Analysis Of Mathematical Model Research Articles

Control Method of HTS Permanent Magnet Synchronous Machine With a Nonlinear Disturbance Observer

The high temperature superconducting (HTS) permanent magnet synchronous machine (HTS-PMSM) uses the HTS armature winding instead of the copper armature winding, having higher torque density and higher efficiency and showing a great application prospect. Although the mathematical analysis model of the HTS-PMSM is similar as that of the conventional PMSM with the copper armature winding, as the load current increases, the stator core of the HTS-PMSM is more likely to be saturated, the inductance of quadrature-axis and direct-axis will be reduced. That leads that the power density and overload capacity of the HTS-PMSM will be affected, the control performance of the controller will be reduced as well. In order to solve the problem of the great change of the inductance values with the load variation, this paper proposes a nonlinear disturbance observer (NDOB) to estimate the disturbance of inductance parameter caused by the core saturation of the HTS-PMSM and builds a compensation strategy, combining with robust sliding mode control (SMC) to improve the stability of the speed and torque of the HTS-PMSM. The effectiveness of the proposed control method is verified by the combination method of the finite element analysis and Matlab/Simulink simulation.

Research on stress curve clustering algorithm of Fiber Bragg grating sensor

The global stress distribution and state parameter analysis of the building's main structure is an urgent problem to be solved in the online state assessment technology of building structure health. In this paper, a stress curve clustering algorithm of fiber Bragg grating stress sensor based on density clustering algorithm is proposed. To solve the problem of large dimension and sparse sample space of sensor stress curve, the distance between samples is measured based on improved cosine similarity. Aiming at the problem of low efficiency and poor effect of traditional clustering algorithm, density clustering algorithm based on mutual nearest neighbor is used to cluster. Finally, the classification of the daily stress load characteristics of the sensor is realized, which provides a basis for constructing the mathematical analysis model of building health. The experimental results show that the stress curve clustering method proposed in this paper is better than the latest clustering algorithms such as HDBSCAN, CBKM, K-mean++,FINCH and NPIR, and is suitable for the feature classification of stress curves of fiber Bragg grating sensors.

Air valve arrangement criteria for preventing secondary pipe bursts in long-distance gravitational water supply systems

Abstract Pipe burst incidents in long-distance gravitational water supply systems (LGWSSs) result in hydraulic characteristic variations and pose significant challenges. This study aims to prevent secondary pipe bursts by addressing the propagation of water hammer waves triggered by primary pipe bursts. Based on an analysis of pipe burst incidents and considering different pipe laying methods, air valve arrangement criteria are developed to mitigate the risk of secondary bursts in LGWSS pipelines. The principal results include a reasonable mathematical analysis model for understanding pipe bursts and the determination of air valve arrangement criteria which considers potentially dangerous pressure variations resulting from primary pipe bursts. This model aims to mitigate the adverse effects of pipe bursts and minimize the likelihood of secondary bursts. Implementing the proposed criteria has important engineering applications, thus improving the reasonable and effective placement of air valves to prevent secondary pipe bursts in LGWSSs. The conclusion involves optimizing the placement of air valves to enhance the flexibility and reliability of LGWSSs. By implementing the proposed air valve arrangement criteria, water supply systems can minimize the potential damage caused by pipe bursts and improve overall operational efficiency.

Nonlinear dynamic analysis and vibration suppression on the composite laminated plates with general boundary conditions in supersonic airflow

This paper performs the nonlinear dynamic analysis and vibration reduction of the panel structures subjected to supersonic airflow. The negative capacitance piezoelectric shunt damping circuit (PSDC) which contains bonded piezoelectric element and external negative capacitance is adopted. Based on the modified Ritz approach and energy approach, the formulations of the nonlinear panel structure with attached piezoelectric element are derived. A unified mathematical model for the nonlinear dynamic analysis of composite panels subjected to general edge boundaries in supersonic airflow is formulated. Furthermore, the Newmark approach and Newton iteration approach are utilized to calculate time domain responses of panel structures under aerodynamic pressure. Several numerical cases are further performed to verify the present formulations. Finally, impacts of several factors on the flutter characteristics of panel structures are investigated and the comparisons concerning the vibration responses of panels having and without PSDC are performed to verify vibration reduction properties of the present method. The numerical results show that the vibration and flutter of panels in supersonic airflow can be sufficiently suppressed by the present simple vibration reduction strategy.

