An example of simulation modeling of the process of functioning of a hydraulic system. What are simulation models? The concept of model time. Discrete and continuous simulation models

Imitation technologies are based on the construction various examples real systems that meet the professional context of a certain situation. Simulation models are compiled that meet the requirements of the given moment, and the trained subject is immersed in working with them. The simulation and simulation-game modeling existing in the methods is accompanied by the reproduction of fairly adequate processes occurring in reality. Thus, training makes it possible to form a real professional experience, despite the quasi- professional activity.

Roles

In the learning process, game procedures are assumed that offer built-up simulation models, which means that the distribution of roles is also provided: students communicate with each other and with the teacher, imitating professional activities. Therefore, simulation technologies are divided into two parts - gaming and non-gaming, and an analysis of the proposed situation helps determine the type. To do this, it is necessary to clarify the system of external conditions that encourage the initiation of active actions. That is, all problems, phenomena, interrelated facts that characterize the situation must be accommodated by simulation models.

A certain event or a specific period of an organization’s activity requires the manager to make adequate orders, decisions and actions. Study Analysis Methodology specific situations- detailed and in-depth study of a real situation or an artificially created one, identifying characteristic properties. This contributes to the development of students in search systematic approach to solving a problem, identifying options for erroneous solutions, analyzing criteria for optimal solutions. This is how professional business contacts are established, decisions are made collectively, and conflicts are eliminated.

Situations

Situations are distinguished into four types: first, a problem situation is considered, where students have to find the causes, pose and resolve the problem, then the situation is subject to evaluation based on the decisions made. After this, a situation is built that illustrates with examples all the stated topics of this course, and the just solved problems are taken as a basis, and the topic ends with a situation-exercise, where simulation models solve simple problems using the analogy method - these are the so-called training situations.

Specific types of situations are different: these are classic and live, an incident situation, a situation with the analysis of business correspondence, as well as actions according to instructions. The choice is determined by many factors: the goals of the study, the level of training, the availability of technical means and illustrative material - everything depends on the individual style of the teacher, whose creativity is not limited by strict regulation either in the choice of varieties or in the methods of analysis. Here are the first stages of developing simulation models.

Practical tasks

In practice, the ideas of the contextual approach are best embodied, because they consist of specific and real life situations: a case, a story, which contains a simulation model, an example of a description of events that took place or are quite possible, ending in errors in solving production problems. The task is to identify and analyze these errors when applying the ideas and concepts of this course.

Professional training of this type is quite realistic and effective in comparison with the formulation of individual issues that are considered purely theoretically. The orientation of situational learning is such that skills and knowledge are taught not as a subject, but as a means for solving various problems that arise in the activities of a specialist. Training situations are based on real professional production fragments, taking into account all interpersonal relationships, which is extremely important for successful work enterprises. Trainees receive the outline and context of future professional activity.

Selection of situations

This is one of the most difficult teaching tasks. An example learning situation usually meets the following requirements:

The script is based on reality or taken from life. This does not mean that it is necessary to submit a production fragment with numerous details and technological subtleties that will distract the student from solving the main problem. Manufacturing jargon in in this case also inappropriate.
The learning situation should not contain more than five to seven points, which are commented on by students using terms in line with the concept being studied. A simulation model whose example is difficult to solve is unlikely to teach students quickly.
But the learning situation should also be devoid of primitiveness: in addition to five to seven points of the problem being studied, there must be two or three connectives in the text. Usually, problems in life are not laid out on separate shelves for consistent resolution. Problems at work are usually associated with social or psychological problems. The application of course ideas is especially important in teaching.

Text of the educational situation

For example, a sales manager at the Lotus Flower company, specializing in hygiene products, cosmetics and perfumes. She came to this place due to a promotion six months ago. A conversation with the general manager based on the results of her work will take place in ten days.

Before this, Irina succeeded for two years in a separate section of the company, for example, selling hygiene products, and she liked it extremely. She was respected, popular among the sellers and gained many regular customers.

Development of the situation

Naturally, she was happy about the promotion and began to work enthusiastically in her new position. However, for some reason things did not go well. She did not have time to work in the office, because she was in the hall almost all the time and monitored the actions of the sellers. I even had to take work home. And still she didn’t have time to do anything: the management’s request to prepare ideas for the exhibition and sale was completed on the last day, because nothing interesting had been thought of beforehand; creativity is not such a simple matter. The sick typist was unable to retype the papers with Irina’s ideas. As a result, Irina did not complete the task by the deadline set by her superiors. It is at this moment that simulation learning models would help her most.

