Mathematical Simulation Methods Research Articles

Design and fabrication of a Fresnel zone plate with an enhanced depth of focus

A Fresnel zone plate (EFZP) with an extended depth of focus can maintain focused monochromatic light at different distances compared to a general Fresnel zone plate (FZP). The focal distances are determined by dividing the zone plate into multiple areas based on the desired order. The EFZP has potential applications in various research fields such as microscopy, direct laser lithography, and optical coherence tomography. However, manufacturing an EFZP is challenging due to the high precision requirements and difficulties associated with the calculation and simulation processes. In this research, a complete process is presented to design, simulate, and fabricate an EFZP using a Fourier optics design, simulations, and a direct laser lithographic machine. The resulting EFZP has an increased depth of focus of about nine times compared to a general Fresnel zone plate with similar parameters, while maintaining the focal spot diameter. The performance of this EFZP is evaluated through optical verification and mathematical simulation methods.

Parametric Study of a Large Active Area PEM Fuel Cell using a MatLab-Simulink Model

A Matlab-Simulink based mathematical model and simulation method is developed by applying appropriate physics and electro-chemistry that adequately describes a proton exchange membrane fuel cell (PEMFC) system. The mathematical model is then simulated for a single low temperature PEMFC with a large, 350cm2, active area. The single cell’s performance was evaluated using different operating conditions and varying values of various crucial system parameters. The Matlab-Simulink model presented in this investigation is used to study various parameters’ effect such as the cell temperature from 50℃ to 90℃, inlet pressure, relative humidity (RH) from 70% to 90%, and the reactant stoichiometry ratio, on the cell performance. Comparison of polarization and power density curves were conducted between the model simulation and experimental data at 60℃ and at 65℃. Except for the higher current densities range (≥1.6 A/cm2), the simulation results match with the experimental results very well. The parametric study was used to determine the optimum value of various parameters. The fuel cell performance with the optimized parameter values show a good improvement using the developed MatLab-Simulink model.

Simulating the Appearance of Aerial Images formed by Aerial Imaging by Retroreflection

Ray tracing, combined with ideal retroreflection and mathematical simulation methods, has been used to design aerial imaging systems based on retroreflection. Although aerial images are blurred and have lower brightness than the light source, existing simulation methods do not focus on the appearance of these characteristics. In this study, we propose a computer graphics (CG)-based simulation using the ray tracing method to generate CG renditions of aerial images with reproduced luminance and blurring. CG models of three optical elements (light source, half-mirror, and retroreflector) were created on the basis of existing optical element models to simulate aerial images obtained through retroreflection in aerial imaging systems. By measuring the image formation positioning, we determined that the rendered aerial images consistently formed at a plane-symmetrical position relative to the axis of the half-mirror model, with a mean absolute error of 0.55mm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${0.55\\,\ extrm{mm}}$$\\end{document}. We also compared rendered and actual aerial images in terms of luminance and sharpness characteristics, and found that the mean absolute percentage error of luminance remained within 0.0376\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.0376$$\\end{document}. Furthermore, the directional dependence of blur was effectively reproduced using the retroreflector bidirectional reflectance distribution function developed in this study.

Методика балістичного планування місій низькоорбітального сервісного обслугову-вання з малою постійною тягою рушійних систем

The current stage of space exploration is characterized by an increased interest in the development, deployment, and operation of low-orbit satellite constellations (LOSC) for Earth and near-Earth space remote sensing for military and civilian purposes and for global and regional satellite communications. Reusable space launch vehicles have significantly reduced the orbital injection cost. As a result, satellite operators are developing and deploying large-scale LOSCs of various orbital structures with a large number of spacecraft. According to current estimates, more than 70% of all the operating satellites operate in low-Earth orbits (LEOs) at altitudes between 160 km and 2,000 km. Since LEO satellites are generally much cheaper than satellites in geostationary orbits, the possibility of their on-orbit servicing (OOS) has not been the focus of research. However, the use of LEO OOS has prospects for growth. Techniques for ballistic planning of LEO OOS missions have been and are being developed. The disadvantages of approximate techniques include the use of simplified flight dynamics models. Most of the existing exact techniques are based on the use of full mathematical models of flight dynamics and the shooting method to solve the boundary value problem of an orbit transfer. Using the shooting method requires a sufficiently accurate initial guess, which is difficult to determine. To obtain a second approximation, use is mainly made of optimization methods, which do not always find a global minimum. In this regard, there is a need to develop new techniques that would be free from the above disadvantages. The goal of the article is to develop a ballistic planning technique for low-orbit servicing missions with low constant thrust propulsion systems. The technique includes the identification of LEO areas promising for OOS, a mathematical model of the dynamics of perturbed OOS orbit transfers in modified equinoctial orbital elements, and a solution algorithm for the boundary value problem of determining the control parameters of perturbed OOS low-orbit transfers. The problem is solved using methods of statistical analysis, flight dynamics, shooting, genetic optimization, and mathematical simulation. The novelty lies in the identification of LEO areas promising for OOS and the development of a mathematical model of orbit transfer dynamics in modified equinoctial orbital elements and a solution algorithm for determining the control parameters of perturbed OOS low-orbit transfers. The results of the work may be used in the justification and planning of LEO OOS missions and the formulation of requirements for LEO OSS mission propulsion systems.

