Vladimir Rykov

Gubkin Russian State University of Oil and Gas · Applied Mathematics and Computer Modelling

The reliability characteristics of a k-out-of-n:F system are studied in the case when a failure of one of the system’s components leads to increasing the load on others, resulting in their residual lifetimes decreasing. The situation is modeled with the help of changing the components and the system hazard rate function. The reliability function an...

As a scientific term "risk'' originally appeared in insurance mathematics and meant the "ruin probability'' in a "collective risk'' model of an insurance company. Recently, this term has become widespread in different spheres of human activity and has been applied to various models of "individual risk". At the same time, despite its increasing popu...

A k-out-of-n : F renewable system with exponentially distributed life-times, and arbitrary distributed repair times of its components under a partial repair regime has been investigated in the paper [1]. This paper deals with the same model under the full repair regime after the system failure. For this model we use Markovization method, based on a...

In different spheres of human activity one needs to make decisions, connected with different risks, under condition of uncertainty. However, the very concept of uncertainty and risk needs clarification. The article discusses various interpretations of the term “uncertainty” and the formation of the term “risk” as a scientific concept. The authors p...

This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for the investigation of the k-out-of-n system. Proposed in 1955 by W. Smith, the regeneration idea has come a long way in terms of development and has found widespread applications. First, we briefly recall the history of the development of the regeneratio...

The flow of a multicomponent fluid through a pipeline system of arbitrary configuration is considered. The problem consists in determining the component composition of the fluid for each pipeline of the system based on the values of the concentration of the components throughout the entire set of measuring points, provided that there are no phase t...

In this paper we study the problem of optimal controlling in a processor sharing (PS) M/M/2 queueing system with heterogeneous servers. The servers differ in the service intensities, operating and usage costs. The objective is to find the optimal policy to allocate the customers either to an idle or partially loaded server, or to the queue at each...

The reliability of a double redundant renewable system with generally distributed life- and repair times of its components is considered. For its investigations the theory of decomposable regenerative processes is used. Reliability function and stationary characteristics of the system with the help of a special integral transformation are founded i...

The reliability study of k-out-of-n systems is of interest both from theoretical and practical points of view. Applications of such models can be seen in many real-world phenomena, including telecommunication, transmission, transportation, manufacturing, and services. A probabilistic study of a real-world k-out-of-n system often helps to develop an...

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation...

The paper provides reliability analysis of a cold double redundant renewable system assuming that both life-time and repair time distributions are arbitrary. The proposed approach is based on the theory of decomposable semi-regenerative processes. We derive the Laplace–Stieltjes transform of two main reliability measures like the distribution of th...

We present three classical methods in the study of dynamic and stationary characteristic of processes of Markovian or Semi-Markovian type which possess points of regeneration. Our focus is on the stationary distributions and conditions of its existence and use. The first approach is based on detailed probability analysis of time dependent passages...

In this paper we study the problem of optimal controlling in a processor sharing (PS) M/M/2 queueing system with heterogeneous servers. The servers differ in the service intensities, operating and usage costs. The objective is to find the optimal policy to allocate the customers either to an idle or partially loaded server, or to the queue at each...

We study a multiple heterogeneous servers queuing model with customers’ impatience and retention of impatient customers where the service is provided by multiple heterogeneous servers. The transient solution of the model is derived by using probability generating function technique. Some important measures of performance are studied. A numerical ex...

A heterogeneous double redundant hot-standby renewable system with Marshal–Olkin failure model is considered. Steady-state characteristics for such system are calculated. The problem of sensitivity of these characteristics to the shape of repair time distributions for this model is studied.

The problem of sensitivity of a redundant system’s reliability characteristics to shapes of their input distributions is considered. In Efrosinin and Rykov, Information Technologies and Mathematical Modelling, 2014, [1] an analytical form for dependence of a two-unit cold standby redundant system reliability characteristics on life and repair time...