After that, everything went wrong. Having spent time talking with a regular client, Irina did not think about her speech when her colleague solemnly received a certificate, and was even late for the ceremony. Then several times her subordinates left their jobs without warning her. The HR department repeatedly reminded her of the need to draw up a training program on the use of medicinal cosmetics, but Irina was unable to contact the teacher from the medical institute. She was always late to introduce even junior salespeople to senior positions. And Irina has not yet prepared a quarterly report with the assortment forecast. And she didn’t even respond to several letters from customers who wanted to receive the goods by mail. And as icing on the cake, a recent quarrel with one of her previously very respected sellers regarding price tags. It turns out that being a good manager is not so easy.

Analysis of the situation

A simulation model is, first of all, a reading of the situation. Here the following picture emerges of six points with sub-points.

There have been changes at my new job. What are their restraining and motivating forces?
Before the changes - having self-esteem and knowledge of the sales mechanism.
Motivation in the desire to succeed, but also to maintain sales abilities - role conflict.
The management style is a complete inability to give part of the authority to subordinates. Clashes with subordinates cannot be avoided.
IN new role: did not determine the specifics of the position, the size of the workload, did not solve a simple problem with reprinting, skimps on planning and control, allows subordinates to fail to show up for work, disrupts the staff training plan, does not know how to organize their time and set priorities, loses creativity - there are no new ideas.
Management style of entrusted staff: allows vertical conflict, interferes in the affairs of subordinates, lacks self-confidence, leads without the help of management.

Identifying problems

The structure of simulation models assumes the second step is to identify emerging problems for their consistent solution. Here you need to follow the same points, taking into account the analysis performed, but considering the situation with a different goal.

Changes: are there ways to manage changes and which ones, how to reduce resistance to the changes that have occurred.
Leadership styles: why the style chosen by Irina is unsuccessful, and which one is better to abandon it in favor of.
Motivation: what management theory says regarding incentives for Irina and sellers.
Specifics of work goals: does Irina know all the details regarding new job what the goals were and how they should be achieved.
Planning and control: did Irina plan her actions as a manager, were they controlled?
Conflict: what is the reason and problem of the conflict that occurred and how it could be dealt with.

Thematic links

The use of simulation models helps to build a situation from its inception (motives), revealing the motives for its beginning, to the transition to a new quality. What it will be depends on how the analysis is carried out and what conclusions are drawn. No situation is complete without connecting themes. Most often, simulation models do not reproduce reality in all aspects, but several such connections must be present in the game. Here they are as follows.

Irina did not see any differences in the work of a manager and a salesperson.
Irina was ill-prepared for her new position.
Irina does not have fundamental knowledge about management.

Development of connecting motifs

What is possible and what must be done regarding connecting topics?

First of all, information transfer is necessary. Irina’s superiors are obliged to present her with specific job requirements immediately after her appointment. Irina must make her subordinates aware of her management style at work.
Secondly, it is necessary to train Irina in the basics of management, her subordinates in sales methods, and, of course, Irina and her subordinates must undergo training in interpersonal interaction.
Thirdly, clear planning is necessary functional responsibilities Irina as a manager and the activities of the entire department as a whole.
Fourthly, there must be proper personnel management: Irina needs help in determining goals and priorities both momentarily and long-term, that is, it makes sense for the HR department to plan advanced training for employees in whom the company is interested.

This whole topic is directly related only to the transfer of information.

When the game reaches the stage of summing up and drawing conclusions, it becomes clear what simulation models are and how they are useful. The conclusions are very accurate and specific for almost everyone, because the situation was analyzed down to the smallest detail.

Firstly, the manager must agree on the specifics of the work with his superiors and convey the results to his subordinates.
Secondly, all priorities and goals must be clear to the manager and also explained to the rest of the staff.

Irina needs to master management techniques in managing her own time, in control and planning, in managing people and any conflict, in circulating new information among the team and in its development.

Irina needs to find out in detail from the HR department about training procedures, as well as about advanced training of employees, in order to apply them as correctly as possible. She will have to improve her professional level on her own, and in the future, complete her studies. These recommendations can frighten an unprepared person, so you need to immediately divide them into three sections: immediate implementation, recommendations of medium urgency, and the last point - clearly long-term. It makes sense for Irina and her superiors to discuss the reasons for the failures and do everything to prevent them from happening again.

Having thus analyzed an artificially constructed situation, each student will understand what simulation models are.

Models of economic development

Socio-economic development has different simulation models from others. This required a separate name in order to specifically know the scope of application of this or that situational artificial construction. Dynamic simulation models are designed specifically to predict the operation of economic systems. The title emphasizes that dynamics are the most main characteristic such constructions, and they are based on the principles of system dynamics.

The stages of construction have the following sequence of actions: first, a cognitive structuring scheme is built, then statistical data is selected, and the scheme is refined. The next step is to form where cognitive connections are described, then the IDM is compiled as a whole. The model is debugged and verified, and finally, multivariate calculations are performed, including predictive ones.

