Types of computer simulation. The concept of "Computer model", computer modeling, the main functions of a computer in modeling. Modeling as a method of scientific knowledge

Effective use of simulation modeling is impossible without the use of computers. The terms "computer modeling" and "simulation modeling" have become almost synonymous.

The use of computers in mathematical modeling opens up the possibility of solving a whole class of problems, and not only for simulation modeling. In other types of modeling, a computer is also very useful. For example, the implementation of one of the main stages of research - the construction of mathematical models based on experimental data - is currently simply unthinkable without the use of a computer. AT last years, thanks to the development of the graphical interface and graphic packages, computer, structural-functional modeling has been widely developed. Started using the computer even in conceptual modeling, where it is used, for example, in building systems artificial intelligence.

Thus, the concept of "computer modeling" is much broader than the traditional concept of "computer modeling". Currently, a computer model is usually understood as:

description of an object or some system of objects (or processes) using interconnected computer tables, flowcharts, diagrams, graphs, drawings, animation fragments, etc., displaying the structure and relationships between the elements of the object. Computer models of this kind are called structural-functional;

individual program, set of programs, software package, which allows, using a sequence of calculations and a graphical display of their results, to reproduce (simulate) the processes of functioning of an object, a system of objects, subject to the influence of various, including random, factors on it. Such models are called simulation.

The concept of "algorithmic model" is closely related to the concept of "computer model". An algorithmic model is a representation of a mathematical model using algorithm description tools (algorithmic languages, block diagrams, etc.). An algorithmic model is, first of all, a description of the sequence of actions and the calculation procedure for the implementation of the model, as well as the relationship of individual stages of calculations. An algorithmic model is built on the basis of a mathematical and, as a rule, simulation model. The algorithmic model, in contrast to the usual mathematical one, takes into account the features of the computer operation and the ways of implementing individual mathematical operators and functions on the computer. After translation or compilation of the algorithmic model into the machine language of a computer, a computer model is obtained.

Computer modeling is a method for solving the problem of analyzing or synthesizing a complex system based on the use of its computer model, i.e. launching the simulation program for execution at various values ​​of the system parameters, influences and initial conditions and obtaining quantitative and qualitative results with its help. Qualitative conclusions obtained from the results of the analysis make it possible to discover previously unknown properties of a complex system: its structure, development dynamics, stability, integrity, etc. Quantitative conclusions are mainly in the nature of predicting some future or explaining past values ​​of the variables characterizing the system.

A kind of computer simulation is a computational experiment. It is based on the use of a simulation model and a computer, and allows you to conduct research similar to full-scale modeling.

The subject of computer simulation can be any real object or process, for example, the cutting process in statics or dynamics. A computer model of a complex system allows you to display all the main factors and relationships that characterize real situations, criteria and limitations. The quantitative and qualitative gains from the use of mathematical modeling on a computer are as follows:

1. Completely or partially there is no need for a long and laborious stage of manufacturing a laboratory model or a semi-industrial installation, and, accordingly, the cost of components, materials and structural elements necessary for the manufacture of models and installations, as well as measuring instruments and equipment for testing the system .

2. Significantly reduces system characterization time and test time.

3. It becomes possible to develop systems containing elements with known characteristics, but in reality absent; to simulate the effects or modes of operation of the system, the reproduction of which during full-scale tests is difficult, requires complex additional equipment, is fraught with danger for the installation or the experimenter, and sometimes is impossible at all; obtain additional characteristics of the object that are difficult or impossible to obtain with the help of measuring instruments (parametric sensitivity characteristics, frequency, etc.).

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FEDERAL STATE AUTONOMOUS EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION

"Baltic federal university named after Immanuel Kant

INSTITUTE OF TRANSPORT AND TECHNICAL SERVICE

KALININGRAD TECHNICAL COLLEGE

COURSE WORK

ON COMPUTER SIMULATION

"MODELINGcomputer»

Fulfilleda:

Baturina Evgenia

Group: 2KS-1

Checked:

Ampilogov D.V.