Today, the number of interconnected Internet of Things (IoT) devices is growing tremendously followed by an increase in the density of cellular base stations. This trend has an adverse effect on the power efficiency of communication, since each new infrastructure node requires a significant amount of energy. Numerous enablers are already in place t...

A heterogeneous double redundant hot standby renewable system with Marshall-Olkin failure model is considered. In one of pre-vious papers the stationary characteristics for such system for the caseof exponential lifetime distributions has been found and its asymptotic insensitivity to the shape of its components repair time distributions hasbeen st...

Motivated by the unprecedented penetration of mobile communications technology, this work carefully brings into perspective the challenges related to heterogeneous communications and offloaded computation operating in cases of fault-tolerant computation, computing, and caching. We specifically focus on the emerging augmented reality applications th...

This book is based on a lecture course to students specializing in the safety of technological processes and production. The author focuses on three main problems in technological risks and safety: elements of reliability theory, the basic notions, models and methods of general risk theory and some aspects of insurance in the context of risk manage...

Risk is connected with a particular event and its consequences expressed in the form of some material or other losses or damages. Adequate social politics might be a more reliable way for different layers of the community protection against social risks. Health loss risk, social risks, financial risks are some of the examples of risk. The peculiari...

An object in reliability theory means a unit, an apparatus, an engineering product and any system or its part at all, considering from the point of view of their reliability. Reliability means the possibility of an object to maintain its workability during a given time period under a given exploitation condition. This chapter discusses the reliabli...

One of the principal instruments of risk management is insurance of risks. The risk insurance procedure demands to evaluate both the time to the occurrence of risk event and the value of damage generated by it. Insurance models usually follow the risk models and divided into short-time insurance models, middle-time insurance models and long-time in...

As it known the optimal policy which minimizes the longrun average cost per unit of time in a multi-server queueing system with heterogeneous servers without preemption has a threshold structure. It means that the slower server must be activated whenever all faster servers are busy and the number of customers in the queue exceeds some specified for...

Broadband wireless data transmission network for providing of automobile transport system safety is considered. The network operates under IEEE802.11n-2012 protocol that guarantees high-speed transmission of multimedia information from stationary and mobile automatic systems of traffic control. The model of stochastic network with dependent service...

The sensitivity analysis of systems' characteristics to the shape of distributions is a very important task of reliability engineering of stochastic systems and networks. One of the earliest result concerning insensitivity of systems' characteristics to the shape of service time distribution was obtained in case of Erlang's formulas for loss queues...

Рассматривается задача оптимального выполнения (потока) задач при возможности их прерывания.

Broadband wireless data transmission network for providing of automobile transport system safety is considered. The network operates under IEEE802.11n-2012 protocol that guarantees high-speed transmission of multimedia information between automatic stationary and mobile systems of traffic control. The model of stochastic network with dependent serv...

This chapter provides some general definitions and mathematical models of risk. It deals with engineering risks of complex technical systems or biological objects, which are usually connected with their failures. Up-to-date complex systems have a hierarchical structure, which should be taken into account for their reliability and risk analysis. A v...

The influence of random environments to technical systems reliability is studied. A Markov model of reliability of the system that operates in a random Markov environment is proposed. General relations for stationary and non-stationary Quality of Service (QoS) characteristics of such system are given. Numerical study and comparison for a cold backu...

The slow server problem is generalized for the case of additional cost structure. With the help of special partial ordering of the system state space it is shown that the optimal policy for the problem has a monotone property consisting in the following: an additional server should be switched on only in the case if the queue length exceeds some le...

Multidimensional alternative processes are introduced, their stationary and quasi-stationary probabilities are investigated, and their applications in reliability models are considered.

For modeling and analysis of the reliability of complex hierarchical partially controllable systems the methods of decomposable semi-regenerative processes are used. A simple example illustrates our approach. Keywords and phrasesReliability of hierarchical systems-Decomposable semiregenerative processes

Most of real technical systems and biological objects with sufficiently high organization are complex hierarchical partially controllable systems. In the paper for modeling and analysis of reliability of such systems the method of decomposable semi-regenerative processes is used. A simple example illustrates our approach.