Scripting method

Scenario analysis, which means a simulation model of a certain project, is needed in order to calculate the dangers on the way to the development of the project and ways to overcome them. The risk that threatens an investment can be expressed in the deviation of the cash flow intended for a given project, contrary to expectations, and the greater the deviation, the greater the risk. Each project demonstrates a possible range of project results, therefore, by giving them a probabilistic assessment, it is possible to evaluate cash flows, taking into account expert assessments of the probabilistic generation of all these flows or the magnitude of deviations of all flow components from the expected values.

The good thing is that on the basis of such expert assessments it is possible to construct at least three possible development situations: pessimistic, the most realistic (probable) and optimistic. Simulation models are the only difference from reality here - it is not the system itself that produces the action, but its model. Simulation models of systems come to the rescue in cases where conducting real experiments is at least unreasonable, and at maximum costly and dangerous. Simulation is a way to study systems without the slightest degree of risk. It is practically impossible, for example, to assess the risk of investment projects without simulations, where only forecast data on costs, sales volumes, prices and other components that determine risks are used.

The financial analysis

Models used to solve many problems facing financial analysis, contain random variables that cannot be controlled by decision makers. These are stochastic simulation models. Simulation allows one to infer possible outcomes based on probability distributions. random variables. Stochastic simulation is also often called the Monte Carlo method.

How are the risks of investment projects modeled? A series of numerous experiments are being conducted that purely empirically evaluate the degree of influence of various factors (that is, initial values) on the results that are entirely dependent on them. Conducting a simulation experiment is usually divided into certain stages.

By establishing relationships between the initial and final indicators in the form of a mathematical inequality or equation, the first step along the path of experimentation is taken. Then you need to give the machine laws that distribute probabilities for key parameters. Next, a computer simulation of all values of the main parameters of the model is carried out, and the characteristics of the distributions of the initial and final indicators are calculated. Finally, an analysis of the results produced by the computer is carried out, and a decision is made.

Designing any object is a multi-stage process that requires data analysis, systematization, construction and verification of results. Depending on the volume of work to be done and the difficulty of its implementation, either real tests or simulations are used. This simplifies the process, makes it less expensive, and also allows you to make adjustments and improvements already at the time of the experiment.

In this article we will talk about simulation math modeling systems - what they are, what models are obtained, where they find their application.

Features of the technology

Any work with models consists of two main stages:

development and creation of a sample;
its analytical analysis.

Then adjustments are made or the plan is approved. If necessary, you can repeat the procedure several times to achieve a flawless build.

Thus, this method can be called a visual knowledge of reality in miniature. There are objects that are expensive and labor-intensive to bring to reality in full size without precise confidence in the effectiveness of all structural elements, for example, spaceships or all uses of photoelastic aerodynamics simulation.

Creating an identical model repeating the features of the entire system helps to achieve not only a reflection of internal patterns, but also external acting forces, for example, air flows or water resistance.

The construction of copies of objects began with the advent of the first computers and at first was of a schematic nature; with the development of technology, it became increasingly developed and began to be used even in small industries because of its clarity.

Where, in what cases is the simulation method used and for what purpose?

the cost of the object is much higher than the cost of developing the model;
product activity is subject to great variability, there is a need to calculate all possible failures;
the design contains a large number of small parts;
it is important to see a visual example with an emphasis on appearance;
operation occurs in difficult-to-study environments - in air or water.

The application is due to the fact that it becomes possible:

calculate real values and coefficients of engineers’ activities;
see shortcomings, eliminate them, make adjustments;
see the operation of the facility in real time;
make a visual demonstration.

The simulation method is used for:

Designing real business processes.

Simulations of combat operations - mock-ups of real ammunition, shells, military equipment and targets. This is how the range of the shot, its destructive abilities and the radius of the affected area are analyzed, and the weapon is checked before being put into production.
Analysis of population dynamics.
Creation of an infrastructure project for a city or region.
An authentic depiction of historical reality.
Logistics.
Designing the movements of pedestrians and cars on the roadway.
The production process is in the form of an experimental method.
Analysts of the market and competing companies.
Car repair.
Enterprise management.
Recreating an ecosystem with flora and fauna.
Medical and scientific experiments.

We will consider the features of simulation modeling using the example of production work and design. But the variety of systems shows the need to apply the method in different areas of activity. This explores the characteristics of specific areas - what changes may occur, how to control them and what to do to prevent possible negative consequences.

All possibilities for creating a model are realized using a computer, but there are two main types of process:

Mathematical - it helps to develop a diagram physical phenomena with the specified parameters.
Simulations - their main task is to show the variability of behavior, so the initial data can be varied.

Both mathematical and computer simulation modeling are based on computer-aided design programs, so you need to take a responsible approach to choosing software. ZWSOFT company offers its products at low prices. – is an analogue of ACAD, but at the same time it becomes more popular over time than the old software. This is due to:

simplified licensing system;
acceptable pricing policy;
translation into Russian and adaptation for users of many countries;
a wide selection of add-ons and modules that are created for specific specialties and expand the basic functionality of ZWCAD.

