDN and NFV) in the current 5G heterogeneous wireless architecture in order to exploit properly proximity-based transmissions among devices. Then, in order to validate the applicability of our proposed architecture, we consider the case of D2D pair handover where we show that our solution is able to decrease the number of signaling messages needed to handoff the D2D pair from a source to a target base station and, at the same time, the time execution for the entire handover process.

Antonino Orsino, Giuseppe Araniti, Li Wang, Antonio Iera

### On Internet of Things Programming Models

In this paper, we present the review of existing and proposed programming models for Internet of Things (IoT) applications. The requests by the economy and the development of computer technologies (e.g., cloud-based models) have led to an increase in large-scale projects in the IoT area. The large-scale IoT systems should be able to integrate diverse types of IoT devices and support big data analytics. And, of course, they should be developed and updated at a reasonable cost and within a reasonable time. Due to the complexity, scale, and diversity of IoT systems, programming for IoT applications is a great challenge. And this challenge requires programming models and development systems at all stages of development and for all aspects of IoT development. The first target for this review is a set of existing and future educational programs in information and communication technologies at universities, which, obviously, must somehow respond to the demands of the development of IoT systems.

Dmitry Namiot, Manfred Sneps-Sneppe

### A Trial of Yoking-Proof Protocol in RFID-based Smart-Home Environment

Owing to significant progress in the Internet of Things (IoT) within both academia and industry, this breakthrough technology is increasingly penetrating our everyday lives. However, the levels of user adoption and business revenue are still lagging behind the original expectations. The reasons include strong security and privacy concerns behind the IoT, which become critically important in the smart home environment. Our envisioned smart home scenario comprises a variety of sensors, actuators, and end-user devices interacting and sharing data securely. Correspondingly, we aim at investigating and verifying in practice the Yoking-proof protocol, which is a multi-factor authentication solution for smart home systems with an emphasis on data confidentiality and mutual authentication. Our international team conducted a large trial featuring the Yoking-proof protocol, RFID technology, as well as various sensors and user terminals. This paper outlines the essentials of this trial, reports on our practical experience, and summarizes the main lessons learned.

Anton Prudanov, Sergey Tkachev, Nikolay Golos, Pavel Masek, Jiri Hosek, Radek Fujdiak, Krystof Zeman, Aleksandr Ometov, Sergey Bezzateev, Natalia Voloshina, Sergey Andreev, Jiri Misurec

### Analysis and Simulation of UHF RFID Vehicle Identification System

In this paper a model of UHF RFID Vehicle Identification System based on EPC Class1 Gen2 is described. The model takes into account the influence of protocol settings, antenna and tranceiver parameters and signal propagation along roads on the system performance. It is shown that the two-ray pathloss model and Rayleigh distribution for BER computation allows to simulate RFID system operation adequately. The estimated protocol settings providing reliable vehicle identification at speed up to 220 kmph are given.

Vladimir Vishnevskiy, Andrey Larionov, Roman Ivanov

### Modeling and Performance Comparison of Caching Strategies for Popular Contents in Internet

The paper is devoted to caching of popular multimedia and Web contents in Internet. We study the Cluster Caching Rule (CCR) recently proposed by the authors. It is based on the idea to store only popular contents arising in clusters of related popularity processes. Such clusters defined as consecutive exceedances of popularity indices over a high threshold are caused by dependence in the inter-request times of the objects and, hence, their related popularity processes. We compare CCR with the well-known Time-To-Live (TTL) and Least-Recently-Used (LRU) caching schemes. We model the request process for objects as a mixture of Poisson and Markov processes with a heavy-tailed noise. We focus on the hit probability as a main characteristic of a caching rule and introduce cache effectiveness as a new metric. Then the dependence of the hit probability on the cache size is studied by simulation.

Natalia M. Markovich, Vladimir Khrenov, Udo R. Krieger

### Transient Change Detection in Mixed Count and Continuous Random Data and the Cyber-Physical Systems Security

The problem of sequential transient change detection is considered in the paper. The original contribution of this paper is twofold: first, a mixed count/continuous statistical model with abrupt changes is considered in the paper; second, a new sequential test for such a mixed count/continuous statistical model is designed and studied. The theoretical findings are applied to the problem of cyber-physical attack detection.

Igor Nikiforov

### Performance Modeling of Finite-Source Cognitive Radio Networks Using Simulation

This paper deals with performance modeling of radio frequency licensing. Licensed users (Primary Users - PUs) and normal users (Secondary Users - SUs) are considered. The main idea, is that the SUs are able to access to the available non-licensed radio frequencies.A finite-source retrial queueing model with two non-independent frequency bands (considered as service units) is proposed for the performance evaluation of the system. A service unit with a priority queue and another service unit with an orbit are assigned to the PUs ans SUs, respectively. The users are classified into two classes: the PUs have got a licensed frequency, while the SUs have got a frequency band, too but it suffers from the overloading. We assume that during the service of the non-overloaded band the PUs have preemptive priority over SUs. The involved inter-event times are supposed to be independent, hypo-exponentially, hyper-exponentially, lognormal distributed random variables, respectively, depending on the different cases during simulation.The novelty of this work is that we create a new model to analyze the effect of distribution of inter-event time on the mean and variance of the response time of the PUs and SUs.As the validation of the simulation program a model with exponentially distributed inter-event times is considered in which case a continuous time Markov chain is introduced and by the help of MOSEL (MOdeling Specification and Evaluation Language) tool the main performance measures of the system are derived. In several combinations of the distribution of the involved random variables we compare the effect of their distribution on the first and second moments of the response times illustrating in different figures.