Mathematical simulation of duration and frequency of water consumption by various water dispensers

Water flow rates calculated by using deterministic models and methods do not describe the real variability in the water supply operation. This problem can be solved by mathematical simulation. The stochastic nature of the water consumption process implies involves random variables with certain distribution laws describing the main process components, namely intensity, duration and frequency.This paper discusses the mathematical simulation of the duration and frequency of water consumption by the most common types of water dispensers (kitchen sink and bathtub faucets (shower cubicle), toilet bowl with flush tank, washing machine and dishwasher).Purpose: The aim of this work is to evaluate and substantiate theoretical laws of the water consumption by the most common types of water dispensers as well as the frequency (probability) of their daily use.Research findings: The duration and frequency are determined for water consumed by various water dispensers using water supply systems of buildings. The empirical data are analyzed. Mathematical simulation method is proposed and justified for the water consumption process.

An Analytic Model for COVID-19 Cases in Iran and Its Neighbors Using Deep Learning and Time Series Methods

Since the pandemic of the coronavirus (COVID-19) in 2019, it has rapidly become a major global health concern. Various mutations and rapid spread of the virus, a lack of specific treatment, and limited hospital facilities highlight the importance of anticipation, risk analysis, and timely treatment. The use of mathematical models, artificial intelligence, and simulation methods are effective tools in predicting the spread and providing effective solutions to prevent virus transmission. Analysis and forecasting require an integrated model to cover different aspects of the problem and use different methods to obtain appropriate results. In this research, a proposed model for analysis and prediction of COVID-19 cases in Iran and neighboring countries is presented. The performance of mathematical and deep learning models in the proposed model has been evaluated using data from Johns Hopkins University from January 29, 2020, to April 30, 2021. Evaluation of the predictive outcomes of daily cases was performed using RMSE criteria. Then, the effect of the trend of cases in neighboring countries of Iran on the rate of new cases in this country has been studied. These models can help governments predict the number of infections to provide the necessary solutions and prevent a new wave of the virus.

Coastline stability analysis of Zhoushan-Liuheng lng terminal project based on remote sensing

Seabed evolution research around Zhoushan Liuheng LNG receiving station project, which mainly includes collecting, analyzing and sorting data of environmental investigation, was conducted by the second Institute of Oceanography, MMR. Based on the data of remote sensing and field survey for different years, the comprehensive research methods of dynamic geomorphology, sedimentology, stratigraphy and mathematical simulation are used to carry out the geomorphological investigation of the sea area near the Zhoushan Liuheng LNG terminal project. This paper makes a detailed analysis of the beach dynamics, seabed scouring and silting change characteristics of the project sea area, and makes a prediction of the beach channel scouring and silting adjustment trend caused by sea related projects, which provides a scientific basis for optimizing the plane layout of Zhoushan Liuheng LNG receiving station project and insight for other researchers who focus on coastline change and remote sensing.

Комбинированная математическая модель нагрева асинхронного двигателя

Existing thermal models of asynchronous motors either require a large number of calculations and source data or have poor accuracy. Thus, it is relevant to develop methods of thermal calculation of electric motors that have adequate accuracy with a small number of calculations. To design a mathematical model of heating an asynchronous motor, methods of mathematical simulation, and the method of equivalent thermal circuits are used to calculate the temperature rise of motor parts. The authors have proposed a combined mathematical model to calculate the temperature of an asynchronous motor. It combines the method of equivalent thermal circuit and the method of calculating the temperature rise of the rotor, which allows reducing the number of nodes of the thermal circuit without increasing the simulation error. An algorithm of parallel calculation of the thermal state of the fixed part of the electric machine and the rotor has been developed. The results obtained allow us to conclude that the developed model can be used to calculate the thermal state of motors. The calculation error of the combined model is lower than when calculating using the equivalent thermal circuit method. The obtained algorithms can be improved and integrated into the general equivalent thermal circuit. It will allow us to use the proposed method to calculate the motors with a phase-wound rotor.