Types of simulation

Agent-based. It is more often used to analyze complex systems, where changes are not determined by the action of certain laws, and therefore are not subject to prediction. Variability depends on agents – non-fixed elements. Often this variety is used in sciences such as sociology, biology, ecology.
Discrete-event. This method is used to isolate specific actions of interest from the general sequence of events. It is often used to manage the production cycle, when it is important to note only the result of certain areas of activity.
System dynamics. This is the main method for calculating cause-and-effect relationships and interactions. It is used in production processes and in the construction of models of a future product in order to analyze its characteristics in real life.

Basics of aerodynamic and hydrodynamic simulation modeling

The most labor-intensive to develop are objects that are manufactured for operation in conditions of high pressure, resistance, or are difficult to reach. They must be approached from the point of view of IM, mathematical schemes are created, the initial data are changed and the influence of various factors is checked, and the model is improved. If necessary, a three-dimensional model is created, which is immersed in a simulation of the real environment. Such objects include:

Structures that are submerged under water or are partially in a liquid, thereby experiencing the pressure of flows. For example, to model a submarine, it is necessary to calculate all the forces that will influence the hull, and then analyze how they will change with increasing speed and diving depth.
Objects designed to fly in the air or even escape the Earth's atmosphere. Artificial satellites, spaceships undergo multiple checks before launch, and engineers are not content with just computer visualization, but make a live model based on the data specified on the computer.

IM aerodynamics is often based on the method of photoelasticity - determining the effects of certain forces on matter due to the double refraction of rays in materials of an optical nature. This way you can determine the degree of stress and deformation of the walls. The same method can determine not only static effects, but also dynamic ones, that is, the consequences of explosions and shock waves.

The hydrodynamic model is specified manually with several parameters; all geological, biological, chemical and physical properties environment and object. Based on this data, a three-dimensional model is created. The initial and maximum limits of impact on the structure are set. Next, adaptation occurs to the conditions where the object is located and subsequent withdrawal final data.

This method is actively used in the mining industry and when drilling wells. This takes into account information about the ground, air and water springs, and possible layers unfavorable for work.

Model development

A reconstructed projection is a simplified version of a real object with preservation of characteristics, features, properties, as well as cause-and-effect relationships. It is the reaction to influences that usually becomes the most important element of study. The concept of “simulation modeling” involves three stages of working with the model:

Its construction after a thorough analysis of the natural system, transfer of all characteristics into mathematical formulas, construction of a graphic image, its three-dimensional version.
Experiment and record changes in the qualities of the layout, derive patterns.
Projecting the received information onto a real object, making adjustments.

System Simulation Software

When choosing a program to implement a project, you must choose software that supports three-dimensional space. The possibility of 3D visualization followed by volumetric printing is also important.

The ZVSOFT company offers its products.

Basic CAD is an analogue of the popular software - AutoCAD. But many engineers switch to ZVKAD because of the simplified licensing system, lower price and convenient Russian-language interface. At the same time, the new development is not at all inferior in functionality:

Supports work in both 2D and three-dimensional space;
integration with almost any text and graphic files;
convenience and a large functional toolbar.

At the same time, you can install many add-ons on ZWCAD aimed at solving certain problems.

– a program for creating and working with complex 3D objects. Its advantages:

Convenient interface accessible to users of any skill level and automated element selection process.
Easy structuring of objects based on a grid that can be changed (they can be compressed, stretched, increased or decreased in height, cloned, projected, made depressions and convexities, and much more).
Elements from NURBZ curves and surfaces, their modification with professional editing tools.
Creation of volumetric figures based on derived basic and complex objects.
Modeling the behavior of objects, described in the form of mathematical functions.
Transformation of some forms into others, highlighting individual transitional elements.
With the RenderZone and V-Ray plugins, detailed rendering of all details and textures becomes possible.
Animation allows you to set the movement of objects both independently and depending on one another.
3D printing of models.
Export to engineering analysis systems.

Another development is the program. A universal CAD system in three versions - lightweight, standard and professional. Possibilities:

Creation of a three-dimensional object of any complexity.
Hybrid modeling.
Using mathematical formulas and functions to construct figures.
Reverse engineering, or reverse engineering of products to make adjustments.
Modeling motion using animation.
Work with a model as a solid, hollow, or wireframe.
Obtaining samples on a 3D printer.
Using variables and mathematical environments to simulate behavior.

In the article we explained what simulation methods are and what their purpose is. The future of science and production lies in new technologies.

Another example of essentially machine-based models are simulation models. Despite the fact that simulation modeling is becoming an increasingly popular method for studying complex systems and processes, today there is no single definition of a simulation model recognized by all researchers.