Janos Sztrik, Tamás Bérczes, Hamza Nemouchi, Agassi Melikov

### Performance Measures and Optimization of Queueing System with Reserve Server

In this paper, we consider a single-server queueing system with infinite buffer and reserve server which can be used for modeling energy saving schemes in some real information transmission and processing systems. An arriving customer is serviced by the main server until the end of the service time or the expiration of the limited time defined by the timer which is set up at the beginning of the service. If the service of a customer has not yet completed while the timer has expired then the reserve server joins to the service of the customer. This allows to avoid too large delays in a system with reasonable energy saving.

### Reliability of a k-out-of-n System with a Repair Facility – Essential and Inessential Services

In this paper we study reliability analysis of a k-out-of-n system with a repair facility which provides an essential and several inessential service with given probabilities. At the epoch the system starts, all components are in operational state. Service to failed components are in the order of their arrival. When a component is selected for repair, we assume that the server may select it either for a service that turns out to be different from what is exactly needed for it, which we call the inessential service with the probability p or for desired service, called essential service with probability (1-p). Once the inessential service process starts, a random clock is assumed to start ticking which decides the event to follow: if the clock realises first (still inessential service going on) the components ongoing service is stopped and it is replaced with a new component. On the other hand if the inessential service gets completed before the realisation of the random clock, then the component moves for the essential service immediately. The life-time of a component, the essential service time and the random clock time have independent exponential distributions and the inessential service time is assumed to follow a phase type distribution. The steady state distribution of the system has been obtained explicitly and several important performance measures derived and verified numerically. The extension of the results reported to the case of more than one essential service is worth examining. This has applications in medicine, biology and several other fields of activity.

M. K. Sathian, Viswanath C. Narayanan, Vladimir Vishnevskiy, Achyutha Krishnamoorthy

### Tractable Distance Distribution Approximations for Hardcore Processes

The Poisson point process (PPP) is widely used in performance analysis of wireless communications technologies as a basic model for random deployment of communicating entities. The reason behind widespread use of PPP is analytical tractability in terms of closed-form distributions of distances to the n-th neighbour needed for performance analysis. At the same time, the process allows for infinitesimally close distances between communicating stations not only contradicting the reality but presenting fundamental difficulties in analysis when used with power-law propagation models. As an alternative suggested in the literature ad free of abovementioned deficiencies are the hardcore processes where a certain separation distance between points is always presumed. Unfortunately, no closed-form expressions for distance distributions is available for these processes. We study distance distributions of Matern hardcore process and propose analytical approximations based on acyclic phase type distributions. The nature of approximation as a mixture of exponentials allows for their use in analytical performance analysis. Results for a range of process intensities are reported.

Pavel Abaev, Yulia Gaidamaka, Konstantin Samouylov, Sergey Shorgin

### The Total Capacity of Customers in the Infinite-Server Queue with MMPP Arrivals

In the paper, the infinite-server queueing system with a random capacity of customers is considered. In this system, the total capacity of customers is analysed by means of the asymptotic analysis method with high-rate Markov Modulated Poisson Process arrivals. It is obtained that the stationary probability distribution of the total customer capacity can be approximated by the Gaussian distribution. Parameters of the approximation is also derived in the paper.

Ekaterina Lisovskaya, Svetlana Moiseeva, Michele Pagano

### On the Queue Length in the Discrete Cyclic-Waiting System of Geo/G/1 Type

We consider a discrete time queueing system with geometrically distributed interarrival and general service times, with FCFS service discipline. The service of a customer is started at the moment of arrival (in case of free system) or at moments differing from it by the multiples of a given cycle time T (in case of occupied server or waiting queue). Earlier we investigated such system from the viewpoint of waiting time, actually we deal with the number of present customers. The functioning is described by means of an embedded Markov chain considering the system at moments just before starting the services of customers. We find the transition probabilities, the generating function of ergodic distribution and the stability condition. The model may be used to describe the transmission of optical signals.

Laszlo Lakatos

### Optimal Control of M(t)/M/K Queues with Homogeneous and Heterogeneous Servers

The paper deals with a multi-server controllable queueing system M(t)/M/K with time-dependent and, in particular, with periodic arrival rates. The models with homogeneous and heterogeneous servers are of interest. In latter case the fastest free server allocation mechanism is assumed and the preemption is allowed. The control problem consists in evaluation of the optimal number of servers during some specified stages and is solved by finite horizon dynamic programming approach. To calculate the transient solutions we use a forth-order Runge-Kutta method for the system with a truncated queue length. The results are compared with corresponding queues operating in a stationary regime. It is shown that the optimal control policies are also time dependent and periodic as arrival rates and heterogeneous systems are superior in performance comparing to the homogeneous ones.

Dmitry Efrosinin, Michael Feichtenschlager

### Algorithmic and Software Tools for Optimal Design of New Generation Computer Networks

Algorithmic and software tools for new generation networks (NGN) design are elaborated and presented in this paper. The tools are based on original methods and algorithms suggested by authors and include algorithms for solution of numerous tasks: channels capacities assignment, flows distribution, survivability analysis and structural synthesis. The elaborated models and algorithms take into account the specificity of NGN technology. The results of experimental investigations and practical implementation of the suggested tools are presented and discussed.

Yuriy Zaychenko, Helen Zaychenko

### One Problem of the Risk Control

A problem of supply order is considered. It is necessary to determine an order which gives the minimal probability of the upsetting of the supply. A corresponding probabilistic model is elaborated. The reduced gradient method is used for the minimization. Numerical example illustrates the efficiency of the suggested approach.