We give a survey of the works of B.V. Gnedenko's reliability school, starting from 1950s and up until the latest years in two directions: (1) invariance of state distributions for queueing systems and networks, (2) asymptotic behavior of a redundant ...

Some degradation models with random life resources for technical and biological objects are introduced and studied. Conditional hazard rate function given fixed consumed resource is in the focus of consideration.

In this paper the problem of optimal control over a Markov queueing system with heterogeneous servers and a joint queue is considered, which is also known in the literature as “the slow server problem.” The classical model is generalized here to the case with delay and call serving penalties. It is proved here that the optimal control policy for se...

New alternative approach to the analysis of polling systems is developed. It is based on the theory of decomposable semi-regenerative processes.

A certain class of nonlinear switched systems is considered. Methods of developing Lyapynov functions for the systems under study are suggested. Conditions are defined, in the fulfillment of which the asymptotic stability of the zero solution will take ...

To model degradation processes in technical and biological objects generalized birth and death processes are introduced and studied.

The problem of optimal control for queueing system (QS) with heterogeneous servers was considering by many authors. In [8] it was shown that the optimal with respect to the number of jobs in the system minimization policy is a threshold type one and it obliges to use the fastest free server if necessary. However, calculation of performance characte...

The generalized birth-death processes were introduced to model ageing of objects of different nature. The results obtained were compared with the model based on the conventional birth-death processes.

Certain characterization properties of time-varying periodic Poisson flows are studied in terms of almost-lack-of-memory (ALM) distributions. Parameter estimation formulas are derived. A method for verifying the hypothesis on the membership of a sample to the class of ALM-distributions is developed. Algorithms for computing critical levels and powe...

An optimal policy to minimize the queue length in a multi-server controllable queueing system with heterogeneous servers has a threshold property, and it uses the fastest server if necessary (see [8] and [17]). This study gives a numerical description of optimal policies that minimize the operational cost for such a system.

In this paper wu use some ideas for analysis of reliability of technical systems to propose similar tools for modeling and investigation of the problem of biological objects longevity, aging, and degradation. The main characteristic for biological objects is their survival function. We focus on evaluation of this function. We deal with the model of...

The problems of reliability control arise in many systems with failures as well as in biological systems. The degradation of some biological object can be devided into stages. The neuron system or controlling system may considerably improve the performance and reliability of the model. It can be done by making a decision in each degradation stage t...

Studies of queuing models with resequencing of jobs to keep the order at the output in the order of arrival are reviewed. A focus on recent authors results regarding optimal jobs assignment to heterogeneous servers is presented.

For a system with several heterogeneous servers, the well-known Howard algorithm was used to study numerically whether the optimal servicing disciplines satisfy the criterion for minimum stationary number of customers in system.

In this paper we show how the present day fast computer could solve non-standard old statistical problems. In most cases statisticians work with approximations of test statistics distributions, and then use respective statistical tables. When approximations do not work the problem is usually tabled. We propose such simulation approach which we do b...

For construction of the optimal service disciplines, different numerical methods of the Howard iterative algorithm type are often used. However because of usually high dimensionality of real problems, direct application of such the calculation approaches is often not efficient. With the help of the known Howard algorithm, numerical study is carried...

INTRODUCTION The problem of optimal jobs assignment to heterogeneous servers arises in many applications. The problem of optimal jobs assignment for two heterogeneous servers with respect to minimization of long run average mean number jobs in the system was considered in [1], where it was shown that the policy, which minimizes the number of custom...

A general model for describing, evaluation and control of most common reliability characteristics of multi-stage systems with gradual failures and repairs of the whole system is proposed. The steady state probabilities and the Laplace transform of the reliability function are calculated.

