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 Âûïóñê 112
- Gorbunova A. Estimates of the copula and quantiles of the response time distribution for a fork-join queueing system with the pareto distribution of service time
A fork-join queueing system is considered. It is assumed that the service time distribution on all servers has a Pareto distribution. The dependence between the sojourn times of subtasks in subsystems is studied, which is the main reason for the complexity of analyzing such systems. The sojourn time of a task in the system (or the average response time) is the maximum of the dependent random variables of the sojourn time of subtasks in the system. Approximations of the joint distribution of the sojourn times of subtasks are obtained using copula theory. An approach is also proposed for determining the quantiles of the system response time distribution using a diagonal section of copulas. This approach was previously used to analyze a similar system, but with an exponential distribution of service time. However, the main difference between the system under study and the exponential case is that the type of the distribution function of the sojourn time of a subtask in the subsystem is unknown. Therefore, an analytical approximation is used for the quantiles of the response time distribution in the subsystem under the assumption that the distribution of the time of stay of a subtask in the subsystem is approximated by the Frechet distribution obtained earlier. The estimates obtained for the quantiles and copula of the response time distribution show good agreement with the simulation data.
- Moiseeva S., Pankratova E. Asymptotic analysis of a multi-flow heterogeneous qs under conditions of extremely rare state changes manager of input flows markov chains
Currently, multimodal systems are gaining popularity with the development of multimodal interfaces. Multimodal streams are integrated streams of different types, including the transmission of voice, text data and video, so it is logical to use non-Poisson models to describe them. As a mathematical model of a multimodal servicing system, a multi-threaded heterogeneous queuing system with flows changing their intensity depending on the states of the Markov random environment is considered. Incoming requests from various flows are serviced during an exponentially distributed random time with parameters determined by the type of flow. Expressions are obtained for finding the maximum values of the main probabilistic characteristics of the number of occupied devices of each type. Asymptotic research is carried out under the condition of extremely rare changes in the states of the environment. The form of the multidimensional asymptotic characteristic function is obtained. It is proven that one-dimensional (marginal) stationary probability distributions of the number of occupied devices of each type are weighted sums of Poisson distributions. A numerical analysis of the range of applicability of the obtained approximation was carried out.
- Paul S., Nazarov A., Lapatin I. Study of two-dimensional marked mmpp under the high rate limit condition
This paper considers a mathematical model of a heterogeneous flow in the form of a two-dimensional marked MMPP. The study of such models is necessary to analyze the load on multimodal systems. Multimodal interfaces are capable of processing multiple natural human input methods, each of which requires specific resources for recognition, processing and transmission. To design such systems, it is necessary to estimate the required resources. These estimates can be based on the joint probability distribution of the number of calls of each type over a certain period of time. The paper proposes an asymptotic method to estimating the two-dimensional probability distribution of the number of arrivals in a high-intensity marked Markov Modulated Process. The limiting condition of high intensity is determined by the parameter of the rate of arrivals in the process over a certain time. The asymptotic analysis method is carried out in two stages. At the first stage, the parameters are obtained that determine the asymptotic mean numbers of arrivals of the first and second types that occurred in the high-intensity flow. At the second stage, the parameters are found that determine the asymptotic variances and the covariance of the number of events of the first and second types. It is shown that the limiting distribution of the number of events that occurred in a high-intensity marked MMPP is a two-dimensional Gaussian. The resulting formulas for finding the distribution and its characteristics have fairly simple expressions, the unknowns in which are found by solving systems of linear equations.
- Mukhin A. About an unusual case in the pole placement problem
The pole placement problem using a static output feedback is considered. If the problem is solvable, then the spectrum of the closed-loop system matrix can be located at any given points of the complex half-plane, symmetric with respect to the real axis. This makes it possible not only to stabilize the system, but also to set the required characteristics, such as stability margin, transition time, and others. It is known that if the multiplication of the number of inputs and outputs is greater than the dimension of the system, then the pole placement problem for a system in the form of a transfer matrix is solvable. The article shows that this ratio is not a sufficient condition for a system defined in the state space. There is an exceptional case in which the pole placement problem is fundamentally unsolvable. This case is simple discovered be means of multiplying of matrixes output and input. If this product gives a zero matrix, then due to the matrix trace consistency of the closed system matrix, the problem is unsolvable both in the real and in the complex domain. Moreover, the product of the output and input matrices is invariant with respect to the basis. A necessary condition for solvability is formulated.