A Mathematical Model and Results of Analysis of Nonlinear Diffraction of Electromagnetic Waves by Magnetic Nanogratings

A Mathematical Model and Results of Analysis of Nonlinear Diffraction of Electromagnetic Waves by Magnetic Nanogratings

Three-dimensional modelling of blur property for conventional optical microscopes

Intensity diffusion caused by optical diffraction limits the imaging resolution of conventional optical microscopes, therefore modelling and measuring the intensity transmission and distribution property of the light sources is a significant research topic in system development and pattern recognition. However, the complicated wave propagation process in optical imaging makes it difficult to provide a direct, analytical and simple mathematical model to measure the relationship between the blur degree and various camera parameters. In this study, an improved intensity transmission and distribution calculation method for conventional optical microscopes was proposed; furthermore, a simple mathematical relation between the blur degree and camera parameters was achieved based on the proposed method. First, the light intensity distribution and propagation characteristics of a conventional optical microscope were modeled based on the property of the Fresnel circular hole diffraction combined with the practical optical parameters. Second, by analyzing the property of intensity distribution and blurring imaging, a quantitative simplified mathematical relationship between the blur degree and camera parameters in optical microscope imaging was obtained, and the three-dimensional (3D) blur property in the optical imaging process was analyzed under different conditions. Third, the connection between diffractive optics and geometric optics was obtained by summarizing and generalizing the 3D blur property curve of each monochromatic light source. Finally, the proposed method was verified through a series of simulations and experiments.

Unsteady incompressible laminar boundary layer: time and space variable molecular viscosity

The subject of this work is two approaches to describe the laminar unsteady flow of an incompressible fluid in the boundary layer. In the first approach, the viscosity of the fluid and the acceleration with which the plane is set in motion are considered constant. In essence, this is Rayleigh's problem. The solution obtained on the basis of these assumptions asymptotically converges to the well-known self-similar Stokes solution. It is important that the solutions of Stokes and Rayleigh asymptotically at large values of time correspond to the disappearance of shear stresses between the liquid and moving plane after acceleration. A paradox emerges the equations derived by Stokes to describe internal friction indicate the absence of the same friction between a moving body and fluid. Since research using the calculus of variation methods revealed that the molecular viscosity inside the stationary boundary layer should depend on the distance to the moving surface, the corresponding non-steady problem was considered. As a result, as before for the steady case, solutions describing both non-gradient and gradient flows of incompressible fluid in the boundary layer are obtained. The asymptotic analysis of the transition to steady flow testifies the consistency of these solutions. For the case of non-gradient flow, a comparison of the classical solution with the solution corresponding to the extreme fluid flow rate carried by the moving surface is made. It is shown that according to the solution obtained on the basis of the calculus of variation approach, the shear stress on the surface does not disappear anywhere after the motion becomes steady but, as expected, acquires a constant value. The research methods are purely theoretical and the results are analyzed by comparison with available theoretical and experimental data and compliance with the fundamental laws of physics, in particular the law of conservation of energy. These methods are based on the construction of analytical mathematical models, which are differential equations in partial derivatives supplemented with appropriate physical initial and boundary conditions. In addition, Euler's differential equations for the extreme of functional theory are used (in this paper, this is the extreme of fluid flow rate across the cross-section of the boundary layer). When solving these equations, the well-known Fourier method of variable separation is used. Arbitrary functions of time arising during partial integration (by one of the variables – the spatial coordinate) are determined from the conditions of asymptotic convergence of the solutions of non-steady problems to the corresponding solutions of steady problems. Conclusions. The presented results are of fundamental importance for understanding the physics of the flow around aircraft parts, as they indicate the contradiction of the existing idea of the reversibility of direct and inverse problems: the motion of a body in a still fluid and the flow of a fluid around an immobile body.