KALININGRAD 2014

Introduction

1. Formalization of the conceptual model

1.1 Definition of model parameters and variables

1.2 Definition of the unit of model time

1.3 Determining the law of system operation

2. Task

2.1 Determination of computing requirements

2.2 Choice of simulation software

2.3 Functional structure of the GPSS language

2.4 Program code

Conclusion

List of used literature

Introduction

Modern time dictates a new rhythm of life, modifying all spheres human activity. Today it is impossible to imagine almost any production process or scientific research process without the use of computer simulation. Like any other modeling, computer modeling is aimed at creating prototypes of various kinds of objects, processes or systems, in particular complex systems that depend on a combination of interrelated and random factors. Computer simulation can significantly reduce the cost of conducting experiments, reduce the time for creating and analyzing models, and also obtain the necessary results in a convenient form. An important feature of modern modeling is the use of various kinds of application packages aimed at modeling certain phenomena. Such software products, to some extent, are already the results of computer simulation and serve to optimize and visualize the processes of modeling specific objects, systems and processes. There are various computer simulation environments that are typical for modeling and analyzing specific problems in specific areas of science and technology. In my work, I used the GPSS environment, which I find the most convenient, easy to use and understand, as well as the easily accessible syntax of my chosen language. The course work will present the solution of the problem, as well as the main aspects related to the modeling of modern computers. It is also necessary to remember that the main goal that faced the implementation of the course work is to consolidate the material received from the lectures. A feature of this work is the implementation of the task on a personal computer in the GPSS software environment.

1. foreconceptual model malization

computer simulation model abstract

Before we start looking at a model, we need to define the type of model. Hence, determine the type of simulation. In this course work, the model will be considered from the point of view of a systematic approach.

The model is not an absolute copy of the original, it already implies a certain degree of abstraction.

At present, the concept of a model has expanded, it includes both real and so-called? ideal? models, such as mathematical models. The properties of the model have such forms of scientific ideas about the world as laws, hypotheses, theories.

Any model - ideal or material, used for scientific purposes, in production or in everyday life - carries information about the properties and characteristics of the original object (object - original), essential for the task being solved by the subject. A model is a physical or abstract object that reflects, to one degree or another, the processes in the system under study.

A program written on a computer is a formalized representation of the data processing process. The formalized model is also a character set, because the machine only understands this representation of information. A computer program is a model for processing various types of information.

Building a model is one of the main tasks that requires analysis and basic information about the research promise. The model is built to evaluate its properties, response to environment etc. Most models are based on hypotheses and assumptions, from which the idea of ​​building a model follows.

In different areas of science and human life, processes are studied from different points of view and, accordingly, there are different models from each other.

Modeling languages ​​can be conditionally divided into artificial and natural. Artificial languages ​​are created by man when there is a need to create special purposes or to divide people into groups. Natural languages ​​develop unexpectedly and over a period of time.

Simulation starts:

First stage

1) Statement of the problem (what do you want to get as a result of modeling. what is the goal you set when starting work)

2) Description of the task (specify or set the task within a certain framework)

3) Study of the characteristics of the object (it is necessary to monitor the consequences that the model can have on the environment and the person)

4) What impact should be made on the object under study so that its parameters satisfy the given condition.

Second phase

1) Development of the scheme of this model (Scheme R)

Considering a model instead of a system entails a simplification.

The model is needed for:

1. Understanding the principle of operation of the device, its structure, consider

how the model develops in different conditions and its behavior in these conditions, as well as see the main properties.

2. You need to learn how to manage the model.

3. Predict the consequences of the model, and also consider what consequences the object interacting with this model will have.

The main properties of the abstract model:

1) Finiteness - the model must have a final result.

2) Simplification - the model should be simple and easily reproducible.

3) Purposefulness - any model must have a purpose, because the model represents part of the system.

4) Approximation - the reality of all actions that occur with the model or their approximation.

5) Completeness - the model must take into account all the basic concepts of the system in order to obtain a more accurate result.

6) Informativeness - in the model, it is necessary to contain all the necessary information about the system and, if possible, obtain information from other sources.

8) Stability - the model should describe the behavior of the system under different conditions, even if the conditions are unstable.

9) Visibility - the main properties and applications of the system to be written.

10) Integrity - the model implements an abstract system and therefore must be a single whole, indivisible.