Application of the Monte-Carlo Method to Assess the Operational Reliability of a Household-Constructed Wetland with Vertical Flow: A Case Study in Poland

The objective of this study was to model the operation of a vertical-flow constructed wetland (VF-CW) for domestic wastewater, using Monte-Carlo simulations and selected probability distributions of various random variables. The analysis was based on collected wastewater quality data, including the values of the pollutant indicators BOD5 (biochemical oxygen demand), CODCr (chemical oxygen demand), and TSS (total suspended solids), in the 2017–2020 period. Anderson–Darling (A–D) statistics were applied to assess the fit of the theoretical distributions to the empirical distributions of the random variables under study. The selection of the best-fitting statistical distributions was determined using the percentage deviation (PBIAS) criterion. Based on the analyses that were performed, the best-fitting statistical distributions for the pollution indicators of the raw wastewater were the generalised extreme value distribution for BOD5, the Gaussian distribution for CODCr, and the log-normal distribution for TSS. For treated effluent, the log-normal distribution was the best fit for BOD5 and CODCr; the semi-normal distribution, for TSS. The new data generated using the Monte-Carlo method allowed the reliability of the VF-CW operation to be assessed by determining the reliability indices, i.e., the average efficiency of the removal of pollutants (η), the technological efficiency index (R), the reliability index (CR), and the risk index of the negative control of the sewage treatment plant operation (Re). The obtained results indicate that only in the case of CODCr, the analysed treatment facility may fail to meet the requirements related to the reduction of organic pollutants to the required level, which is evidenced by the values of the indicators CR = 1.10, R = 0.49, and η = 0.82. In addition, the risk index of the negative operation of the facility (Re) assumes a value of 1, which indicates that during the period of its operation, the VF-CW system will not operate with the required efficiency in relation to this indicator. The novelty of this work is the implementation of the indicated mathematical simulation methods for analysing the reliability of the operation of the domestic wastewater treatment facility.

Mathematical Simulation in Nuclear Medicine for Optimization Diagnostic Accuracy of SPECT/CT

Purpose: To develop the method of mathematical simulation in the field of nuclear medicine and its
 practical application in research aimed at improving the diagnostic accuracy of the SPECT/CT method.
 The basic principles of the method of mathematical simulation in nuclear medicine and the main modules of the software package “Virtual Platform for Simulation Tests of the SPECT/CT Method”, created
 at the laboratory for simulation in nuclear medicine of Novosibirsk State University and the Institute of
 Theoretical and Applied Mechanics.
 Material and methods: The main principles of the developed software package are the realism of the ‘virtual patient’ mathematical model, the accuracy in modeling of physical processes in visualization, as
 well as simulation conducting close to clinical practice. All studies were carried out in collaboration
 with clinicians. The software complex was verified by comparison with clinical data. Numerical experiments have shown a close correspondence between the results of clinical and virtual studies. In simulation tests, the same errors were obtained on images that were observed on clinical images. Simulation
 computer tests were carried out using the software package “Virtual Platform...” in the field of nuclear
 oncology, cardiology and neurology, aimed at studying the accuracy of images of pathological foci to assess the possibility of switching to quantitative SPECT, as well as optimizing the protocol for examining
 patients.
 Results: Simulation tests have shown that in order to move to quantitative SPECT, it is not enough to be
 limited to the development of a methodology for calibrating SPECT systems for a particular radionuclide. There are problems without understanding and solving which it is impossible to talk about the diagnostic accuracy of the quantitative SPECT method. Such problems are edge artifacts that appear on
 the images of pathological foci, and the rule of stopping the iterative algorithm when the values of activity in the area of interest (pathological focus) that are closest to the true values are reached. A stopping
 criterion based on Pearson's modified chi-square test of goodness of fit is proposed. There is a significantly good correlation between the proposed stop criterion and the minimum RMS error of the image
 reconstruction. The results of simulation modeling with the aim of optimizing SPECT examinations of
 brain perfusion demonstrated the possibility of reducing the data recording time compared to the standard protocol by at least two times.
 Conclusion: The computer simulation method presented in this paper is a practical technology that
 contributes to the optimization and development of a quantitative SPECT method to achieve the best
 possible results in the imaging of pathological foci. Further development of the software package is focused on applications in radionuclide therapy and theranostics.

