Galina Adolfovna Timofeeva

Ural State University of Railway Transport · Department of Mathematics

The research is devoted to the analysis of the uneven distribution of passenger traffic between the settlements of the Russian Federation. The data were analyzed obtained as a result of processing the database of the automated control system (ACS) "Express". The hypothesis was tested that incoming and outgoing passenger flows obey the generalized Z...

Many multi-master replication systems are based on a two-phase commit mechanism. One of its problems is waiting for a response from the database servers by the coordinator, which may not come due to problems on the network or on the database server itself, which leads to delays in the activity of the multi-master replication system. Usually, such p...

A hierarchical game with a random second player is considered, optimal strategies are defined on the base of Stackelberg equilibrium. The random second player is understood as a randomly selected person from a homogeneous set of decision-makers. The proposed model can be used in various problems. First of all, it is may be used for optimal price ch...

The paper considers methods for modeling passenger traffic splitting at presence on a route of various competing modes of transport. The authors suggest a method based on a hypothesis that passengers of various population groups make decisions based on assessment of importance of route (mode of transport) parameters such as ride time, cost and comf...

A study presented in the paper is dedicated to calculation and analysis of a gravity model of passenger transportation by railway transport between Russian settlements. The model is created on the basis of data gained in result of processing of a base of the automated control system for railway ticket sales «Express». The paper describes an author’...

The choice of the optimal strategy for a significant number of applied problems can be formalized as a game theory problem, even in conditions of incomplete information. The article deals with a hierarchical game with a random second player, in which the first player chooses a deterministic solution, and the second player is represented by a set of...

The problem of reconstructing the origin-destination matrix for transport following fixed routes is studied. Estimates are based on statistics on passengers entering and leaving at each stop. Various models for estimating of origin-destination matrices are analyzed, including the entropy model and the generalized gravitational model. The properties...

Probabilistic solutions are used when the amount of decision-makers is large. Each of them chooses the optimal solution independently of the others by solving his optimization problem. In this case, the optimal solution constructed by a randomly selected person (e.g. a consumer of goods) can be considered as a random vector. In particular, probabil...

В работе рассматриваются вопросы устойчивости обобщенной модели Блэка - Шоулза. Предполагается, что динамика цены опциона зависит от случайных скачкообразных изменений волатильности. Показано, что исследование вопроса среднеквадратической устойчивости стохастической системы Блэка - Шоулза можно свести к исследованию устойчивости детерминированной с...

Determining the rational parameters of the structure and technology of railway transport facilities activity is one of the most important tasks in the field of operational management. Analysis of existing regulatory documents and literature sources has shown that the choice of technical and technological parameters of railway stations is made with...

Традиционный подход к решению задач оптимизации со случайными параметрами состоит в нахождении детерминированного решения, удовлетворяющего тому или иному критерию: оптимизации среднего ожидаемого значения целевой функции, оптимизации вероятности достижения определенного уровня или оптимизации квантили. В данной обзорной работе рассматривается реше...

Optimization problems with random parameters are studied. The traditional approach to their solution consists in finding a deterministic solution satisfying a certain criterion: optimization of the expected value of the objective function, optimization of the probability of attaining a certain level, or optimization of the quantile. In this review...

The paper considers a task of a correspondence matrix recovery for transport with a fixed number of routes according to the statistical data on incoming and departing passenger traffic. A classic gravity model was generalized for several modes of transport that resulted in combination of a correspondence matrix calculation and a calculation of pass...

In the situation of rapidly developing e-commerce, there is a need to expand the possibilities of cargo delivery. Of course, there is the problem of optimizing transport routes. The problem of probabilistic mathematical modeling of the carriers preferences of and their clients is considered. Patterns of preferences are formulated based on the solut...

A mathematical model for describing passenger preferences is studied. The model was proposed earlier by the authors for predicting passenger traffic for high-speed links of the railway network. Choosing a route by a randomly selected passenger is considered as a problem of minimizing of the generalized transportation cost. This cost is a linear com...