- Yurchenkov A. Anisotropy-based control design for linear time--invariant systems with moments constraints of disturbances
In this paper, a linear discrete time-invariant system with control under the influence of a colored disturbance is considered. The external disturbance is selected from the class of non-centered stationary Gaussian sequences of random vectors with a known restriction on the level of mean anisotropy. For the specified class of control objects, a dynamic regulator is introduced, with the help of which it is necessary to ensure the boundedness of the anisotropic norm from an external disturbance to the controlled output of a closed--loop system. The control design problem is to construct an anisotropy--based dynamic regulator in terms of state--space representation. The boundedness of the closed--loop system is provided by anisotropy--based small gain theorem. Using linearizing reversible variable change, the problem can be reduced to a numerical solution of the convex optimization problem with special constraints characteristic of anisotropy--based theory. In the formulation of the problem, it is assumed that the expectation of the external disturbance is unknown, but a condition on it in the form of inequality is known. This parameter causes an additional constraint to appear in the convex optimization problem. The resulting system of inequalities is linear matrix inequalities in combination with an inequality of a special type, which is nonlinear with respect to unknown parameters, but at the same time convex in these parameters. The problem of finding the regulator matrices can be solved by standard methods.
- Gasanov I. The project of the order distribution system within the association of manufacturers through multiple auctions
The paper describes the design of a system ordered by a company that coordinates the joint assembly production of products from components, the manufacture of which employs a large number of independent enterprises. The entire production of end products can be represented as a directed acyclic graph, in which parts of a lower rank are used to assemble parts of a higher rank. Coordination of such production among a large number of independent manufacturers requires significant efforts from the parent company to coordinate plans, take into account the interests of participants, and constantly monitor their capabilities. At the same time, it is not possible to achieve an optimal solution and minimize costs. The task was formulated to develop an alternative approach to the formation of a production plan using modern ideas of distributed solutions based on network principles, similar to the organization of interaction within the blockchain, when the functioning of the system as a whole is determined by the individual interests and actions of its participants. The author proposed a system of interaction within the association of manufacturers based on multiple local auctions, where participants' offers for the production of components necessary to fulfill a common order are traded. This approach has its advantages, but it also carries certain risks. The article provides an overview of the auction scheme and discusses the difficulties associated with its implementation.
- Gubanov D., Chkhartishvili A. The influence of ranking algorithms, bots and content moderation on opinion formation in social networks
This paper considers a model of information cascade formation in online social networks, accounting for the influence of content ranking algorithms, bot actions, and content moderation. Special attention is given to opinion dynamics, which is critically important for predicting and managing social processes. Unlike traditional models, in this case, the opinions of agents (users) are not directly observable: their actions, such as posting comments, act as indirect indicators of their opinions. These actions influence the opinions of other users, leading to the formation of an information cascade within the network. The model incorporates additional factors such as comment ranking algorithms, bot behavior, and content moderation. Computational experiments demonstrate that ranking algorithms significantly affect the dynamics of opinions and actions, particularly when users have a limited view depth. Moreover, the introduction of bots and moderation can substantially alter the course of discussions. The study explores the interaction of strategic players, including the moderator and bots with opposing views, and predicts the outcome of their interactions based on Nash equilibria. Finally, the problem of a control subject (principal) is formalized and solved for a specific case, where it seeks to advance a specific viewpoint in the network by influencing bots within the network.
- Avdeeva Z., Kovriga S. Integrating forecasting of non-stationary processes represented by time series. overview
The review covers the main directions and approaches to integration forecasting of non-stationary processes represented by time series. The key source of non-stationarity generation is rapid and poorly predictable changes in the external environment, under the influence of which structural shifts occur in the complex economic and socio-political processes. The solution of problems of forecasting the dynamics of such objects in the context of improving the accuracy of the forecast becomes more complex as the forecast horizon increases. It determines the need for models and methods capable of processing heterogeneous information. Integration methods are methods that allow, along with quantitative data, to take into account judgments (of forecasters, experts, analysts) and information from heterogeneous information sources at different stages of problem solving, and thus directly or indirectly include them in the forecast being formed. The development of such methods is aimed at increasing the accuracy of the forecast through the use of all available information about the forecasting object, including data on endogenic and exogenic factors of influence on it. The review focused on the current state of integration forecasting, on the existing problems and ways to solve them.