Determination of the Effective Electrical Conductivity of a Fluid–Saturated Core from Computed Tomography Data

Abstract—This paper proposes a technique for determining the effective specific electrical conductivity of rock samples when their digital models are used. A modified algorithm for reconstructing the internal structure of the sample from the core’s nondestructive imaging data can be used to construct a relevant discrete model that approximates the pore space with a high degree of accuracy. Unlike existing approaches, the reconstructed discrete geometric model of a heterogeneous medium sample is hierarchical and oriented to the application of parallel computational schemes of multiscale finite element methods for a forward mathematical simulation of electromagnetic processes. The paper presents the results of solving the problem of determining the effective specific electrical conductivity of fluid–saturated rock samples and compares them with the data from laboratory experiments.

ON THE DETERMINATION OF THE SPECIFIC HEAT FLUX VALUE IN A PULSE DETONATION ENGINE’S CHAMBER

Abstract. The development of detonation engines (DE) is one of the most promising areas of rocket and space engine manufacturing. They are more efficient as compared to the liquid rocket engines and are structurally simpler. At the same time, the detonation engine chamber’s structure is subjected to much higher thermal loads. Therefore, at the development stage of the DEs, to create an efficient cooling system for the engine’s chamber, it is necessary to be able to determine the value of thermal energy, which is absorbed by the walls of the DE’s chamber. The goal of this research is to determine the specific heat flux from the detonation products towards the walls of the pulse detonation engine’s (PDE) chamber. The task of the work is to establish the methodology for calculating the values of the specific heat flux transmitted to the walls of the PDE’s chamber. The main tools for solving this problem are the method of mathematical simulation using computational fluid dynamics (CFD), and the method of regression analysis. The main results of this study: the possibility to utilize the well-known Ievlev methodology to determine the convective specific heat flux for the PDE’s chamber was analyzed; it was shown that for the conditions of the PDE’s chamber, the Ievlev methodology calculation results differ significantly from the experimental data, which can be explained by the presence of a clearly pronounced non-stationary nature of the detonation process; it was proven the utilization of the Viegas formula to obtain the values of the convective specific heat flux for the PDE’s chamber gives better results as compared to the known experimental data and the results of the mathematical simulations; it was also demonstrated that the average integral value of the specific heat flux, determined by the described methodology, can be used to calculate the thermal state of the PDE's chamber. Conclusion: a methodology for calculation of the specific heat flux value for the pulse detonation engine's chamber was proposed. The obtained calculation results are in good agreement with the results of mathematical simulations and known experimental data. The described methodology can be used in the design of cooling systems for the pulse detonation engine’s chambers.

DEVELOPMENT OF AN APPLICATION FOR THE THERMAL PROCESSING OF OIL SLIME IN THE INDUSTRIAL OIL AND GAS SECTOR

The production activities of oil refineries and oil and gas-producing enterprises inevitably have an anthropogenic impact on the environment, so environmental issues and the rational use of natural resources are important. The most dangerous pollutants of all components in the natural environment are oil waste, and one of the most effective methods of processing is heat treatment. The task was set to neutralize oil waste by thermal processing of oil slime to an environmentally safe level. The studies are carried out by methods of mathematical and numerical simulation of thermal processing, the results of which describe changes in temperature and mass of the stream over time. Extensive calculations with varying current operating and other parameters allow us to optimize the flow of heat and mass transfer during the thermal processing of oil slime. Numerical modeling is implemented using the method of alternating directions in an implicit iterative scheme until a convergence condition is met. The purpose of this work is to create an application for solving research and practical problems of oil waste processing. The application used allows the solution of the problems of oil slime processing. With the help of color-animated illustrations and a graphical interface, it supports the visualization of the results obtained, and provides the possibility of interactive interaction with the user, while providing instant control of the results obtained for timely decision-making to prevent environmental pollution in the industrial oil gas sector.