In the course of solving problems of managing and planning the development of large transport networks, a big amount of heterogeneous data from various sources is accumulated. The methods of graph theory are used to systematize information, process it, and calculate network characteristics. However, the problem arises of the enormous complexity and...

Markov model of the loan portfolio dynamics considering the process of new customers attraction as a control action from the bank management is described. Unlike the models, that do not take into account the attraction of new customers, the proposed model describes not only the structure, but also the volume of the loan portfolio, which allows to m...

The problem of passenger traffic forecasting under transformation of the transport network structure is considering. Modelling of passenger traffic in transformed network is based on Markov chains with incompletely known transition probabil-ities. Estimation of transition probabilities is performed via the original networks traffic and patterns of...

The study aims to validate a mathematical model of influence of applications’ selection process on a loan portfolio structure expected by the end of a planned period. When predicting risks and profitability of a loan portfolio, many authors use a mathematical model of a loan portfolio in the form of a Markov chain with discrete time. This model usu...

The problem of modeling preferences of passengers and carriers in conditions of changing the transport network structure is considered. The patterns of passengers and carriers preferences of are formulated on the basis of the bicriterial problem solution. The choice of a route by a random passenger (carrier) is considered as an optimization problem...

The problem of choosing an optimal solution in stochastic optimization problem containing both random perturbations with given distributions and nonrandom perturbations about which only the regions of their possible values are known. As a criterion of optimality, the quantile criterion is used, i.e. the objective function value guaranteed with some...

Features of the use dynamic programming for transportation planing under uncertainty are investigated. A multi–step decision–making process for the multi-modal transportation planning problem is constructed. It should be noted that the application of the dynamic programming method allows to include in the consideration additional criteria such as u...

We consider the problem of mathematical modelling of flows of loan portfolio payments. We assume that the change in the quality of each loan is described by a simple Markov chain with a finite number of states. In this case, the flow of loan payments is a random process, which depends on the Markov chain. On the basis of the proposed model and know...

The problem of forecasting the state probabilities vector for a stationary Markov chain with discrete time in case of transition probabilities are not exactly known and measured during the system operation is investigated. An auxiliary dynamic system with uncertainty and observation showing the dynamics of the state probabilities vector is construc...

Vector model representations of text documents are widely used in the intelligent search. In this approach a collection of documents is represented in the form of the term-document matrix, reflecting the frequency of terms. In the latent semantic analysis the dimension of the vector space is reduced by the singular value decomposition of the term-d...

Mathematical model of loan portfolio in the form of a controlled Markov chain with discrete time is considered. It is assumed that coefficients of migration matrix depend on corrective actions and external factors. Corrective actions include process of receiving applications, interaction with existing solvent and insolvent clients. External factors...

Probabilistic models of cash flow for an investment project and for a loan portfolio are considered. The approaches to the estimation of profitability and risk of the project and the loan portfolio are obtained on the basis of calculation of statistical moments multistep system, which depends on the Markov chain. Models, taking into account the cha...

Most of data-mining methods are based on the vector space model of knowledge representation. The vector space model uses the frequency of a term in order to determine its relevance in a document. Terms can be similar by semantic meaning but be lexicographically different ones, so the classification based on the frequency of terms does not give desi...

Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described...

The monograph deals with mathematical modeling and predicting the dynamics of the loan portfolio structure. The portfolio structure is understood as the percentage of groups in the portfolio. Analysis of the dynamics of the loan portfolio is based on the model of the Markov chain, taking into account the incompleteness of information on the transit...

В статье предложен алгоритм машинного обучения, основанный на разбиении данных на категории и построении категориальных векторов для пользовательских запросов и базы вакансий. Предлагаемый метод имеет высокую скорость получения результата. "Экономика и менеджмент систем управления" 2015. № 4-2 (18). С. 215-221

Выделение семантического ядра широко используется для компактного представления документов при решении задач классификации и интеллектуального поиска. Для выделения семантического ядра вводится матрица корреспонденций термов, отражающая взаимосвязи между документами, проводится её сингулярное разложение. Результаты сравниваются с сингулярным разлож...