A. M. Andronov, T. Jurkina

### Analysis of the Throughput in Selective Mode of Transport Protocol

The proposed model is a virtual connection managed by the transport protocol with a forward error correction mechanism for selective repeat mode in the form of Markov chain with discrete time. The analysis of the impact of protocol parameters window size and the duration of the timeout of waiting confirmation, the likelihood of distortion of the segments in the individual links of the transmission path data, the duration of the round-trip delay, the parameters of mechanism to restore the distorted segments (without retransmissions) on throughput of a transport connection. In the area of protocol parameters, the characteristics of the transmission channel and parameters of the forward error correction mechanism found in the area of superiority of the management procedures of the transport protocol with forward error correction over the classic procedure with decision feedback on the criterion of the throughput of a transport connection. The expediency of applying of the method of forward error correction for transport links with large round-trip delay.

Vladimir Kokshenev, Pavel Mikheev, Sergey Suschenko, Roman Tkachyov

### A Cyclic Queueing System with Priority Customers and T-Strategy of Service

We review the queuing system, the input of which is supplied with the Poisson process of priority customers and N number of the Poisson processes of non-priority customers. Durations of service for both priority and non-priority customers have a distribution functions of A(x) and $$B_n(x)$$ for applications from priority flow and for customers from n flow ($$n = 1\ldots N$$) respectively. By using methods of systems with server vacations and asymptotic analysis in conditions of a large load we have found the asymptotic probability distribution of a value of an unfinished work. It is shown that this distribution is exponential.

Anatoly Nazarov, Svetlana Paul

### Comparative Analysis of Reliability Prediction Models for a Distributed Radio Direction Finding Telecommunication System

We consider the problem of reliability assurance of a local ground-based distributed radio direction finding system (RDFS), which consists of a local dispatching center (LDC) and unattended radio terminals (URT), which are up to several hundred kilometers apart from the LDC and are connected to the LDC via communication channels. The performance criteria of the RDFS are defined according to its topology and structure. Requirements on the mean time between failures (MTBF) and the availability factor are imposed. A methodic has been developed for determining the reliability parameters both in approximate analytical form and in the form of a formalized simulation model that takes into account different hierarchy levels of the system from the topology of the network and communication channels to the printed board assemblies and individual types of electronic components. Simulation and calculation of reliability measures was performed using an automated system for reliability calculation of electronic modules and reconfigurable manufacturing calculation (ASONIKA). The weak spots (least reliable elements) of the RDFS have been revealed and recommendations were given to ensure the reliability of individual elements and the RDFS as a whole. The composition of spare parts for LDC, URT equipment and communication channels is proposed.

Dmitry Aminev, Alexander Zhurkov, Sergey Polesskiy, Vladimir Kulygin, Dmitry Kozyrev

### Low-Priority Queue and Server’s Steady-State Existence in a Tandem Under Prolongable Cyclic Service

A mathematical model of a tandem of queuing systems is considered. Each system has a high-priority input flow and a low-priority input flow which are conflicting. In the first system, the customers are serviced in the class of cyclic algorithms. The serviced high-priority customers are transferred from the first system to the second one with random delays and become the high-priority input flow of the second system. In the second system, customers are serviced in the class of cyclic algorithms with prolongations. Low-priority customers are serviced when their number exceeds a threshold. A mathematical model is constructed in form of a multidimensional denumerable discrete-time Markov chain. Conditions of low-priority queue stationary distribution existence were found.

Victor Kocheganov, Andrei Zorine

### On Regenerative Envelopes for Cluster Model Simulation

We continue to develop a novel approach for confidence estimation of the stationary measures in the model describing high performance multiserver queueing systems, such as high performance clusters (HPC). We call this model cluster model. This model is described by a stochastic process, and in the framework of the approach, we construct two envelopes, minorant and majorant regenerative processes for the queue size process in the original system. These envelopes have classical regenerations while the original process may not be regenerative or its regenerations happen too rare to be useful for statistical estimation. It allows to construct confidence intervals for the steady-state queue size of the cluster model. We use simulation to illustrate the applicability of the approach and give recommendations how to select the predefined parameters of the envelopes to increase the efficiency of estimation. As simulation shows, the constructed envelopes allow to estimate the mean stationary queue size in the original system with a given accuracy in an acceptable time.

Evsey Morozov, Irina Peshkova, Alexander Rumyantsev

### Two Asymptotic Conditions in Queue with MMPP Arrivals and Feedback

We consider infinite-server queue with Markov modulated Poisson arrivals and feedback. Asymptotic analysis of the aggregate arrival process is made under conditions of frequent changing of the underlying chain states of the arrival process and increasing service time. It is proved that the aggregate arrival process is Poisson asymptotically. Parameter of the Poisson approximation is obtained. Applicability area of the asymptotic results is derived by means of numerical experiments.

Agassi Melikov, Lubov Zadiranova, Alexander Moiseev

### Applications of Augmented Reality Traffic and Quality Requirements Study and Modeling

The further development of communication networks appears today on the basis of the concept of the Internet of Things. At the same time gaining popularity technology “augmented reality” that allows you to manage different objects and processes in networks. Sharing the “augmented reality” and the concept of the Internet of Things technology, requires the development of the new service model and traffic pattern and establishment of a new approach of the Quality of Experience estimation.