11) Closure - take into account the cyclical nature of the system, relationships and connections.

12) Availability.

13) Adaptability - models need to adapt to any outcome.

14) Manufacturability for reproducing a model that describes a particular system.

15) Evolvability - the possibility of development and increasing the level of complexity.

16) Manageability - models need to have at least one change parameter.

One of the main properties of the model is its adequacy. It has various dependencies:

a) the degree of completeness and reliability of information about the system under study;

b) the degree of detail of the model;

c) the correctness of the parameterization of the model, which is understood as establishing a correspondence between the parameters of the system and the model;

d) the level of training and experience of the researcher himself.

Formalization - displaying the results of thinking in precise terms or statements.

The structural model of the system is also called the block diagram. On the block diagram reflects the composition of the system and its internal connections.

A conceptual model is a model represented by a set of concepts and relationships between them that determine the semantic structure of the subject area under consideration or its specific object.

Most often, the conceptual model is presented in the form of an entity-relationship diagram, which will be given below. To understand how the model works, you need to build its diagram. At this stage, there is a transition from the verbal description of the modeling object to its mathematical model. One of the main goals is to simplify the description of the system, to separate the system itself S from the external environment E and choosing the main content of the model by discarding everything secondary in terms of the goal of modeling.

Let us construct a formal circuit (R-circuit) of a given computing system:

Drawing No. 1 (R-circuit)

C-1 - network machine

C-2 - network machine

S-3 - network machine

Oh - queue

E - electronic computer (computer)

Before entering the computer, the initial data must be queued (data structure with the discipline of access to the elements "first in - first out"). And only then the data from the queue gets into the computer.

The data for the computer are prepared in the form of a package of control and defining maps, which is compiled according to the model scheme, typed from standard symbols. The created GPSS program, working in interpretation mode, generates and transmits transactions from block to block. Each transition of a transaction is assigned to a certain point in the system time.

1.1 Definitionmodel parameters and variables

An analysis of the development of the most complex technical systems allows us to conclude that computers are increasingly penetrating into their structure. Computers are becoming an integral, and often the main part of such systems. First of all, this applies to complex radio-electronic systems. Among them are various automatic systems, including automatic switching systems (electronic exchanges), radio communication systems, radio telemetry systems, radar and radio navigation systems, and various control systems.

When building such systems, the principles and structures of the organization of computers and computer systems (CS) are largely used. characteristic feature is the presence in the systems of several processors, combined in various ways into a specialized aircraft. At the same time, the transition from the "hard" logic of the functioning of technical systems to the universal "program" logic is carried out. Because of this, an increasingly significant role in such systems, along with hardware, is played by specialized system and application software.

The experiment requires only one personal computer without external devices. The duration of the experiment is limited only by the time of access to the personal computer.

A deterministic model is an analytical representation of patterns, operations, etc., under which for a given aggregates input values ​​at the output system, a single result can be obtained. To create a deterministic model of a given computing system, it is necessary to replace stochastic flows with their mathematical expectations:

Interval between user arrivals 10 min

Task preparation time by the 1st user 16 min

Task preparation time by the 2nd user 17 min

Task preparation time by 3rd user 18 min

Time to complete the task on the computer 0.8 min

The probability of arrival of each of the users is 0.33

1.2 Determination of the unit of model time

Model time - time that you can choose at your discretion, depending on the condition of the problem.

In the original problem, it is necessary to take the minimum real time interval as a unit of model time (emd). The minimum real time interval (emd) during which the system does not change its initial state. In the current task, the model time is 0.1 min.

1.3 Determination of the law of system functioning

The operation of this computing system can be represented in the form of timing diagrams.

Figure No. 2 (dependence of the model time Emd on the incoming information from the network machine C-1)

Figure No. 3 (dependence of the model time Emd on the incoming information from the C-2 network machine)

Figure No. 4 (dependence of the model time Emd on the incoming information from the C-3 network machine)

Figure No. 5 (time dependence on how data enters the computer - computer)

2. Exercise

The condition of the problem is shown in the figure:

Figure No. 6 (problem condition)

2.1 Defining Computing Requirements

To solve the original problem, you will need one computer on which the GPSS program is installed. The time spent on the solution of the problem is limited by the time of access to the computer.