Most of the definitions used imply that a simulation model is created and implemented using a set of mathematical and instrumental tools that allow, using a computer, targeted calculations of the characteristics of the simulated process and optimization of some of its parameters.

There are also extreme points of view. One of them is associated with the statement that a simulation model can be recognized as any logical-mathematical description of a system that can be used during computational experiments. From these positions, calculations associated with varying parameters in purely deterministic problems are recognized as simulation modeling.

Supporters of another extreme point viewpoints believe that a simulation model is necessarily a special software package, which allows you to simulate the activity of any complex object. “The simulation method is experimental method research of a real system using its computer model, which combines the features of the experimental approach and specific conditions for the use of computer technology. Simulation modeling is a computer modeling method; in fact, it never existed without a computer, and only the development of information technology led to the establishment of this type of computer modeling.” This approach denies the possibility of creating the simplest simulation models without the use of a computer.

Definition 1.9. Simulation model- a special type of information models that combines elements of analytical, computer and analog models, which allows, using a sequence of calculations and graphical display of the results of its work, to reproduce (simulate) the processes of functioning of the object under study when exposed to various (usually random) factors.

Simulation modeling is used today to model business processes, supply chains, warfare, population dynamics, historical processes, competition and other processes to predict the consequences of management decisions in a variety of areas. Simulation modeling allows one to study systems of any nature, complexity and purpose and with almost any degree of detail, limited only by the complexity of developing a simulation model and the technical capabilities of the computing tools used to conduct experiments.

Simulation models that are developed to solve modern practical problems usually contain big number complex interacting stochastic elements, each of which is described a large number parameters and is subject to stochastic influences. In these cases, as a rule, full-scale modeling is undesirable or impossible, and an analytical solution is difficult or also impossible. Often, the implementation of a simulation model requires the organization of distributed computing. For these reasons, simulation models are essentially machine-based models.

A simulation model involves representing the model in the form of an algorithm implemented by a computer program, the execution of which simulates the sequence of changes in states in the system and thus reflects the behavior of the simulated system or process.

Note!

In the presence of random factors, the necessary characteristics of the simulated processes are obtained as a result of repeated runs of the simulation model and subsequent statistical processing of the accumulated information.

Note that from the point of view of a scientific scientist, it is legitimate to interpret simulation modeling as an information technology: “Simulation modeling of a controlled process or a controlled object is a high-level information technology that provides two types of actions performed using a computer:

1) work on creating or modifying a simulation model;
2) operation of the simulation model and interpretation of the results."

Modular principle of constructing a simulation model. So, simulation modeling presupposes the presence of constructed logical-mathematical models that describe the system being studied in connection with the external environment, the reproduction of the processes occurring in it while maintaining their logical structure and sequence over time using computer technology. It is most rational to build a simulation model of the system’s functioning using a modular principle. In this case, three interconnected blocks of modules of such a model can be identified (Fig. 1.7).

Rice. 1.7.

The main part of the algorithmic model is implemented in a block for simulating object functioning processes (block 2). Here, the countdown of model time is organized, the logic and dynamics of the interaction of model elements are reproduced, and experiments are carried out to accumulate data necessary for calculating estimates of the characteristics of the object’s functioning. The random influences simulation block (block 1) is used to generate values of random variables and processes. It includes generators of standard distributions and tools for implementing algorithms for modeling random effects with the required properties. In the simulation results processing block (block 3), the current and final values of the characteristics that make up the results of experiments with the model are calculated. Such experiments may consist of solving related problems, including optimization or inverse ones.

Lychkina II. II. Decree. op.
Distributed computing is a way to solve labor-intensive computing problems using several computers, most often combined into a parallel computing system.
Emelyanov A. A., Vlasova E. A., Duma R. V. Simulation modeling of economic processes. M.: Finance and Statistics, 2006. P. 6.

In this article we will talk about simulation models. This is a rather complex topic that requires separate consideration. That is why we will try to explain this issue in an accessible language.

Simulation models

What are we talking about? Let's start with the fact that simulation models are necessary to reproduce any characteristics of a complex system in which elements interact. However, such modeling has a number of features.

Firstly, this is a modeling object, which most often represents a complex complex system. Secondly, these are random factors that are always present and have a certain impact on the system. Thirdly, there is the need to describe the complex and lengthy process that is observed as a result of modeling. The fourth factor is that without the use of computer technology it is impossible to obtain the desired results.

Development of a simulation model

It lies in the fact that each object has a certain set of its characteristics. All of them are stored on the computer using special tables. The interaction of values and indicators is always described using an algorithm.

The peculiarity and beauty of modeling is that each stage is gradual and smooth, which makes it possible to change characteristics and parameters step by step and obtain different results. The program, which uses simulation models, displays information about the results obtained, based on certain changes. A graphical or animated representation of them is often used, which greatly simplifies the perception and understanding of many complex processes that are quite difficult to comprehend in an algorithmic form.