FORECASTING VOLUMES OF ACCUMULATED WASTE

Problem statement. The task of assessing the volume of accumulated waste in the territory of the Dnipropetrovsk region, which is constantly increasing, occupying a larger area and causing damage to the environment, is under consideration. To solve this forecasting problem, it is necessary to create a regression mathematical model for statistical evaluation and analysis of the factor variables’ influence to the total volume of accumulated waste. The purpose of the article. Creation of a mathematical model for forecasting assessment of possible volumes of accumulated waste in the territory of the Dnipropetrovsk region by adjusting the volumes of factor variables. Methodology. Analysis of the dynamics of changes in the volumes of generated, utilized, incinerated, removed waste and capital investments and costs for waste management and establishment of trends in their changes based on descriptive statistics. Application of correlation analysis methods to establish the most statistically significant relationships between factor variables and the resulting feature. The use of regression analysis methods to obtain the coefficients of the regression mathematical model and statistical indicators that explain the probability of the significance of these coefficients. Scientific novelty. A multiple regression mathematical model was developed, which takes into account the factor variables affecting the process of waste accumulation in the territory of the Dnipropetrovsk region. Practical value. The developed regression mathematical model makes it possible to estimate the required amount of investment and forecast the amount of current costs to adjust the total amount of accumulated waste. Conclusions. A mathematical model was created to analyze the volume of accumulated waste in the territory of the Dnipropetrovsk region. Based on this model, the volumes of accumulated waste were calculated. The average value of the relative error of the calculated data is 1.03 %, while the maximum value of the error is 1.97 %, which confirms the adequacy of the developed mathematical model.

THE PROGRAM FOR ASSESSING THE CONNECTIVITY OF NODES OF WIRELESS EPISODIC NETWORKS UNDER THE CONDITION OF USING UAVS

Background. Based on analytical mathematical models, the duration of connectivity of mobile subscribers (nodes) (MS) of a wireless episodic network (WEN, consisting of MS and UAV) was investigated in conditions of direct radio visibility and considering the relaying.
 Objective. The purpose of the work is to find methodological approaches to ensure the connectivity of WSN nodes, which is a necessary condition for obtaining information from WSN in the absence of communication infrastructure.Methods. Simulation modelling based on MAPLE 14 software package and analytical calculation methods are used.
 Results. It is shown that the duration of connectivity is directly proportional to the size of the coverage area and inversely proportional to the movement speed of nodes. The mobility nature (scenario) of nodes also affects the duration of connectivity. The simulation of the nodes' movement was carried out under 4 scenarios: "march", "incoherent", "random wandering in the field" and "random wandering in the city". The largest values of the connectivity duration correspond to the third scenario, and the smallest - to the second (with a fixed radius of the coverage area and the movement speed of nodes). Thus, the average connectivity duration of the UAV-pedestrian connection in the event of an "incoherent" will be about 36 minutes, and the UAV-car connection - about 5 minutes.
 Conclusions. The system and functional parameters of the networks, which were obtained as a result of the research, will form the basis of the initial data and limitations of the mathematical model, and will also make it possible to determine the initial placement of the UAV network at the planning stage.

ЕЛЕКТРОМАГНІТНІ МОМЕНТИ УПРАВЛІННЯ ПРЕЦЕСІЙНИМ РУХОМ ТРИСТУПЕНЕВОЇ ЕЛЕКТРИЧНОЇ МАШИНИ

The main known structures and principles of functioning of electric machines with three degrees of freedom of rotational motion of the rotor are considered. The type of such machines in which it is possible to realize a high frequency of the rotor rotation is highlighted, which gives it the property of gyro-stabilization. The structure of the magnetic system of the machine of this type is presented and a hypothesis is put forward about the adequacy of the expressions of the classical analytical mathematical model, but the need for accurate calculation of the concentrated parameters that make up it. The distribution of magnetic flux density is analyzed based on a numerical mathematical model of a three-dimensional mag-netic field. The dependences of electromagnetic torque components and flux linkages on the rotor axis orientation and the angle of its rotation are calculated. It was concluded that the classical analytical mathematical model are adequate pro-vided that the calculating of its coefficients is based on the results of the modeling of three-dimensional magnetic field in the machine active volume and the surrounding space. It is underlined that, the amplitude of the flux linkage vector of the control winding and the fluctuations of the vector components to use in lumped parameter model must be calculated from the corresponding values of the electromagnetic torque components. Taking into account the results of the analysis of the three-dimensional field demonstrates a significant decrease in the speed of controlled precession and an increase in the amplitude of nutation. References 9, figures 10, tables 2.