2.2 Choice of simulation software

To write the program, I chose the environment GPSS. The language that is used in this environment is called GPSS. GPSS (General Purpose)

Simulation System is a language that is used to model abstract systems and queuing systems (QS), as well as for the spatial movement of objects. Objects of the GPSS language are associated with the QS - a system that provides services to incoming requests. Maintenance of requirements in QS is performed by service devices. These objects, which were discussed earlier, are called transactions. Transactions can be created and deleted as needed to solve any problem. In any model, there are certain blocks, each of which is responsible for its own function. The function tells transactions to understand where to move or move to get the end result. The data for the computer are prepared in the form of a package of control and defining maps, which is compiled according to the model scheme, typed from standard symbols. The created GPSS program, working in interpretation mode, generates and transmits transactions from block to block. Each transition of a transaction is assigned to a certain point in the system time.

2.3 Functional structure of the languageGPSS

I) The level is defined by a combination of basic functional entities such as:

Devices

Logic switch

Turn

Transactions;

II) Level - a block diagram of the model, made up of typical blocks, between which transactions move.

1) Transactions are abstract moving elements that are analogues of various objects in the real world (messages, vehicles, people, parts, etc.) Transactions move along the model, they can be created and destroyed.

Moving between model blocks in accordance with the logic of modeling, transactions cause (and experience) various actions:

Their delays are possible at some points of the model (associated with service, waiting in line),

Change of routes and direction of movement,

Creating a copy of transactions.

2) Devices model objects in which transactions can be processed, which is time consuming. The devices are analogues of QS channels (each device in this moment time, maybe take only one transaction). GPSS has the ability to check the status of the device.

3) Memory - designed for modeling objects with a capacity. An analogy with multi-channel QS - memory can serve several transactions simultaneously. In this case, the transaction occupies a certain part of the memory.

4) Logical switches - take the value on or off, allow you to change the path of transactions in the model.

5) Queue. In the process of movement, transactions can be delayed at certain points in the model. If it is necessary to collect information about the length of the transaction queue and the delay time of transactions, use the appropriate statistical objects.

6) Tables. Tables process statistical information, build a histogram of distributions for any variable.

2.4 Programthe code

10 generate 100,500

40 release ustr1

50 transfer ,evm

100 generate 200,500

130 release ustr2

140 transfer evm

200 generate 300,500

230 release ustr3

300 evm seize ustr4

320 release ustr4

Table No. 1 shows the main blocks that were required as a result of writing the program:

Table No. 1

Program text

Under computer modeling in the broadest sense, we mean the process of creating and researching models using a computer. There are the following types of modeling:

Physical Simulation: Computer - Part experimental setup or a simulator, it perceives external signals, performs the corresponding calculations and issues signals that control various manipulators. For example, a training model of an aircraft, which is a cockpit mounted on appropriate manipulators connected to a computer that responds to the actions of the pilot and changes the cockpit tilt, instrument readings, view from the window, etc., simulating the flight of a real aircraft;

Dynamic or numerical simulation, which involves the numerical solution of a system of algebraic and differential equations by the methods of computational mathematics and the conduct of a computational experiment with various system parameters, initial conditions and external influences. It is used to model various physical, biological, social and other phenomena: pendulum oscillations, wave propagation, changes in the population, the population of a given animal species, etc.;

Simulation modeling consists in creating a computer program (or software package) that simulates the behavior of a complex technical, economic or other system on a computer with the required accuracy. Simulation modeling provides a formal description of the logic of the functioning of the system under study over time, which takes into account the significant interactions of its components and ensures the conduct of statistical experiments. Object-oriented computer simulations are used to study the behavior of economic, biological, social and other systems, to create computer games, the so-called "virtual world", educational programs and animations. For example, a model of a technological process, an aerodrome, some industry, etc.;

Statistical modeling is used to study stochastic systems and consists in repeated testing with subsequent statistical processing of the results. Such models make it possible to study the behavior of all kinds of queuing systems, multiprocessor systems, information and computing networks, and various dynamic systems that are affected by random factors. Statistical models are used in solving probabilistic problems, as well as in processing large data arrays (interpolation, extrapolation, regression, correlation, calculation of distribution parameters, etc.). They differ from deterministic models, the use of which involves the numerical solution of systems of algebraic or differential equations, or the replacement of the object under study by a deterministic automaton;