- Bazilevskiy M. Constructing non-elementary quasilinear regressions using mathematical programming apparatus
In non-elementary quasilinear regressions, the explanatory variables are first transformed using elementary functions, after which the pairs of resulting factors are again transformed using the non-elementary functions min and max. Such models are nonlinear in both factors and parameters, so even their estimation seems to be a complex computational task. And if the composition of the variables included in the model, as well as their elementary and non-elementary transformations, is unknown, then the complexity of the problem increases significantly. This study aims to solve this problem. Instead of labor-intensive exhaustive search procedures, a well-developed mathematical programming apparatus has been used recently. The method for constructing non-elementary quasilinear regressions is formalized as a mixed 0-1 integer linear programming problem. The proposed method is implemented in a special computer program. Its advantage is that the user can regulate the number of transformed variables during the construction process, so the program can be used both for solving simple control problems on ordinary personal computers and for processing large data arrays using cloud services. Non-elementary quasilinear regressions can be used to solve control problems in technical, socio-economic, medical and other systems.
- Chernov I. Analysis of the methodology of scenario planning and national security management
The article is devoted to the development of a methodology for scenario planning and management of ensuring the national security of the Russian Federation. The results of developing a conceptual framework for scenario research are presented, on the basis of which a general scheme for the procedure for generating scenarios has been developed. The expert description of the development model of the processes under consideration is based on the concept of an expert-significant partition of the extended phase space, as well as expert-significant events that occur in the sequence specified in the ordering system within the framework of the basic model. As a result of the study of this model, scenarios for the behavior of the control object or the development of the security situation are formed. A multi-level model of the life cycle of planning and managing security measures has been developed, providing the possibility of proactive verification of the results of the implementation of key stages of the management cycle, which allows us to move from passive accounting of accomplished events to proactive management. The results obtained can serve as the basis for automating scenario research, as well as analytical predictive support for the processes of preparing and making management decisions in the field of ensuring the security of complex organizational systems.
- Galin R., Mamchenko M., Galina S., Zorin V. Approach to allocation of task of technological processes among crs heterogeneous participants taking into account their state
The paper describes the results of a series of experiments for the problems of forming an optimal composition of performers, and minimizing the execution time of the tasks in the technological process (three cases for each problem). Criteria of the efficiency of task allocation and work distribution among the participants and human-robot collaboration are presented. An overview of computational experiments of other authors on task allocation and work distribution in multi-agent and collaborative robotic systems (CRS) is shown. Qualitative comparative analysis of the results obtained from the experiments, and their evaluation based on the established criteria are given. The analysis shows comparable results of the authors’ solutions compared to the reviewed works. The authors’ statement of the problem of task allocation and work distribution in CRS compared to other sources has complexity. In particular, when selecting optimal composition of the performers, minimizing tasks/technological process execution time or costs, the results are verified to ensure that people and robots always collaborate. The degree of engagement of each participant is monitored. In addition, when optimal number of people and cobots from the CRS is chosen, the feasibility of the technological process for the calculated composition is also checked.
- Trefilov P. Sensor data integration algorithm for state estimation of autonomous robots in an intelligent transport system
This paper deals with the development and experimental testing of a sensor data integration algorithm for estimating the state of autonomous objects in intelligent transport systems (ITS). The main attention is paid to ensuring accuracy and reliability of navigation in complex and dynamically changing conditions of urban environment, where traditional navigation methods, such as GPS, may be insufficiently effective. The proposed algorithm combines data from different sensors (LIDAR, cameras, inertial sensors, GPS) and ITS elements to provide accurate position and trajectory estimation of autonomous systems. Experimental results obtained in simulation and field tests confirmed high accuracy and adaptability of the algorithm, which makes it promising for application in autonomous vehicles. The paper also discusses the possibilities of further development of machine learning algorithms and data protection methods to improve the efficiency and safety of navigation systems in ITS.