Determinism

Simulation mathematical models are built on the fact that they copy the qualities and characteristics of certain real systems. Let's consider an example when it is necessary to study the quantity and population dynamics of certain organisms. To do this, using modeling, you can separately consider each organism in order to analyze its specific indicators. In this case, the conditions are most often set verbally. For example, after a certain period of time, you can set the reproduction of an organism, and after a longer period - its death. The fulfillment of all these conditions is possible in the simulation model.

Very often they give examples of modeling the movement of gas molecules, because it is known that they move chaotically. You can study the interaction of molecules with the walls of a vessel or with each other and describe the results in the form of an algorithm. This will allow you to obtain average characteristics of the entire system and perform analysis. It should be understood that such a computer experiment, in fact, can be called real, since all characteristics are modeled very accurately. But what is the point of this process?

The fact is that the simulation model allows you to highlight specific and pure characteristics and indicators. It seems to get rid of random, unnecessary and a number of other factors that researchers may not even be aware of. Note that very often determination and mathematical modeling are similar if the result is not to create an autonomous strategy of action. The examples we looked at above concern deterministic systems. They differ in that they do not have elements of probability.

Random processes

The name is very easy to understand if you draw a parallel from ordinary life. For example, when you are standing in line at a store that closes in 5 minutes, and you are wondering whether you will have time to purchase the goods. Another manifestation of randomness can be seen when you call someone and count the rings, wondering how likely you are to get through. This may seem surprising to some, but it is thanks to such simple examples At the beginning of the last century, the newest branch of mathematics was born, namely the theory of queuing. She uses statistics and probability theory to draw some conclusions. Later, researchers proved that this theory is very closely related to military affairs, economics, production, ecology, biology, etc.

Monte Carlo method

An important method for solving the self-service problem is the statistical test method or Monte Carlo method. Note that the possibilities of studying random processes analytically are quite complex, and the Monte Carlo method is very simple and universal, which is its main feature. We can consider the example of a store where one or several customers enter, patients arriving at the emergency room one by one or in a crowd, etc. At the same time, we understand that all these are random processes, and the time intervals between some actions are independent events, which are distributed according to laws that can only be deduced by conducting a huge number of observations. Sometimes this is not possible, so the average option is taken. But what is the purpose of modeling random processes?

The fact is that it allows you to get answers to many questions. It is trivial to calculate how long a person will have to stand in line, taking into account all the circumstances. It would seem that this is a fairly simple example, but this is only the first level, and there can be a lot of similar situations. Sometimes timing is very important.

You can also ask how you can allocate time while waiting for service. An even more difficult question concerns how the parameters should be correlated so that the buyer who has just entered will never get to the line. It seems pretty easy question, but if you think about it and start to complicate it even a little, it becomes clear that the answer is not so easy.

Process

How does random simulation happen? Mathematical formulas are used, namely the laws of distribution of random variables. Numeric constants are also used. Note that in this case it is not necessary to resort to any equations that are used in analytical methods. In this case, the same queue that we talked about above is simply imitated. Only first, programs are used that can generate random numbers and correlate them with a given distribution law. After this, a volumetric statistical processing obtained values, which analyzes the data to determine whether they meet the original purpose of the modeling. Continuing further, let's say that you can find the optimal number of people who will work in the store so that the queue never appears. Moreover, the mathematical apparatus used in this case is the methods of mathematical statistics.

Education

Little attention is paid to the analysis of simulation models in schools. Unfortunately, this could have quite serious consequences for the future. Children should know some basic principles of modeling from school, since the development of the modern world without this process is impossible. In a basic computer science course, children can easily use the Life simulation model.

More thorough study can be taught in high school or specialized schools. First of all, we need to study the simulation of random processes. Remember that in Russian schools this concept and methods are just beginning to be introduced, so it is very important to maintain the level of education of teachers, who are 100% guaranteed to face a number of questions from children. At the same time, we will not complicate the task, focusing on the fact that we are talking about an elementary introduction to this topic, which can be examined in detail in 2 hours.

After the children have mastered the theoretical basis, it is worth covering technical issues that relate to generating a sequence of random numbers on a computer. At the same time, there is no need to overload children with information about how a computer works and on what principles analytics is based. For practical skills, they need to be taught to create generators of uniform random numbers on a segment or random numbers according to the law of distribution.

Relevance

Let's talk a little about why simulation control models are needed. The point is that in modern world It is almost impossible to do without modeling in any field. Why is it so in demand and popular? Simulation can replace real events, necessary to obtain specific results, the creation and analysis of which are too expensive. Or there may be a case where conducting actual experiments is prohibited. People also use it when it is simply impossible to build an analytical model due to a number of random factors, consequences and causal relationships. The last time this method is used is when it is necessary to simulate the behavior of some system over a period of time. of this segment time. For all this, simulators are created that try to reproduce as much as possible the qualities of the original system.