Data mining widely employs vector model of document submission – every text document from the database is given as a vector whose dimension is equal to the number of words (terms) in the body. When developing algorithms for the selection of the most appropriate documents from the database, the problem of compact representation of user queries and d...

The estimation problem of the loan portfolio profitability is considered. The payment flows generated by the portfolio are modeled as a Markov process with incomplete information. The loans in the portfolio are divided into several groups depending on presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is descri...

A change of shares of credits portfolio is described by Markov chain with discrete time. A credit state is determined on as an accessory to some group of credits depending on presence of indebtedness and its terms. We use a model with discrete time and fix the system state through identical time intervals - once a month. It is obvious that the matr...

We consider the forecasting problem for components of a bank’s credit portfolio, in particular, for the share of non-performing loans. We assume that changes in the portfolio are described by a Markov random process with discrete time and finite number of states. By the state of a loan we mean that it belongs to a certain group of loans with respec...

The state estimation problem for a dynamic system described by the Markov chain model with discrete time is considered. It is assumed that a matrix of the transition probabilities is incompletely known. Pro-posed approach is based on the confidence estimates.

We consider the parameters estimation problem for a statistically uncertain linear model, i.e., a model whose observations contain both random perturbations with known distributions and uncertain perturbations for which we only know the domain of their possible values. To solve this problem, we use an approach related to the maximum likelihood meth...

The research work is divoted to the solving for optimum traffic light parameters under the given car flow intensity. The approach is based on the queuing systems theory and compute simulation.The author's program uses a microscopic simulation applying a simplified version of the Intelligent Driver Model (IDM). The optimal solution is chosen on the...

Efficient traffic organization is one of the most urgent problems of modern society. The choice of optimal control regimes for intersecting traffic flows is a component of this problem. At present, a detailed description of the motion of an individual car and of a traffic flow has been developed and simulation programs that model traffic flows at a...

A stochastic optimization problem with incomplete information is considered. Optimal solutions are selected using the minimax quantile criterion. This problem is related to a confidence estimation problem for a random vector with incompletely known distribution. Generalized confidence regions are used as confidence estimates for a statistically unc...

This paper presents the mathematical model describing movement of vehicles through adjustable crossroads. The model is based on the theory of queuing. The stationary modes of the system are investigated, the problem of optimal duration of traffic light cycle is studied.

Consideration is given to the problem of confidence estimation for statistically uncertain systems with observation, i.e., for systems in the description of which there are both random perturbations with known distributions and unknown perturbations with the information only about domains of their possible values. Confidence estimates for a state o...

Consideration is given to the problem of large-scale projects competition in the formulation motivated by real problems of defining the rational development of oil and gas transportation systems. The problem is formulated as a noncooperative game of ...

In this paper, problems of stochastic optimization under incomplete information on distribution of random perturbations with the quintile and probability criteria are considered. The minimax approach is used when optimal solutions are chosen. Conditions for equivalency of direct and inverse problems of stochastic optimization under incomplete stati...

In this paper, we consider a problem of confidence sets design for the estimation problem with observations in the system that contains both random perturbations with given distributions and uncertain perturbations with information completely defined by the domain of their possible values. Two approaches are compared: the first is based on applicat...

The state estimation problem for statistically un- certain systems with observation is investigated. A system is called statistically uncertain one if it contains random perturbations with incompletely known distributions, or it contains both random and nonrandom uncertain perturbations. Confidence estimates for the system states are studied. It is...

Confidence sets are constructed for the phase state of a multistep nonlinear system, the description of whose dynamics contains both random perturbations with given distributions and uncertain perturbations with information defined by their value domains. The design of optimal confidence sets is reduced to optimization of a quantile function. Its s...

Problems of optimal control containing random perturbations with incomplete information about their distribution are considered. The optimality criterion is the minimax quantile criterion. Such problems of quantile control are closely related to the problem of constructing confidence estimates for a random vector with an inexactly known distributio...

The probabilistic stability of the perturbed motion of a system with parameters under the action of a general Markov process is studied. The phase vector is assumed to experience random jumps when the structure the system suffers random jumps. Such a situation is encountered, for example, in the motion of a solid with random jumps in its mass. The...