- Ostrer L., Rusev V., Skorikov A. The asymptotics of moments and moment’s derivatives for excess distribution
The functioning of modern complex systems is characterized by various types of risks. Data analysis of such systems shows that data sets have characteristic properties: heavy distribution tails. An important issue is the impact of individual extreme events on the global behavior of the entire system too. The proposed article discusses classes of distributions with heavy tails, which are important in the theory of insurance claims and reliability theory: Gnedenko-Weibull distribution; Benktander I, II; Burr XII. The moment`s asymptotics have been derived for mean excess function and excess variance function especially for the heavy-tailed distributians. The paper studies in detail the error estimate for the asymptotic expansion of the mean excess function of the Gnedenko–Weibull distribution for any values of the shape parameter. There is a significant difference in the behavior of error estimates for values of the shape parameter less than one corresponding to the heavy tail of the Gnedenko –Weibull distribution. The values of the shape parameter are found for which the decompositions are accurate in particular. That is, the expansion has finite quantity members. Asymptotic expansions of derivatives of residual moments are proved for Gnedenko-Weibull; Benktander I, II; Burr XII distributions. The description of the behavior of the system as a region of attraction of the ultimate extreme state is also considered. These results serve as a tool for the applications to risk theory, reliability and extremal event.
- Granichin O., Granichina O., Trofimov S., Shcherbakov P. Calibration of a large array of ultrasound sensors
The paper presents a method for calibration of planar circular arrays of sensors used in ultrasound tomography, which enables the estimation of sensor coordinates and signal reception/transmission delays. The method uses an ultrasound wave propagation model and is based on the triangulation approach to identify the model parameters. At each iteration of the method, the estimates of coordinates and delays are recalculated separately from each other by solving systems of linear equations of low dimensionality. Simulation over synthetic data demonstrated high efficiency and accuracy of the approach: It is noise-resistant and is capable of operating in diverse conditions, including non-ideal model of ultrasound wave propagation. The proposed approach can be easily scaled to calibrate devices with large nuber of sensors, which makes it relevant to correct industrial practical implementation. This method can significantly improve the accuracy of ultrasound imaging results, making it a valuable tool for a variety of applications, such as medical diagnostics, robotics, etc.
- Lempert A., Zharkov M., Kazakov A., Vu G. Modeling of a sea container terminal using a queuing network
The article focuses on the problem of modeling and forecasting the operation of a sea container terminal under the unevenness of cargo arrival and the influence of random factors on the service duration. The mathematical model takes the form of a queuing network (QN), whose nodes simulate the operation of the terminal structural elements. The movement of requests between nodes occurs according to a given route matrix. To describe transport flows arriving from sea and land, we use both ordinary and batch Poisson flows of requests. The constructed model is identified for a sea container terminal in the north of Vietnam – one of the largest in Southeast Asia. The model consists of 14 nodes and includes two incoming Poisson flows, one of which is batch. The route matrix and the parameters of incoming flows are determined by statistical processing of data from open sources and field observations. The mathematical model is implemented, and scenario simulation is performed. Based on the results obtained, we conclude the current capacity of the system and forecast its performance with an increase in the volume of container flows, in particular, with the arrival of ultra-large container vessels in the future.
- Roganov V., Korop G., Mikheev M. Imitator of visual environment synthesizing in the visual range of electromagnetic waves the external appearance of the space around the cabin of an air training simulator
An aviation simulator is a complex of several imitators combined for the purpose of training pilots in professional piloting and aircraft navigation skills in training situations. The purpose of flights on an aviation simulator is to form in pilots the components of its cognitive model, which will allow them to successfully operate in normal and pre-emergency situations in the future. Of all the imitators of an aviation simulator, the ergatic optical-software-hardware imitator stands out, synthesizing for the pilot a visually observable 3D-model of the external environment with a quality sufficient for solving navigation problems, including the use of the eye to estimate the distance to visible 3D-models of reference objects, from which a 3D-model of a given flight area is collected. This task is divided into a number of subtasks including the construction of 3D-models of reference objects, their description and placement in the database of a computer image generator, the selection of a 3D-indicator, and training the pilot to see 3D-objects while he sees a video sequence of 3D-projections of 3D-models of reference objects. The article analyzes visual environment imitators and 3D-indicators from the point of view of the formation of constantly updated components of the pilot's cognitive model during both real approaches to an aircraft and flights on flight simulators, allowing him to successfully pilot an aircraft and solve navigation problems both "during flights in continuous cloud cover" and during flights with visual observation of reference objects in order to determine the location of the aircraft model and the direction of its flight.
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