Kinds

Simulation research models can be of several types. So, let's consider simulation modeling approaches. The first is system dynamics, which is expressed in the fact that there are interconnected variables, certain accumulators and feedback. Thus, two systems are most often considered in which there are some General characteristics and points of intersection. The next type of modeling is discrete-event. It refers to cases where there are certain processes and resources, as well as a sequence of actions. Most often, in this way, the possibility of a particular event is explored through the prism of a number of possible or random factors. The third type of modeling is agent-based. It consists in studying the individual properties of the organism in their system. In this case, indirect or direct interaction between the observed object and others is necessary.

Discrete-event modeling suggests abstracting from the continuity of events and considering only the main points. Thus, random and unnecessary factors are excluded. This method is highly developed and is used in many areas: from logistics to production systems. It is best suited for modeling production processes. By the way, it was created in the 1960s by Jeffrey Gordon. System dynamics is a modeling paradigm where research requires a graphical representation of connections and mutual influences of some parameters on others. In this case, the time factor is taken into account. Only on the basis of all the data is a global model created on the computer. It is this type that allows you to very deeply understand the essence of the event under study and identify some causes and connections. Thanks to this modeling, business strategies, production models, disease development, city planning, and so on are built. This method was invented in the 1950s by Forrester.

Agent-based modeling dates back to the 1990s and is relatively new. This direction is used to analyze decentralized systems, the dynamics of which are determined not by generally accepted laws and rules, but by the individual activity of certain elements. The essence of this modeling is to gain an understanding of the new rules, characterize the system as a whole, and find connections between individual components. At the same time, an element is studied that is active and autonomous, can make decisions independently and interact with its environment, and also change independently, which is very important.

Stages

Now let's look at the main stages of developing a simulation model. They include its formulation at the very beginning of the process, the construction of a conceptual model, the choice of a modeling method, the choice of a modeling apparatus, planning, and execution of the task. At the last stage, all received data is analyzed and processed. Building a simulation model is a complex and lengthy process that requires a lot of attention and understanding of the matter. Please note that the stages themselves take maximum time, and the computer modeling process takes no more than a few minutes. It is very important to use the right simulation models, as without it you will not be able to achieve the desired results. Some data will be obtained, but it will not be realistic or productive.

Summing up the article, I would like to say that this is a very important and modern industry. We looked at examples of simulation models to understand the importance of all these points. In the modern world, modeling plays a huge role, since on its basis the economy, urban planning, production, and so on are developed. It is important to understand that simulation system models are in great demand, as they are incredibly profitable and convenient. Even when creating real conditions, it is not always possible to obtain reliable results, since there are always many scholastic factors that are simply impossible to take into account.

Model is an abstract description of the system, the level of detail of which is determined by the researcher himself. A person makes a decision about whether a given element of the system is essential, and, therefore, whether it will be included in the description of the system. This decision is made taking into account the purpose underlying the development of the model. The success of the modeling depends on how well the researcher is able to identify essential elements and the relationships between them.

The system is considered as consisting of many interrelated elements combined to perform specific function. The definition of a system is largely subjective, i.e. it depends not only on the purpose of processing the model, but also on who exactly defines the system.

So, the modeling process begins with defining the goal of developing the model, on the basis of which the system boundaries And required level of detail simulated processes. The chosen level of detail should allow one to abstract from aspects of the functioning of a real system that are not precisely defined due to a lack of information. In addition, the system description must include criteria for the effectiveness of the system and evaluated alternative solutions that can be considered as part of the model or as its inputs. Evaluations of alternative solutions based on given performance criteria are considered as model outputs. Typically, evaluation of alternatives requires changes to the system description and, therefore, restructuring of the model. Therefore, in practice, the process of building a model is iterative. Once recommendations can be made based on the assessments of alternatives, the implementation of the modeling results can begin. At the same time, the recommendations should clearly formulate both the main decisions and the conditions for their implementation.

Simulation modeling(in a broad sense) is the process of constructing a model of a real system and conducting experiments on this model in order to either understand the behavior of the system or evaluate (within the imposed constraints) various strategies that ensure the functioning of this system.

Simulation modeling(in a narrow sense) is a representation of the dynamic behavior of a system by moving it from one state to another in accordance with well-known operating rules (algorithms).

So, to create a simulation model, it is necessary to identify and describe the state of the system and the algorithms (rules) for changing it. This is then written in terms of some modeling tool (algorithmic language, specialized language) and processed on a computer.

Simulation model(IM) is a logical-mathematical description of a system that can be used during experiments on a digital computer.

MI can be used to design, analyze and evaluate the functioning of systems. Machine experiments are carried out with IM, which allow us to draw conclusions about the behavior of the system:

· in the absence of its construction, if it is a designed system;

· without interfering with its functioning, if it is an existing system, experimentation with which is impossible or undesirable (high costs, danger);

· without destroying the system, if the purpose of the experiment is to determine the impact on it.