This work is devoted to analyzing the syntax contents of an animation. In the paper we present the ANIMATION system - a system for animation scene and contents creation, retrieval and display. The object recognition mechanism in the ANIMATION system includes three steps: (1) Low level animation images analysis - element recognition based on the Att...

Recently a new class of Markov network processes was introduced, characterized by so-called string transitions. These are continuous-time Markov processes on a discrete state space. It is known that they possess an invariant measure of a special form, ...

Consideration was given to the model of a queuing network for transparent calls with arbitrarily distributed service times. Its operation was described and studied in terms of the multidimensional alternating process and a method for its Markovization. The stationary probability distribution of this process was shown to be representable in the mult...

A multi-server controllable queueing system with heterogeneous servers is considered. Several monotonicity properties of optimal policies for such a system are proved.

The problem of decomposition of closed data communication networks admitting the dependence of times taken to transfer messages over different channels is considered.

One of the topical problems of the theory of controllable queuing systems is the a priori (prior to actual determination) study of the qualitative properties of optimal control policies such as monotonicity. Their knowledge enables one to simplify appreciably the procedure of their determination and, sometimes, establish their explicit form. The pr...

A single-server system with controllable service rates in relation to the discount factor and the average cost criterion is considered. It is known that in the absence of holding (waiting or sojourn) costs, the optimal control policies display the monotonicity property, in this work, numerical methods are used for establishing other qualitative pro...

This paper is a direct continuation of an earlier paper of ours [Autom. Remote Control 58, No.10, Pt. 1, 1628–1639 (1997); translation from Avtom. Telemekh. 1997, No.10, 91–104 (1997; Zbl 0920.68004 )] and gives an alternative approach to the problem of the decomposition of complex systems, based on the idea of their aggregativity, which, in turn,...

In the first part of this work, the decomposition of systems with continuously interacting subsystems had been considered. In this second part, systems with discretely interacting subsystems are considered. A concept of aggregate system is introduced that generalizes the concept of piecewise-linear aggregates of N.P. Buslenko, V.V. Kalashnikov and...

Two approaches are considered to solving the decomposition problem of operation processes of complex hierarchical systems based on the conditions of interaction between their subsystems. The first approach described in this work is connected with the study of systems with continuously interacting subsystems. Information-computation systems are typi...

Semi-Regenerative Decision Models Description of Basic Decision Model Rigorous Definitions and Assumptions Examples of Controlled Queues Optimization Problems Renewal Kernels of the Decision Model Special Classes of Strategies Sufficiency of Markov Strategies Dynamic Programming Discounting in Continuous Time Dynamic Programming Equation Bellman Fu...

Criteria for semi-, wide-sense-, traditional regeneration and a coupling construction of stochastic processes with embedded point processes are presented.

This paper reviews publications on warranty theory accessible to us. It is known that products, industrial wares, technical equipment, etc. are usually sold together with a certain warranty which is valid during a given warranty period. During this period the producer guarantees tile correct operation of his product and the repair, replacement or c...

Recursive algorithms are considered for construction of optimal policies for some special classes of controllable stochastic processes, which are called discrete-time controllable semi-regenerative processes. By means of these processes many controllable queueing systems can be modelled. Numerical examples are given for the investigation of optimal...

The fundamental results relating to queuing systems with dependencies are presented in condensed form in the present survey. Particular attention is paid to the extension of the results obtained earlier for classical systems to systems with dependencies, and certain early classical results in queuing theory are discussed.

The present paper deals with the class of regenerative processes. Thereby the ease is investigated that on its regeneration periods the considered process can again be seen as a regenerative process. In connection with this the notions of the decomposable regenerative Process and of the embedded regenerative process have been introduced. An example...

Reliability control model for fault tolerance units under different repair policies with respect to cost mini- mization and/or availability maximization criteria are proposed. Optimization algorithms and appropriate computer routines are given. Some numerical examples for the approach illustration are considered.