Information modeling consists in creating an information model, that is, a set of specially organized data (signs, signals) that reflect the most significant aspects of the object under study. There are visual, graphic, animation, text, tabular information models. These include all kinds of schemes, graphs, graphs, tables, diagrams, drawings, animations made on a computer, including a digital map of the starry sky, a computer model earth's surface etc.;

Knowledge modeling involves the construction of an artificial intelligence system, which is based on the knowledge base of a certain subject area (part of the real world). Knowledge bases consist of facts (data) and rules. For example, computer program A person who can play chess must operate with information about the "abilities" of various chess pieces and "know" the rules of the game. This type of models includes semantic networks, logical knowledge models, expert systems, logical games etc. Logical models are used to represent knowledge in expert systems, to create artificial intelligence systems, to perform inference, to prove theorems, to mathematical transformations, to build robots, to use natural language for communication with a computer, creating an effect virtual reality in computer games, etc.

Based on the goals of modeling, computer models are divided into groups:

Descriptive models used to understand the nature of the object under study, to identify the most significant factors influencing its behavior;

Optimization models that allow you to choose the best way to control a technical, socio-economic or other system (for example, a space station);

Prognostic models that help predict the state of the object at subsequent points in time (a model of the earth's atmosphere that allows you to predict the weather);

Educational models used for education, training and testing of students, students, future professionals;

Game models that allow you to create a game situation that simulates the management of an army, state, enterprise, person, aircraft, etc., or playing chess, checkers and other logic games.

LECTURE 4

"Classification of types of system modeling"

Modeling is based on similarity theory, which states that absolute similarity can only take place when one object is replaced by another exactly the same. When modeling, absolute similarity does not take place and they strive to ensure that the model reflects the studied side of the object's functioning well enough.

Classification signs. As one of the first features of the classification of types of modeling, you can choose the degree of completeness of the model and divide the models according to this feature into full, incomplete and approximate.

At the core full simulation lies a complete similarity, which manifests itself both in time and in space.

Incomplete modeling is characterized by incomplete similarity of the model to the object under study.

Approximate modeling is based on approximate similarity, in which some aspects of the functioning of a real object are not modeled at all.

Classification of types of system modeling S shown in fig. one.

Depending on the nature of the studied processes in the systemS all types of modeling can be divided into deterministic and stochastic, static and dynamic, discrete, continuous and discrete-continuous.

Deterministic Simulation displays deterministic processes, i.e. processes in which the absence of any random influences is assumed.

Stochastic simulation displays probabilistic processes and events. In this case, a number of implementations of a random process are analyzed and the average characteristics are estimated, i.e., a set of homogeneous implementations.

Static Simulation is used to describe the behavior of an object at some point in time, and dynamic simulation reflects the behavior of an object over time.

Discrete Simulation serves to describe processes that are assumed to be discrete, respectively continuous simulation allows you to reflect continuous processes in systems, and discrete-continuous simulation is used for cases when one wants to highlight the presence of both discrete and continuous processes.

Depending on the form of representation of the object (systemS ) can be distinguished mental and real modeling.