Fractional study of radiative Brinkman-type nanofluid flow across a vertical plate with the effect of Lorentz force and Newtonian heating

Contaminant removal from water is accomplished using a variety of technologies, with adsorption being the simplest, successful, cost-effective, and long-term solution. Nanocomposites made from clay minerals and polymers have developed as a new method for cleaning contaminated water in recent years. Therefore, in this paper, clay-based water nanoliquid has been analyzed across a vertical sheet. For flow analysis, Brinkman-type fluid model has been considered along with the consequences of first-order chemical reaction and heat generation/heat absorption. Conditions for Slippage velocity and Newtonian heating also have been taken into account. Using relative constitutive equations, a mathematical model for the flow analysis has been formulated in terms of coupled partial differential equations and then generalized by using constant proportional caputo fractional derivative. The fractional Laplace transform approach was used to solve the problem for exact analytical solutions. The physics of several essential flow constraints vs velocity, thermal energy, and concentration propagation have been addressed graphically using the exact solutions. To check the validity and correctness, the obtained solution is evaluated with the published work. It is worth mentioning that the heat transition rate in the fluid increases by 8.7671% by the accumulation of clay nanoparticulates, while the rate of mass transmission increases by 11.830%.

Spectral characteristics of an open resonator with a plasma cylinder

Statement of the problem. Approximate models of open structures with plasma inclusion describe the spectral characteristics of such electrodynamic objects rather roughly. In this regard, it is of interest to study them on the basis of a rigorous model in order to clarify the features of their behavior on various geometric and electrodynamic parameters. Objective. To propose a methodology for modeling the spectral and diffraction characteristics of open resonators containing inhomogeneous inclusions, allowing a unified approach to the study of their electrodynamic characteristics. Results. Analytical physical and mathematical models of the spectral characteristics of the resonator based on the calculation of the matrix operator function in the case of an inhomogeneous dielectric inclusion are presented. Practical significance. It is of great interest for various areas of plasma physics and biophysics to study the spectral and diffraction characteristics of the open resonators containing various inhomogeneous inclusions, the material parameters of which depend on spatial coordinates or on the frequency parameters of the structure. The results obtained can be used in the study of the properties of such objects.

QMC-consistent static spin and density local field factors for the uniform electron gas

Analytic mathematical models for the static spin (${G}_{\ensuremath{-}}$) and density (${G}_{+}$) local field factors for the uniform electron gas (UEG) as functions of wave vector and density are presented. These models closely fit recent quantum Monte Carlo (QMC) data and satisfy exact asymptotic limits. A simple functional form for ${G}_{\ensuremath{-}}$ is developed; the same functional form parametrized for ${G}_{+}$ yields an improvement over previous work. The QMC-computed ${G}_{\ifmmode\pm\else\textpm\fi{}}$ are consistent with a rapid crossover between theoretically derived small-$q$ and large-$q$ expansions of ${G}_{\ifmmode\pm\else\textpm\fi{}}$. These expansions are completely determined by ${r}_{\mathrm{s}}$, the UEG correlation energy per electron, and the UEG on-top pair distribution function. We demonstrate their utility by computing uniform electron gas correlation energies over a range of densities. These models, which hold over an extremely wide range of densities, are recommended for use in practical time-dependent density functional theory calculations of simple metallic systems. A revised model of the spin susceptibility enhancement is developed that fits QMC data, and does not show a ferromagnetic instability at low density.

Review of linear and nonlinear models in breath analysis by Cyranose 320

Analysis of volatile organic compounds (VOCs) in breath specimens has potential for point of care (POC) screening due to ease of sample collection. While the electronic nose (e-nose) is a standard VOC measure across a wide range of industries, it has not been adopted for POC screening in healthcare. One limitation of the e-nose is the absence of mathematical models of data analysis that yield easily interpreted findings at POC. The purposes of this review were to (1) examine the sensitivity/specificity results from studies that analyzed breath smellprints using the Cyranose 320, a widely used commercial e-nose, and (2) determine whether linear or nonlinear mathematical models are superior for analyzing Cyranose 320 breath smellprints. This systematic review was conducted according to the guidelines of the Preferred Reporting Items for Systematic Review and Meta-Analyses using keywords related to e-nose and breath. Twenty-two articles met the eligibility criteria. Two studies used a linear model while the rest used nonlinear models. The two studies that used a linear model had a smaller range for mean of sensitivity and higher mean (71.0%–96.0%; M = 83.5%) compared to the studies that used nonlinear models (46.9%–100%; M = 77.0%). Additionally, studies that used linear models had a smaller range for mean of specificity and higher mean (83.0%–91.5%; M = 87.2%) compared to studies that used nonlinear models (56.9%–94.0%; M = 76.9%). Linear models achieved smaller ranges for means of sensitivity and specificity compared to nonlinear models supporting additional investigations of their use for POC testing. Because our findings were derived from studies of heterogenous medical conditions, it is not known if they generalize to specific diagnoses.