Енергетичні витрати на переміщення об’єктів космічного сміття з низьких навколоземних орбіт на орбіти утилізації

The ever-increasing clogging of near-Earth space by space debris objects of various sizes significantly limits the possibilities of space activities and poses a great danger to the Earth’s objects. This is especially true for low orbits with altitudes up to 2,000 km. The risk of collision of operating spacecraft with space debris threatens their functioning in near-Earth space. To control space debris, use is made of active and passive methods of space debris removal from operational orbits. At present, promising means of space debris removal are a space debris transfer to low-Earth orbits with a lifetime of less than twenty-five years, a transfer to a junk obit, and in-orbit utilization. According to the latest recommendations, space debris objects moved to low-Earth orbits should have a lifetime of less than twenty-five years. In the dense atmosphere, small space debris objects usually burn up completely, while large ones burn up only partially and may reach the Earth. Since space debris motion in the atmosphere can only be predicted with large errors, a timely and accurate prediction of the place and time of fall of large space debris objects onto the Earth is impossible. Space debris objects can remain in junk orbits for hundreds of years without interfering with space projects. This method of space debris removal reduces the risk of collision with space debris objects in the initial orbit, but increases it in the junk one. According to the concept of in-orbit utilization, space debris is considered a resource for the in-orbit industry. An active space debris removal involves high energy expenditures of service spacecraft. In this regard, the task of their estimation becomes important. The goal of this paper is a comparative assessment of the energy expenditures for moving space debris objects into utilization orbits using service spacecraft with electrojet propulsion systems. The problem is solved using methods of flight dynamics, averaging, and mathematical simulation. The novelty of the obtained results lies in the development of a ballistic scheme and a fast procedure to calculate energy expenditures for moving space debris objects to a disposal orbit using service spacecraft with constant low-thrust electrojet propulsion system. The procedure may be used in substantiating and planning space debris transfer from low-eccentricity low-Earth orbits to utilization orbits.

Location and turbine parameter selection for offshore wind power maximization

Offshore wind turbines can capture more wind than onshore because of their larger structure and location. This higher yield even fails to reduce the high installation and maintenance cost of an offshore wind farm (OWF). Appropriate turbine parameters and installation site selection may maximize the power generation which is a way to trade off these costs. Knowing the wind thrust force, air density, and power coefficient beforehand can help select an appropriate site for turbine location. Once the site is selected, the optimal value of turbine variables such as height and radius can contribute to higher power yield. In this paper, a MINLP (Mixed Integer Non-Linear Programing) model is formulated with these important variables and the optimal values of these variables are determined to maximize the annual power production ([Formula: see text]) from offshore wind farm. The estimated power production, [Formula: see text], is calculated using two methods, mathematical programing method and simulation method. Computational result indicates that mathematical programing method is time consuming but more accurate whereas the accuracy of simulation method is proportional to the number of iterations. Although the result of a simulation can be improved to some extent, it cannot be as accurate as mathematical modeling for this study. These study results have great impact on the managerial decision and long range strategic and technical planning for maximizing power generation from an offshore wind farm.

Методика проведення чисельного дослідження камери імпульсного детонаційного двигуна

The subject of research in this article is the process of detonation propagation in the chamber of a pulse detonation engine. Experimental research on detonation engines is a complex and expensive process that requires high-speed, high-precision equipment to obtain high-quality reliable results. Therefore, to conduct preliminary research, numerical experiment methods using mathematical simulation tools should be used. This work analyzes the possibility of applying known calculation models to study the detonation propagation process in the chamber of a pulse detonation engine. The task: to study the influence of the application of existing calculation models on the accuracy of numerical simulation of the detonation process; analyze the use of existing calculation models for the study of the detonation propagation process. The main method used in this work is the method of mathematical simulation using CFD technologies. The following results were obtained. The work considered the application of various turbulence models, chemical transition models, solvers and mesh sizes in modeling processes in the chamber of a pulse detonation engine. The application k-ε and k-ω turbulence models and their modifications are considered. The closest to the real result is obtained when applying k-ω model turbulence with SST modification. Generalized modification of this model averages the parameters on the front of the detonation wave, which leads to the destruction of the structure of the front. Taking into account the peculiarities of the processes occurring at the front of the detonation wave, the eddy-dissipation concept method will be better for modeling chemical transition, compared to the finite-rate method. Using the finite-rate method shows instantaneous combustion at the front of the detonation wave. This leads to a sharp increase in the parameters at the detonation front with its further separation from the main flow. To obtain a qualitatively reliable result of the parameters at the front of the detonation wave, cell dimensions of no more than 1/16 mm should be used. The application of the eddy-dissipation concept method with k-ω SST turbulence model allows obtaining the closest results to the experimental data. The deviation of pressure and velocity values obtained during modeling does not exceed 5% from their actual values. The temperature deviation does not exceed 10%. This is determined by the selected kinetic scheme of chemical transitions. All considered models and methods affect only the structure and development of the detonation wave front. There are no significant differences in the values of the parameters along the front (in the Taylor zone). Conclusion. The obtained results are of practical importance for the design and research of detonation engines. The use of the proposed calculation models will allow conducting numerical experiments for the pulse detonation engine chamber with sufficient accuracy, in comparison with experimental data.