mental modeling often is the only way to model objects that are either practically unrealizable in a given time interval, or exist outside the conditions possible for their physical creation. For example, on the basis of mental modeling, many situations of the microworld that are not amenable to physical experiment can be analyzed. Mental modeling can be implemented in the form visual, symbolic and mathematical. At visual modeling , on the basis of a person's ideas about real objects, various visual models are created that display the phenomena and processes occurring in the object. The basis hypothetical simulation the researcher lays down some hypothesis about the patterns of the process in a real object, which reflects the level of knowledge of the researcher about the object and is based on cause-and-effect relationships between the input and output of the object under study. Hypothetical modeling is used when knowledge about the object is not enough to build formal models. Analog simulation is based on the application of analogies of various levels. highest level is a complete analogy, which takes place only for sufficiently simple objects. With the complication of the object, analogies of subsequent levels are used, when the analog model displays several or only one side of the object's functioning. An important place in mental visual modeling is occupied by prototyping . A mental layout can be used in cases where the processes occurring in a real object are not amenable to physical modeling, or it can precede other types of modeling. The construction of mental models is also based on analogies, however, they are usually based on cause-and-effect relationships between phenomena and processes in an object.. If you enter symbol individual concepts, i.e. signs, as well as certain operations between these signs, then you can implement iconic modeling and using signs to display a set of concepts - to make separate chains of words and sentences. Using the operations of union, intersection and addition of set theory, it is possible to give a description of some real object in separate symbols. At the core language modeling lies some thesaurus. The latter is formed from a set of incoming concepts, and this set must be fixed. It should be noted that there are fundamental differences between a thesaurus and a regular dictionary. Thesaurus is a dictionary that is cleared of ambiguity, i.e. in it only a single concept can correspond to each word, although in a regular dictionary several concepts can correspond to one word.

Symbolic modeling is an artificial process of creating a logical object that replaces the real one and expresses the main properties of its relations using a certain system of signs or symbols.

Math modeling. To study the characteristics of the process of functioning of any system S by mathematical methods, including machine methods, this process must be formalized, i.e., a mathematical model must be built.

By mathematical modeling we will understand the process of establishing correspondence to a given real object of some mathematical object, called a mathematical model, and the study of this model, which allows obtaining the characteristics of the real object under consideration. The type of mathematical model depends on both the nature of the real object and the tasks of studying the object and the required reliability and accuracy of solving this problem. Any mathematical model, like any other, describes a real object only with some degree of approximation to reality. Mathematical modeling for the study of the characteristics of the process of functioning of systems can be divided into analytical, simulation and combined.

For analytical modeling, it is characteristic that the processes of functioning of the elements of the system are written in the form of some functional relationships (algebraic, integro-differential, finite-difference, etc.) or logical conditions. The analytical model can be explored by the following methods:

analytical, when they strive to obtain explicit dependencies for the desired characteristics in a general form;

numerical when, not being able to solve equations in a general form, they strive to obtain numerical results with specific initial data;

quality, when, without having an explicit solution, it is possible to find some properties of the solution (for example, to estimate the stability of the solution).

The most complete study of the process of system functioning can be carried out if explicit dependencies are known that connect the desired characteristics with the initial conditions, parameters and variables of the system S. However, such dependencies can be obtained only for relatively simple systems. As systems become more complex, their study analytical method encounters significant difficulties, which are often insurmountable. Therefore, wishing to use the analytical method, in this case they go to a significant simplification of the original model in order to be able to study at least general properties systems. Such a study on a simplified model by the analytical method helps to obtain indicative results for determining more accurate estimates by other methods. The numerical method allows us to study a wider class of systems compared to the analytical method, but the solutions obtained are of a particular nature. The numerical method is especially effective when using a computer.

In some cases, studies of the system can also satisfy the conclusions that can be drawn using the qualitative method of analyzing a mathematical model. Such qualitative methods are widely used, for example, in the theory of automatic control to evaluate the effectiveness of various options for control systems.

At present, methods of machine implementation of the study of the characteristics of the process of functioning of large systems are widespread. To implement a mathematical model on a computer, it is necessary to build an appropriate modeling algorithm.

When simulating the algorithm that implements the model reproduces the process of functioning of the system S in time, and the elementary phenomena that make up the process are simulated, while maintaining their logical structure and sequence of flow in time, which allows, according to the initial data, to obtain information about the states of the process at certain points in time, making it possible to evaluate the characteristics of the system S.

The main advantage of simulation modeling compared to analytical modeling is the ability to solve more complex problems. Simulation models make it possible to easily take into account such factors as the presence of discrete and continuous elements, non-linear characteristics of system elements, numerous random effects, etc., which often create difficulties in analytical studies. Simulation is currently the most effective method studies of large systems, and often the only practically accessible method for obtaining information about the behavior of the system, especially at the stage of its design.