Modeling and Simulation of a TFET-Based Label-Free Biosensor with Enhanced Sensitivity

This study discusses the use of a triple material gate (TMG) junctionless tunnel field-effect transistor (JLTFET) as a biosensor to identify different protein molecules. Among the plethora of existing types of biosensors, FET/TFET-based devices are fully compatible with conventional integrated circuits. JLTFETs are preferred over TFETs and JLFETs because of their ease of fabrication and superior biosensing performance. Biomolecules are trapped by cavities etched across the gates. An analytical mathematical model of a TMG asymmetrical hetero-dielectric JLTFET biosensor is derived here for the first time. The TCAD simulator is used to examine the performance of a dielectrically modulated label-free biosensor. The voltage and current sensitivity of the device and the effects of the cavity size, bioanalyte electric charge, fill factor, and location on the performance of the biosensor are also investigated. The relative current sensitivity of the biosensor is found to be about 1013. Besides showing an enhanced sensitivity compared with other FET- and TFET-based biosensors, the device proves itself convenient for low-power applications, thus opening up numerous directions for future research and applications.

Development of economic and mathematical models of dynamics and analysis of insurance markets in the regions of the Volga federal district

: Insurance is an integral part of the financial system of any state. As of October 1, 2022, there were 143 insurance companies, 57 insurance brokers and 19 mutual insurance companies operating in the Russian Federation. The insurance market of the Russian Federation is characterized by the dominance of large insurers with an extensive network throughout the country. Regional insurance companies are represented by a small number of organizations due to the high requirements for insurers and the difficulty of competing with the leaders of the insurance market. The insurance market of the state and individual territories has developed gradually in an evolutionary way under the influence of market mechanisms and regulatory documents that establish requirements for insurance companies. The regions of the Volga Federal District, which are the object of analysis of this article, are diverse in terms of territorial location, GRP volume and its structure, and differ in dominant sectors of the economy. The analysis of insurance markets presented in the article revealed a stable composition of regions leading in terms of collected insurance premiums. In the regions of the Volga Federal District, there are no significant differences in the structure of collected insurance premiums by type of insurance, which indicates that there is no direct dependence of demand for insurance services on the GRP structure. The leaders of the insurance markets in the regions under consideration have been identified the TOP 5 insurers are companies registered in Moscow. Among the leaders are such companies as JSC Sogaz, PJSC IC Rosgosstrakh, CAO VSK, LLC IC Sberbank Life Insurance, SPAO Ingosstrakh, JSC Alfa Insurance. The competitive advantages of large insurance companies allow them to occupy more than 50% of the regional insurance market. The concentration of the markets of the VFD regions, estimated using the Herfindahl-Hirschman index, ranges from 0.235 to 0.367, which indicates a high concentration of markets. The dynamics of collected insurance premiums in the analyzed regions has a different growth rate for the period under review from 2004 to 2020 and is described using exponential and linear trend functions. The analysis of the unprofitability of the insurance markets of the regions made it possible to determine the most unattractive for insurers, as well as to identify differences in the unprofitability of various types of insurance in the regions of the Volga federal district.

Explicit three-piece quadratic model for accurate analytic representation of S-shaped solar cell current–voltage characteristics

Some interest has been recently directed towards analytic mathematical models for reproducing the current–voltage (I–V) characteristics of solar cells, mainly due to their convenient property of expressing current as an explicit function of voltage (which is not true for the traditional one-diode model). However, as is the case with the one-diode model itself, existing analytic models do not yield a good fit in the case of S-shaped I–V characteristics. In this brief paper, an analytic explicit model based on a three-piece quadratic curve is proposed that surpasses such difficulty and enables accurate representation of S-shaped curves. To evaluate the proposed model, validation was carried out against three empirical solar cell I–V characteristics. In all cases, simulation results show that the proposed approach is more accurate than other closed-form models in the literature.