An estimation problem under incomplete information on random perturbations distributions is considered. The confidence estimation problem is considered in connection with a stochastic optimization problem with a quantile criterion under incomplete information. A concept of generalized confidence sets is introduced for a statistically uncertain vect...

A problem is considered for the construction of confidence sets for a random vector, the information on distribution parameters of which is incomplete. To obtain exact estimates and a detailed analysis of the problem, the notion is introduced of a generalized confidence set for a statistically indeterminate random vector. Properties of generalized...

The problem is studied of the probabilistic stability of perturbed motion in systems with parameters being under action of Markov process of rather general form. It is assumed that in a random jump-like system structure change, the phase vector changes with jump as well. Such the situation occurs, e.g. in motion of rigid body with mass varying with...

The problem is considered of confident sets construction for a random vector with information about distribution parameters being incomplete. The conception of generalized confident set is introduced for statistically uncertain random vector to obtain exact estimates and analyze the problem in detail. The properties of the generalized confident set...

An optimal control problem for statistically uncertain system described by stochastic differential equation is considered. It arises in the dynamic investment portfolio selection problem in case of incomplete information on the assert returns mean values. An assert prices motion is described by the geometrical Brownian motion thus considered proble...

A problem of esimation of parameters in a statistically uncertain model is discussed. A generalized case is investigated when the measurement error has both a random component with the normal distribution and a statistically uncertain component that obeys only a geometric constraint. An approach to estimation of the set of the most probable states...

The linear stochastic optimization problem with incomplete information on a random purpose vector is considered. It arises in one-period portfolio selection problem in case of unknown statistical parameters of assert returns distributions. The optimal solutions are chosen on a base of minimax and mean-variance approaches. A notion of an adjoint sto...

An efficient control problem for bilinear multistage system with random perturbations is considered. The efficient solutions are chosen by two criteria: the first is maximization of a mean value, the second is minimization of a variance of utility function. Such approach has been suggested by Markovitz H. to solve one-stage problem of the portfolio...

The problem of finding the minimal value of a linear functional on a polyhedron is considered. It is assumed that the goal vector is a random vector with a given nondegenerate covariation matrix and an imprecisely given mean value. The problem stated is considered as bicriterial. On the one hand, we want to minimize the greatest mean value of the g...

Consideration is given to finding the maximum of a linear functional on a polyhedron. The objective vector is assumed to be stochastic with given moments of distribution. The problems of portfolio selection and revision can be regarded as special cases of the formulated problem of stochastic programming. Following the approach of financial analysis...

The state estimation problem for linear multistage system with observation is considered. Random perturbations present in the system and in the observation channel, information about their distributions is uncompleted. The sets of aposteriory means were used for system state estimation in this case. Other estimates are obtained by using of the maxi...

Estimation problem is considered for the linear many-stop system states in presence of deterministic and random interference as in the measurement channel. A suggested modified residual method allows to construct a solution of a statistically indefinite filtration problem converging to a solution of corresponding deterministic problem when the cova...

The problem of estimating the state of a linear multistep system is considered, in which, as in the measurement channel, deterministic and random interference is present. The proposed modified method of residuals allows us to construct a solution that can be used to solve a deterministic problem while striving for the expectation of covariance pert...

The problem of estimating the state vector of a linear discrete system with additive interference is considered. Using the minimax approach, confidence sets are constructed for the state of the system, that is, sets X kα such that P {χ k qq X kα < α where P {A} is the probability of the event A. Dynamic relationships are obtained that enable one to...

We construct algorithms for recursive estimation of a parameter when the unknown vector x * is observed with random errors z k =x * +ξ k , k=0,1,2,···, where ξ k are independent identically distributed random variables. The specific feature of the problem is the assumption that the distributional information about the random errors is exhausted by...

Traditional statements of control problems motivated by financial management are based on the approaches of the probability theory and stochastic calculus. In this paper we consider one of the problems of this area, which is related to the dynamic selection of an investment portfolio. A formalized setting and solution are based on a combination of...