A. Koucheryavy, M. Makolkina, A. Paramonov

### Rate of Convergence to Stationary Distribution for Unreliable Jackson-Type Queueing Network with Dynamic Routing

In this paper we consider a Jackson type queueing network with unreliable nodes. The network consists of $$m <\infty$$ nodes, each node is a queueing system of M/G/1 type. The input flow is assumed to be the Poisson process with parameter $$\varLambda (t)$$. The routing matrix $$\{r_{ij}\}$$ is given, $$i, j=0,1,...,m$$, $$\sum _{i = 1 } ^ m r_ {0i} \le 1$$. The new request is sent to the node i with the probability $$r_{0i}$$, where it is processed with the intensity rate $$\mu _i(t,n_i(t))$$. The intensity of service depends on both time t and the number of requests at the node $$n_i(t)$$. Nodes in a network may break down and repair with some intensity rates, depending on the number of already broken nodes. Failures and repairs may occur isolated or in groups simultaneously. In this paper we assumed if the node j is unavailable, the request from node i is send to the first available node with minimal distance to j, i.e. the dynamic routing protocol is considered in the case of failure of some nodes. We formulate some results on the bounds of convergence rate for such case.

Elmira Yu. Kalimulina

### On the Method of Group Polling upon the Independent Activity of Sensors in Unsynchronized Wireless Monitoring Networks

It is considered the model of large monitoring networks with working independently sensors for an alarm signalization. Outlined in the previous papers the method of group polling for alarming sensors identification used the time synchronization. The last condition is very strong for vide distributed monitoring networks. Recently proposed method of group polling for the alarming sensors identification in unsynchronized wireless monitoring network is investigated. Based on numerical simulations, it is found that the group polling method may be effective for unsynchronized networks with thousands or more sensors and the decoding algorithm may be realized on-time using parallel executions. Recommended number of the code signal repetitions is proposed.

Alexander Shtokhov, Ivan Tsitovich, Stoyan Poryazov

### A Noising Method for the Identification of the Stochastic Structure of Information Flows

The paper demonstrates a way for application of a methodology for the stochastic analysis of random processes based on the method of moving separation of finite normal mixtures to analyze the non-negative time series. We suggest to noise the initial data by adding i.i.d. normal random variables with known parameters. Then the one-dimensional distributions of observed processes are approximated by finite location-scale mixtures of normal distributions. The finite normal mixtures are convenient approximations to general location-scale normal mixtures or normal variance-mean mixtures which are limit laws for the distributions of sums of a random number of independent random variables or non-homogeneous and non-stationary random walks and hence, are reasonable asymptotic approximations to the statistical regularities in observed real processes. This approach allows to analyze the regularities in the variation of the parameters and capturing the low-term variability in the case of complex internal structure of data. An implementation of the methodology is shown by the examples of the intensity for the simulated information system.

Andrey Gorshenin, Victor Korolev

### Efficiency of Redundant Multipath Transmission of Requests Through the Network to Destination Servers

It is not uncommon that delay-sensitive requests cannot be processed repeatedly in case of delivery failures, especially in real-time systems, which results in a strong need to enhance reliability of sending of requests. This can be achieved through concurrent transmission of copies of a request over multiple routes in a given network to a number of similar destination nodes. However, the increase in the initial flow of requests leads to the rise of the network load and the average residence time and potentially to the excess of the ultimate residence time. In the research, the usefulness of redundant distribution of requests through the network was estimated, with the maximized probability of successful delivery and the minimized average residence time. It was found possible to determine the optimal redundancy order for a given set of parameters, namely the intensity of the flow of incoming requests and the bit error rate.

V. A. Bogatyrev, S. A. Parshutina

### The Fault-Tolerant Structure of Multilevel Secure Access to the Resources of the Public Network

The paper presents the evaluation of the effectiveness of the structural organization of the system of multi-level secure access to external network resources. We conducted a comparative analysis and optimization of the pattern of access ‘Direct connection’, with its various forms of implementation during the organization of a secure connection of end-node internal network to the resources located in the external network. The study was conducted on the basis that each security element is included in the pattern of the secure access is able to detect and eliminate the threats of the other elements of the system of protection. Pattern of access ‘Direct connection’ in a general form has four variants of construction, differing from each other by mutual arrangement of the key elements: firewall with packet-filtering, firewall with adaptive detailed packet inspection and the router. It was a mathematical model to calculate the reliability of the ways of construction of the pattern of access. It is shown that the most reliable way of construction of pattern of access is one that includes a single group of routers for the entire system. Ways are not very different from each other reliability value that include two groups of routers on the overall system.

### Formation of the Instantaneous Information Security Audit Concept

This publication covers the problem of formation the concept of the instantaneous information security (IT-Security) audits, including protection against zero-day threats. Various recent materials are presented to the actual problem of counter zero-day threats notes that “any process-driven people, is unreliable. In this situation it is proposed to use not only a technical methods to counter zero-day threats, but to offer a combined method based on the concept of instantaneous IT-Security audits. Methodological basis of this concept for instantaneous audits defined both ISO 27001 and ISO 19011 standards, which extended with the set of IT-security metrics for quantify the object protection level. In the example for one variable was demonstrated an increase in the rate of growth of the ISMS level variables with known IT-Security audits process.

I. I. Livshitz, D. V. Yurkin, A. A. Minyaev

### Computer Simulation of Average Channel Access Delay in Cognitive Radio Network

Cognitive radio (CR) is a new wireless communication concept of the future networks, that can help to use all available radio resources at a local area with a great effectiveness. Cognitive radio is based on the dynamic spectrum access (DSA) where available spectrum segments are used in an intelligent manner with help of advanced spectrum analysis and probing for unoccupied radio frequencies. An implementation of the cognitive radio networks raises an issue of the medium access control (MAC) protocol researching, in particular MAC protocol impacts on the access delay to radio channels. In this paper uncoordinated access method is studied where the event of spectrum and channel accessing is random and determined by probabilistic value from 0.1 to 0.99 named as channel availability. The subject of research was impact of channel availability on the access delay with simulation on the base ns2 program simulator with CRNC patch.