Environmental Impact Assessment of a Wharf Oil Spill Emergency on a River Water Source

In recent years, there have been frequent water pollution emergencies, which seriously threaten the environment of water supply sources and affect the safety and quality of the water supply. These emergencies have aroused concern from the public and the government and highlight the necessity of plans for the emergency treatment of the affected water sources. In this paper, a sudden pollution of a river drinking water source is used as the research object. A mathematical simulation method was used to investigate the water quality near and downstream of a wharf in the state of a sudden oil spill. The wharf is located 1.34 km upstream of the water intake position of this river water source. Based on our investigation, we have established a risk assessment method for an oil spill emergency pollution event. Our aim was to provide a basis for the assessment of the water intake quality and water safety status of a river-based water plant and to provide technical support for developing an effective treatment plan in the event of a sudden environmental pollution accident.

The aircraft hydraulic system units and pipelines heat exchange parameters study

A method of mathematical simulation of the aircraft hydraulic system thermal state is proposed. The mathematical model is a system of partial differential equations for carbon-fiber composite thermal insulation and ordinary differential equations for hydraulic system elements that describe their heat exchange with the air and surrounding surfaces. To solve the direct problem of the hydraulic system elements thermal state, that is, to solve stiff ordinary differential equations, a Rosenbrock-type second order approximation numerical scheme for non-autonomous systems and the solution of a system of partial differential equations, the Monte Carlo method based on a probabilistic representation of the solution in the form of a diffusion process functional expectation were used. The inverse problem of the hydraulic system elements thermal state is solved by the composition of the steepest descent method, the Newton method and the quasi-Newton method of Broyden-Fletcher-Goldfarb-Shanno. A thermal state mathematical model of the hydraulic system unit in an aircraft unpressurized compartment has been developed and the confidence intervals of each of the required model coefficients have been estimated using 12 at a confidence probability = 0.95.

Estimation of the thermophysical properties of heat-protective composite materials

The paper proposes a mathematical simulation method for identifying thermophysical properties using a developed software package based on a composite material model presented as a combination of plates of alternating heterogeneous components, fiber material and air, oriented parallel and perpendicular to the heat flux. The effect of the orientation angle of the fibers and their volume content on the effective thermal conductivity has been determined.

INCREASING THE SPEED OF FREIGHT TRANSPORTATION BY MEANS OF OPTIMIZATION

The article considers increasing the speed of freight delivery by rail using the existing capacity, infrastructure and resources. Possible options and technologies to speed up the delivery of freight are analyzed on the basis of experience of other countries. A mathematical solution to the optimization problem is proposed – achieving a certain level of service with minimal costs associated with the downtime of handling facilities. The purpose of the study is to determine to what extent such characteristics as transit time, queueing time for loading of goods, etc., can change during the transition from conventional freight transportation to high-speed one. Mathematical simulation methods were used to estimate the change in the characteristics of freight transportation when the speed increases. Freight transportation was considered as a mathematical queuing system (QS). Accordingly, the characteristics of two QSs with the same intensity of the order workflow and different intensities of the service workflow at a service are compared. That is, the characteristics of movement of freight trains in the transition from regular traffic to high-speed traffic are compared. The formulas proposed in the paper will allow to study the dependence of the number of freight trains and the downtime of handling facilities on the intensity of the service workflow, i.e. on the speed of movement. It will also allow to determine intensity of a service workflow which is necessary to achieve the given average time which an order stays in system, i.e. to find the speed of freight traffic required to achieve the given average trip time. Conducting this research will allow to conclude about advantages or disadvantages of transportation by high-speed freight trains in comparison with conventional freight trains and expediency of their introduction on certain sites.