146 Development of a Mathematical Model for Cost Calculation and Sustainability Analysis of Beef Cattle Grazing Systems

Abstract A mathematical model to estimate: a) the cost of beef cattle production in grazing systems; and b) the environmental sustainability of production systems using the Emergy Synthesis Model was evaluated. All items were considered and allocated, according to the precepts of the Economic Theory, under Fixed Cost (FC), Variable Cost (VC), and Total Cost (TC). The model estimated costs in the case-study for the entire property and the different production lots within the same property. Costs were allocated per animal and per kg of beef cattle produced. The total cost per animal of cattle produced was US$ 416.86. It was observed that the VC represented 66% of the TC. The cattle purchase price, including under VC, was the factor that represented the most significant portion of the production cost, in which the current operation reached 59% of the TC. Therefore, the currently developed tool may be used to facilitate understanding and potentially help to manage risk and profit. To examine from the environmental point of view, the synthesis of emergy was utilized. Emergy is the memory of the available energy used directly and indirectly to produce a service or product. It was observed that the property considered in the current case-study showed a renewability of 47.6%, indicating that less than one-half of all the energy used came from renewable resources. The emergetic yield ratio (EYR), which measures how much natural energy was incorporated into produced goods or services, was 1.91. The survey showed that the emergetic exchange ratio (EER), which indicates how balanced the exchange ratio between the energy in products and the energy gross revenue, was 12.45, showing that the system delivers much more energy than it receives in a monetary form. It seems like the current system analysis was highly dependent on cost-effective resources. The fuel used for pasture management services was the non-renewable resource that mostly affected the design. For the emergy synthesis, such input represented 51.2% of the total energy used, but from the economic point of view, such resource represented only 1% of the total production cost. The system could be less dependent on market variability if good pasture management practices were adopted, such as using a reasonable pasture stocking rate. By using the emergy indexes, it was possible to analyze the cattle system from an environmental perspective, allowing to assist technology/technique adoptions capable of increasing the sustainability indicators, which has been recently valued by worldwide beef consumers.

Аналитическая модель малых колебаний сжимаемой магмы с реологией Максвелла в питающей системе вулкана. Часть 1. Осцилляции плотности

The analytical mathematical model is presented that describes one of the possible mechanisms for the occurrence of long-period seismic events that are often recorded near active volcanic centers. The feeding system of the volcano is modeled in the simplest form of a cylindrical channel filled with a compressible magmatic melt with the rheology of a Maxwell body. It is shown that such a magmatic body can experience harmonic damped oscillations, the damping coefficient of which is determined by the relaxation time of the magmatic melt. These fluctuations may appear as a response to a density perturbation caused by the influx of denser magma from deep layers or a change in pressure in the supply system of the volcano. The dependence of the natural oscillatory frequency on the physical characteristics of the magmatic melt and the geometric dimensions of the feed channel is shown. When the compressibility of the magmatic melt is taken into account, density perturbations depend on the size of the feeding system and are characterized by periodic oscillations, which are most pronounced near the channel axis. Oscillations are also experienced by the flow velocity component directed along the radius of the cylinder. The source mechanism of the long-period seismic events is discussed. The model is used to describe long-period oscillations recorded near Santiaguito (Guatemala).

APPLICATION OF TRANSPORT MODELING IN URBAN PLANNING USING THE EXAMPLE OF VINNYTSIA

The issues of using transportation modeling for decision-making in urban planning are discussed using the example of Vinnytsia. Macro-simulation allows for analyzing overall traffic flow without reproducing the movement of individual vehicles in detail. It enables a quick evaluation of different scenarios for the development of the transportation network and determining the effectiveness of road traffic management strategies. The transportation model of the city enables analyzing the load on the road network in the current state and predicting this parameter for scenarios of implementing new infrastructure projects. Examples of load maps for the road network of Vinnytsia and an individual transport hub are shown from the transportation model of the city. Micro-modeling is the process of creating a mathematical model for a detailed analysis of vehicle movement in small areas (intersections, street sections, enterprise areas, etc.). An example of micro-modeling results for one intersection is presented. The application of micro-modeling in evaluating changes to the transportation network is an effective tool that allows municipalities to avoid inefficient use of funds and transportation mistakes that worsen traffic conditions. A list of tasks for micro and macro-modeling is analyzed. The main advantages and disadvantages of modeling and the risks that may arise from its use are described. The importance of the transportation model of the city is shown in both strategic and tactical approaches.