A. Yu. Grebeshkov, A. V. Zuev, D. S. Kiporov

### Efficiency of Redundant Service with Destruction of Expired and Irrelevant Request Copies in Real-Time Clusters

Possible ways of increasing the probability of timely and faultless execution of delay-sensitive requests in real-time clustered computing systems, when multiple copies of requests are created and served in different cluster nodes, are investigated. The proposed models for queueing and functional reliability prove the existence of scope of efficiency for service disciplines with redundant execution of copies of requests, when the probability of their prompt and error-free servicing can be increased significantly, despite the rise of load in the nodes. It was examined how the ways to arrange redundancy and the redundancy order affected timely and reliable servicing of requests, with possible faults and errors in the nodes. It was shown that destruction of expired copies, whose waiting time in the queue exceeded a given ultimate time, and copies which became irrelevant, after one of them had been processed, produced an essential enhancement of efficiency of the system.

V. A. Bogatyrev, S. A. Parshutina, N. A. Poptcova, A. V. Bogatyrev

### Stationary Waiting Time Distribution in G|M|n|r with Random Renovation Policy

Recent recommendation RFC 7567 by IETF indicates that the problem of active queue management remains vital for modern communications networks and the development of new active queue management is required. Queueing system with renovation when customers upon service completion pushes-out other customers residing in the queue with a given probability distribution may have potential application as an alternative active queue management. In this paper one presents the analytic method for the computation of the customer’s stationary waiting time distribution in G|M|n|r queue with random renovation under FCFS (and non-preemptive LCFS) scheduling in the terms of Laplace-Stieltjets transform. The method is illustrated by one particular case: stationary waiting time distribution of the customer, which either received service or was pushed-out under FCFS scheduling.

Ivan Zaryadov, Rostislav Razumchik, Tatiana Milovanova

### Analysis of the Packet Path Lengths in the Swarms for Flying Ubiquitous Sensor Networks

The article gives an approach for estimating the packet path length between the nodes for Flying Ubiquitous Sensor Networks. Authors show that such networks may be represented as three-dimensional swarms of nodes. The mathematical models for the ball and cubic swarms are given, as well as the simulation approach for the other shapes. Also two types of network architecture are considered – direct transfer and multi-hop.Simulation shows that the shape of the swarm significantly impact on the average packet path length both for direct and multi-hop data transfer cases: more centralized shapes (e.g. ball) give better results (smaller path length) than less centralized (e.g. cube), and this difference becomes more significant in the multi-hop mode. Number of hops for multi-hop mode also shows the same dependency.

Anastasia Vybornova, Alexander Paramonov, Andrey Koucheryavy

### Properties of Fluid Limit for Closed Queueing Network with Two Multi-servers

A closed network consists of two multi-servers with n customers. Service requirements of customers at a server have a common cdf. State parameters of the network: for each multi-server empirical measure of the age of customers being serviced and for the queue the number of customers in it, all multiplied by $$n^{-1}$$.Our objective: asymptotics of dynamics as $$n\rightarrow \infty$$. The asymptotics of dynamics of a single multi-server with an arrival process as the number of servers $$n\rightarrow \infty$$ is currently studied by famous scientists K. Ramanan, W. Whitt et al. Presently there are no universal results for general distributions of service requirements—the results are either for continuous or for discrete time ones; the same for the arrival process. We develop our previous asymptotics results for a network in discrete time: find equilibrium and prove convergence as $$t\rightarrow \infty$$.Motivation for studying such models: they represent call/contact centers.

Svetlana Anulova

### On Strong Bounds of Rate of Convergence for Regenerative Processes

We give strong bounds for the rate of convergence of the regenerative process distribution to the stationary distribution in the total variation metric. For this aim we propose a new modification of the coupling method which we call stationary coupling method. Use of this stationary coupling method improves the classic results about the convergence rate of the distribution of the regenerative process in the case of a heavy tail. Also this method can be applied for obtaining the bounds of the rate of the convergence for the queueing regenerative processes.

Galina Zverkina

### Convergence Evaluation of Adaptation to Losses: The Case of Subscription Notification Delivery to Mobile Users in Smart Spaces

Dmitry Korzun, Andrey Vdovenko, Olga Bogoiavlenskaia

### Sojourn Time Analysis for Processor Sharing Loss Queuing System with Service Interruptions and MAP Arrivals

Processor sharing (PS) queuing systems are widely investigated by research community and applied for the analysis of wire and wireless communication systems and networks. Nevertheless, only few works focus on finite queues with both PS discipline and service interruptions. In the paper, compared with the previous results we analyze a finite capacity PS queuing system with Markovian arrival process, unreliable server, service interruptions, and an upper limit of the number of customers it serves simultaneously. For calculating the mean sojourn time, unlike a popular but computational complex technique of inverse Laplace transform we use an effective method based on embedded Markov chain. A practical example concludes the paper.

Konstantin Samouylov, Eduard Sopin, Irina Gudkova

### The Estimation of Probability Characteristics of Cloud Computing Systems with Splitting of Requests

Growing popularity of cloud services is explained by many advantages of them. The accessibility, flexibility, scalability, ease of management, the relatively low cost of implementation can be listed among the main advantages. The demand for cloud services with the ability to change one cloud service provider to another one without any significant cost for a user result in a high competition between cloud providers. Due to this reason, it became important to find the optimal performance measures of cloud systems. These measures, on the one hand, must meet all the requirements of Service Level Agreement (SLA), on the other hand, do not lead to excessive costs for provider. The paper presents the evaluation of the main service quality characteristics of cloud systems, including formulas for variance of residence time in the synchronization buffer. For the analysis of a cloud system, fork-join queues with corresponding methods of its approximation were used.