The process of forming a simulation model can be briefly represented as follows ( Fig.2):

Fig.2. Scheme of formation of a simulation model

Conclusion: IM is characterized by the reproduction of phenomena described by a formalized process diagram, preserving their logical structure, sequence of alternations in time, and sometimes physical content.

Simulation modeling (IM) on a computer is widely used in the study and control of complex discrete systems (CDS) and the processes occurring in them. Such systems include economic and production facilities, sea ports, airports, oil and gas pumping complexes, irrigation systems, software for complex control systems, computer networks and many others. The widespread use of IM is explained by the fact that the size of the problems being solved and the lack of formalizability of complex systems do not allow the use of strict optimization methods.

Under imitation we will understand numerical method conducting computer experiments with mathematical models, describing the behavior of complex systems over long periods of time.

Simulation experiment is a display of a process occurring in the SDS over a long period of time (minute, month, year, etc.), which usually takes several seconds or minutes of computer operating time. However, there are problems for which it is necessary to carry out so many calculations during modeling (as a rule, these are problems related to control systems, modeling support for making optimal decisions, developing effective control strategies, etc.) that the IM works slower than the real system. Therefore, the ability to simulate a long period of VTS operation in a short time is not the most important thing that simulation provides.

Simulation capabilities:

1. Machine experiments are carried out with the IM, which allow us to draw conclusions about the behavior of the system:

· without its construction, if it is a designed system;

· without interfering with its functioning, if it is an existing system, experimentation with which is impossible or undesirable (expensive, dangerous);

· without its destruction, if the purpose of the experiment is to determine the maximum impact on the system.

2. Experimentally explore complex interactions within the system and understand the logic of its functioning.

4. Study the impact of external and internal random disturbances.

5. Investigate the degree of influence of system parameters on performance indicators.

6. Test new management and decision-making strategies in operational management.

7. Predict and plan the functioning of the system in the future.

8. Conduct staff training.

The basis of the simulation experiment is the model of the simulated system.

IM was developed to model complex stochastic systems - discrete, continuous, combined.

Modeling means that successive moments in time are specified and the state of the model is calculated by the computer sequentially at each of these moments in time. To do this, it is necessary to set a rule (algorithm) for the transition of the model from one state to the next, that is, a transformation:

where is the state of the model at the -th moment in time, which is a vector.

Let us introduce into consideration:

Vector of the state of the external environment (model input) at the th moment of time,

Control vector at the th moment of time.

Then the IM is determined by specifying the operator, with the help of which you can determine the state of the model at the next moment in time based on the state at the current moment, the control vectors and the external environment:

We write this transformation in recurrent form:

Operator defines a simulation model of a complex system with its structure and parameters.

An important advantage of IM is the ability to take into account uncontrolled factors of the modeled object, which are a vector:

Then we have:

Simulation model is a logical-mathematical description of a system that can be used during experiments on a computer.

Fig.3. Composition of the IM of a complex system

Returning to the problem of simulation modeling of a complex system, let us conditionally highlight in IM: model of the controlled object, model of the control system and model of internal random disturbances (Fig.3).

The inputs of the controlled object model are divided into controlled controlled and uncontrolled uncontrolled disturbances. The latter are generated by random number sensors according to a given distribution law. Control, in turn, is the output of the control system model, and disturbances are the output of random number sensors (model of internal disturbances).

Here is the control system algorithm.

Simulation allows you to study the behavior of a simulated object over a long period of time – dynamic simulation. In this case, as mentioned above, it is interpreted as the number of the moment in time. In addition, you can study the behavior of the system at a certain point in time - static simulation, then treated as a state number.

With dynamic simulation, time can change in constant and variable steps ( Fig.4):

Fig.4. Dynamic simulation

Here g i– moments of events in the VTS, g * i– moments of events during dynamic simulation with a constant step, g ' i- moments of events at a variable step.

With a constant step, the implementation is simpler, but the accuracy is lower and there may be empty (that is, extra) time points when the state of the model is calculated.

With variable steps, time moves from event to event. This method is a more accurate reproduction of the process; there are no unnecessary calculations, but it is more difficult to implement.

Basic provisions, arising from what has been said:

1. MI is a numerical method and should be used when other methods cannot be used. For complex systems this is this moment main research method.

2. Imitation is an experiment, which means that when conducting it, the theory of planning an experiment and processing its results must be used.

3. The more accurately the behavior of the modeled object is described, the more accurate the model is required. The more accurate the model, the more complex it is and requires more computer resources and time for research. Therefore, it is necessary to seek a compromise between the accuracy of the model and its simplicity.

Examples of tasks to be solved: analysis of system projects at various stages, analysis existing systems, use in control systems, use in optimization systems, etc.