Anastasia Gorbunova, Ivan Zaryadov, Sergey Matyushenko, Eduard Sopin

### Simulation of Medical Sensor Nanonetwork Applications Traffic

Nanonetworks is one of the most dynamically developing areas in the field of telecommunications. Nanonetworking promises new opportunities in different fields of science and technology. However along with obvious advantages, the implementation of nanonetwork applications can cause a number of problems for the functioning of modern telecommunication networks. One of them is a large number of data packets generated by nanonetwork applications. In this regard, the actual problem is the study of traffic nanoceramic applications and its impact on traditional telecommunication networks. The article deals with simulation of traffic from sensor nanetwork applications. The paper presents results of nanonetwork applications traffic simulation. Simulation based on the traffic models developed for M2M. In the simulation considered the possibility of gateway working in two modes: without processing messages received from nanonetwork and with it. Typical architecture of nanonetwork medical applications involving the use of remote Internet servers, was described. The results of traffic flow simulation were analysed on the self-similarity properties.

Rustam Pirmagomedov, Ivan Hudoev, Daria Shangina

### Long-Range Data Transmission on Flying Ubiquitous Sensor Networks (FUSN) by Using LPWAN Protocols

Flying Ubiquitous Sensor Networks (FUSN) are one of the new Internet of Things applications. In such networks, Unmanned Aerial Vehicles (UAVs) are used to collect data from the wireless sensor nodes, located in hard to reach remote areas, and the subsequent data delivery to the Internet. For the stable operation, it is required to solve complex scientific problems, one of which is the choice of connectivity technologies for the data delivery from the sensor nodes to the gateway with the IP-network as well as the calculation of quality of service parameters. The paper considers the problem of data delivery with the terrestrial segment of the flying ubiquitous sensor network over long distances using repeater chain. As technology of interaction nodes terrestrial sensor network considered IEEE 802.15.4 (6LoWPAN protocol), and technology IEEE 802.15.4g is considered for UAV interaction (LoRaWAN protocol). In the study, analytical and simulation models of the flying ubiquitous sensor network have been developed. As a result of experiments with the simulation model, delay and packet loss were investigated, occurring in the all stations of transmission network at different data rates, and conclusions on the optimal data rate of the network were made.

Ruslan Kirichek, Vyacheslav Kulik

### Hardware-Software Simulation Complex for FPGA-Prototyping of Fault-Tolerant Computing Systems

The article presents the concept of building hardware-software complex based on field programmable gate array (FPGA) prototyping, which implements the methodology of fault-tolerant gate array (GA) or FPGA-based aerospace-born systems-on-chip (FTS) modeling, based on extended concept of fault injection. This complex allows to define functional FTS design for the given parameters of the negative impact of the external environment through the estimation of the FTS project fault tolerance level (FTL).

Oleg Brekhov, Alexander Klimenko

### Numerical and Analytical Modeling of Guided Modes of a Planar Gradient Waveguide

The mathematical model of light propagation in a planar gradient optical waveguide consists of the Maxwell’s equations supplemented by the matter equations and boundary conditions. In the coordinates adapted to the waveguide geometry, the Maxwell’s equations are separated into two independent sets for the TE and TM polarizations. For each there are three types of waveguide modes in a regular planar optical waveguide: guided modes, substrate radiation modes, and cover radiation modes. We implemented in our work the numerical-analytical calculation of typical representatives of all the classes of waveguide modes.In this paper we consider the case of a linear profile of planar gradient waveguide, which allows for the most complete analytical description of the solution for the electromagnetic field of the waveguide modes. Namely, in each layer we are looking for a solution by expansion in the fundamental system of solutions of the reduced equations for the particular polarizations and subsequent matching them at the boundaries of the waveguide layer.The problem on eigenvalues (discrete spectrum) and eigenvectors is solved in the way that first we numerically calculate (approximately, with double precision) eigenvalues, then numerically and analytically—eigenvectors. Our modelling method for the radiation modes consists in reducing the initial potential scattering problem (in the case of the continuous spectrum) to the equivalent ones for the Jost functions: the Jost solution from the left for the substrate radiation modes and the Jost solution from the right for the cover radiation modes.

Edik Ayrjan, Migran Gevorkyan, Dmitry Kulyabov, Konstantin Lovetskiy, Nikolai Nikolaev, Anton Sevastianov, Leonid Sevastianov, Eugeny Laneev

### Diagram Representation for the Stochastization of Single-Step Processes

Background. By the means of the method of stochastization of one-step processes we get the simplified mathematical model of the original stochastic system. We can explore these models by standard methods, as opposed to the original system. The process of stochastization depends on the type of the system under study. Purpose. We want to get a unified abstract formalism for stochastization of one-step processes. This formalism should be equivalent to the previously introduced. Methods. To unify the methods of construction of the master equation, we propose to use the diagram technique. Results. We get a diagram technique, which allows to unify getting master equation for the system under study. We demonstrate the equivalence of the occupation number representation and the state vectors representation by using a Verhulst model. Conclusions. We have suggested a convenient diagram formalism for unified construction of stochastic systems.

Ekaterina G. Eferina, Michal Hnatich, Anna V. Korolkova, Dmitry S. Kulyabov, Leonid A. Sevastianov, Tatiana R. Velieva

### Construction and Analysis of Nondeterministic Models of Population Dynamics

Three-dimensional mathematical models of population dynamics are considered in the paper. Qualitative analysis is performed for the model which takes into account the competition and diffusion of species and for the model which takes into account mutual interaction between the species. Nondeterministic models are constructed by means of transition from ordinary differential equations to differential inclusions, fuzzy and stochastic differential equations. Using the principle of reduction, which allows us to study stability properties of one type of equations, using stability properties of other types of equations, as a basis, sufficient conditions of stability are obtained. The synthesis of the corresponding stochastic models on the basis of application of the method of construction of stochastic self-consistent models is performed. The structure of these stochastic models is described and computer modelling is carried out. The obtained results are aimed at the development of methods of analysis of nondeterministic nonlinear models.

A. V. Demidova, Olga Druzhinina, Milojica Jacimovic, Olga Masina

### Model of Diatomic Homonuclear Molecule Scattering by Atom or Barriers

The mathematical model of quantum tunnelling of diatomic homonuclear molecules through repulsive barriers or scattering by an atom is formulated in the s-wave approximation. The 2D boundary-value problem (BVP) in polar coordinates is reduced to a 1D BVP for a set of second-order ODEs by means of Kantorovich expansion over the set of parametric basis functions. The algorithm for calculating the asymptotic form of the parametric basis functions and effective potentials of the ODEs at large values of the parameter (hyperradial variable) is presented. The solution is sought by matching the numerical solution in one of the subintervals with the analytical solution in the adjacent one. The efficiency of the algorithm is confirmed by comparing the calculated solutions with those of the parametric eigenvalue problem obtained by applying the finite element method in the entire domain of definition at large values of the parameter. The applicability of algorithms and software are demonstrated by the example of benchmark calculations of discrete energy spectrum of the trimer Be$$_3$$ in collinear configuration.

A. A. Gusev, O. Chuluunbaatar, S. I. Vinitsky, L. L. Hai, V. L. Derbov, P. M. Krassovitskiy

### The Coupled-Channel Method for Modelling Quantum Transmission of Composite Systems

The description of quantum transmission of composite systems of barriers or wells using the coupled-channel method is presented. In this approach the multichannel scattering problem for the Schrödinger equation is reduced to a set of coupled second-order ordinary differential equations with the boundary conditions of the third type and solved using the finite element method. The efficiency of the proposed approach is demonstrated by the example of analyzing metastable states that appear in composite quantum systems tunnelling through barriers and wells and give rise to the quantum transparency and total reflection effects.

S. I. Vinitsky, A. A. Gusev, O. Chuluunbaatar, A. Góźdź, V. L. Derbov

### The Stochastic Processes Generation in OpenModelica

This paper studies program implementation problem of pseudo-random number generators in OpenModelica. We give an overview of generators of pseudo-random uniform distributed numbers. They are used as a basis for construction of generators of normal and Poisson distributions. The last step is the creation of Wiener and Poisson stochastic processes generators. We also describe the algorithm to call external C-functions from programs written in Modelica. This allows us to use random number generators implemented in the C language.

Migran Gevorkyan, Michal Hnatich, Ivan M. Gostev, A. V. Demidova, Anna V. Korolkova, Dmitry S. Kulyabov, Leonid A. Sevastianov

### Metric Analysis as a Tool for Interpolating Multivariate Functions in the Case of an Information Lack

In report the ill-posed problems in view arising at the solution of applied problems by means of the metric analysis are considered. In the report new schemes and algorithms for smoothing and restoration based on the metric analysis were presented. These schemes and algorithms have demonstrated a high accuracy of smoothing and retrieving the values of functions of one or many variables. Examples of such problems are problems of interpolation, filtration and forecasting of values of functions of one and many variables claimed at the solution of applied problems physicists, technicians, economy and other areas of researches.

Alexander Kryanev, Gleb Lukin, David Udumyan

### Systems of Differential Equations of Infinite Order with Small Parameter and Countable Markov Chains

Tikhonov-type Cauchy problems are investigated for systems of ordinary differential equations of infinite order with a small parameter $$\mu$$ and initial conditions. It is studying the singular perturbated systems of ordinary differential equations of infinite order of Tikhonov-type $$\mu \dot{x}=F(x(t,g_x),y(t,g_y),t)$$, $$\dot{y}=f(x(t,g_x),y(t,g_y),t)$$ with the initial conditions $$x(t_0)=g_x$$, $$y(t_0)=g_y$$, where $$x, \, g_x \, \in X$$, $$X\subset l_1$$ and $$y, \, g_y \, \in Y$$, $$Y \, \in \mathbf {R}^n$$, $$t \in \left[ t_0, t_1 \right]$$ ($$t_0 < t_1$$), $$t_0, t_1 \in T$$, $$T\in \mathbf {R}$$, $$g_x$$ and $$g_y$$ are given vectors, $$\mu >0$$ is a small real parameter. The results may be applied to the queueing networks, which arise from the modern telecommunications.

Galina Bolotova, S. A. Vasilyev, Dmitry N. Udin

### Applying OpenCL Technology for Modelling Seismic Processes Using Grid-Characteristic Methods

This paper is concerned with CUDA and OpenCL technologies used to solve seismic problems in elastic media. We solve the problem of the dynamic wave disturbances spreading in geologic environment in an elastic approach in the two-dimensional case. A grid-characteristic method is used for numerical solution. Performance of problem solving algorithm with the GPU is compared with the performance of solving it on a single core CPU. We also study the influence of various optimizations on the performance of the algorithm. We measured the effectiveness of parallelization on multiple graphics processors.

Nikolay Khokhlov, Andrey Ivanov, Michael Zhdanov, Igor Petrov, Evgeniy Ryabinkin

### Linear Approach for Mathematical Modelling as a Tool for Efficient Portfolio Selection

This report introduces two approaches to the efficient portfolio selection problem, wherein the criteria and the constraints are linear with respect to control variables. The first approach consists of unconditioned optimization of the average expected efficiency value of a portfolio without imposing any additional constraints on the structure of selected portfolio. For this scheme the problem of effective portfolio formation is reduced to two linear programming problems, solving these for an efficient frontier may be effectively accomplished in closed form. The second scheme considers an additional set of group constraints, which can also be reduced to the problem of finding the Pareto fronts of two linear programming problems.

Alexander Kryanev, Darya Sliva, Andrey Sinitsin

### Mathematical Modeling of Smoothly-Irregular Integrated-Optical Waveguide and Mathematical Synthesis of Waveguide Luneburg Lens

In this paper we consider a class of multilayer integrated-optical waveguides consisting of homogeneous dielectric layers of constant or variable thickness, which are being systematically numerically studied using the cross-section method. The method is based on the adiabatic approximation of the asymptotic expansion on the one hand and the expansion in the complete system of modes of regular comparison waveguide. The paper discusses the problems of numerical implementation of the cross-section method to the transformation of particular mode in a smooth transition from one planar regular open waveguide to another.Luneburg proposed a model of the ideal optical instrument (in the framework of geometrical optics), afterwards called Luneburg lens. Later classical Luneburg lens was included in the family of the ideal optical instruments - generalized Luneburg lenses. Zernike in his work showed that a local increase in thickness of the waveguiding layer leads to a local deceleration of phase velocity of the propagating waveguide mode. This effect has led to the idea of manufacturing the waveguide (two-dimensional) Luneburg lenses instead of volume (three-dimensional) lenses. In this work we synthesized mathematically the thickness profiles of the additional (irregular in thickness) waveguide layer forming the thin-film generalized waveguide Luneburg lens.

Edik Ayrjan, Genin Dashitsyrenov, Konstantin Lovetskiy, Nikolai Nikolaev, Anton Sevastianov, Leonid Sevastianov, Eugeny Laneev

### Damping Problem for Multidimensional Control System with Delays

We consider damping problem for control system with delay described by the system of differential-difference equations of neutral type, and establish the relationship of the variational problem for the nonlocal functionals and the corresponding boundary value problem for differential-difference equations. We prove the existence and uniqueness of generalized solution to the boundary value problem for this system of differential-difference equations.

A. S. Adkhamova, A. L. Skubachevskii

### Nonclassical Hamilton’s Actions and the Numerical Performance of Variational Methods for Some Dissipative Problems

The use of variational methods for the construction of sufficiently accurate approximate solutions of a given system requires the existence of the corresponding variational principle - a solution of the inverse problems of the calculus of variations. In the frame of the Euler’s functionals there may not exist variational principles. But if we extend the class of functionals then it could allow to get the variational formulations of the given problems. There naturally arises the problem of the constructive determination of the corresponding functionals - nonclassical Hamilton’s actions - and their application for the search of approximate solutions of the given boundary value problems. The main goal of the paper is to present a scheme for the construction of indirect variational formulations for given evolutionary problems and to demonstrate the effective use of the nonclassical Hamilton’s action for the construction of approximate solutions with the high accuracy for the given dissipative problem.

### Modeling of Spinning Sphere Motion in Shear Flow of Viscous Fluid

Modeling the motion of a small rigid spinning spherical particle in viscous Navier—Stokes fluid, we generalize the Rubinow—Keller and Maxey—Riley method of estimating the force and the torque acting on the particle to the case of shear flow and arbitrary Reynolds number. We represent the velocity of the flow near the particle as solid body part and small perturbation. As for the velocity far from the particle, it includes a steady external shear flow part and again small perturbation. We use the simplest quadratic polynomial approximation for the small velocity parts and insert it in matching condition at some intermediate spherical surface. It appears that the force parallel to the angular velocity of the particle proves to contain the oscillatory part, with the frequency being proportional to the gradient of the external steady velocity.

Yuri P. Rybakov

### Fast Two-Dimensional Smoothing with Discrete Cosine Transform

Smoothing is the process of removing “noise” and “insignificant” fragments while preserving the most important properties of the data structure. We propose a fast spline method for two-dimensional smoothing. Data smoothing usually attained by parametric and nonparametric regression. The nonparametric regression requires a prior knowledge of the regression equation form. However, most of the investigated data can’t be parameterized simply. From this point of view, our algorithm belongs to nonparametric regression. Our simulation study shows that smoothing with discrete cosine transform is orders of magnitude faster to compute than other two-dimensional spline smoothers.

Pavel Lyubin, Eugeny Shchetinin

### Cluster Method of Description of Information System Data Model Based on Multidimensional Approach

Multidimensional data cube is a data model at the information systems based on the multidimensional approach. If one uses a large set of aspects for the analysis of data domain the data cubes are characterized by substantial sparseness. It complicates the organization of data storage. The proposed cluster method of description of multidimensional data cube is based on the investigation of data domain semantics. The dimensionalities of the multidimensional cube are the dimensions corresponding to the aspects of analysis. The basis of the cluster method is a construction of the groups of members which are semantically related to the groups of other members. Building of associations between the groups of different members allows to reveal the clusters in the data cube – the sets of cells with similar properties which may be described in a same way. Clusters are used as the main element of information system data model.

Maxim Fomin

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