The simulation method allows solving the problems of analyzing large systems S, including the problems of evaluating: options for the structure of the system, the effectiveness of various algorithms for controlling the system, the impact of changing various system parameters. Simulation modeling can also be used as the basis for structural, algorithmic and parametric synthesis of large systems, when it is required to create a system with specified characteristics under certain restrictions, which is optimal according to some criteria for evaluating efficiency..

When solving problems of machine synthesis of systems based on their simulation models, in addition to developing modeling algorithms for analyzing a fixed system, it is also necessary to develop algorithms for finding the optimal system variant. Further, in the methodology of machine modeling, we will distinguish two main sections: statics and dynamics, the main content of which are, respectively, the issues of analysis and synthesis of systems specified by modeling algorithms.

Combined (analytical-simulation) modeling in the analysis and synthesis of systems allows you to combine the advantages of analytical and simulation modeling. When building combined models, a preliminary decomposition of the process of functioning of an object into constituent subprocesses is carried out, and for those of them, where possible, analytical models are used, and simulation models are built for the remaining subprocesses.. Such a combined approach makes it possible to cover qualitatively new classes of systems that cannot be studied using only analytical and simulation modeling separately.

Other types of modeling. In real modeling, the possibility of studying various characteristics is used either on a real object as a whole or on its part. Such studies can be carried out both at facilities operating in normal modes, and when organizing special modes for assessing the characteristics of interest to the researcher (for other values ​​of variables and parameters, on a different time scale, etc.). Real simulation is the most adequate, but at the same time, its capabilities, taking into account the characteristics of real objects, are limited. For example, carrying out a real simulation of an automated control system by an enterprise will require, firstly, the creation of such an automated control system, and secondly, experiments with a controlled object, i.e. an enterprise, which is impossible in most cases. Consider the varieties of real simulation.

Full-scale modeling called conducting a study on a real object with subsequent processing of the results of the experiment based on the theory of similarity. When the object functions in accordance with the goal, it is possible to identify the patterns of the real process. It should be noted that such types of full-scale experiment as a production experiment and complex tests have a high degree of reliability.

With the development of technology and penetration into the depths of the processes occurring in real systems, the technical equipment of a modern scientific experiment increases. It is characterized by the wide use of automation tools, the use of very diverse information processing tools, the possibility of human intervention in the process of conducting an experiment, and in accordance with this, a new scientific direction has appeared - the automation of scientific experiments.

The difference between the experiment and the real course of the process lies in the fact that individual critical situations may appear in it and the boundaries of the stability of the process can be determined. During the experiment, new factors and disturbing influences are introduced during the operation of the object. One of the varieties of the experiment is complex tests, which can also be attributed to full-scale modeling, when, as a result of repeated testing of products, general patterns are revealed about the reliability of these products, about quality characteristics, etc.. In this case, modeling is carried out by processing and summarizing the information passing in a group of homogeneous phenomena. Along with specially organized tests, it is possible to implement full-scale simulation by summarizing the experience gained during the production process, i.e., we can talk about a production experiment. Here, on the basis of the theory of similarity, statistical material on the production process is processed and its generalized characteristics are obtained.

Another type of real simulation is physical, which differs from natural in that the study is carried out on installations that preserve the nature of phenomena and have a physical similarity. . In the process of physical modeling, some characteristics of the external environment are set and the behavior of either a real object or its model is studied under given or artificially created environmental influences. Physical modeling can proceed in real and unreal (pseudo-real) time scales, and can also be considered without regard to time. In the latter case, the so-called "frozen" processes, which are fixed at some point in time, are subject to study. The greatest complexity and interest in terms of the fidelity of the results obtained is physical modeling in real time.

From the point of view of the mathematical description of the object and depending on its nature, models can be divided into models analog (continuous), digital (discrete) and analog-to-digital (combined).

Under analog model a model is understood that is described by equations relating continuous quantities.

Digital means a model, which is described by equations relating discrete quantities presented in digital form.

Analog-to-digital refers to the model, which can be described by equations relating continuous and discrete quantities.

A special place in modeling is occupied by cybernetic modeling, in which there is no direct similarity of physical processes occurring in models to real processes. In this case, they tend to display only some function and consider the real object as a “black box” with a number of inputs and outputs, and model some connections between outputs and inputs. Most often, when using cybernetic models, an analysis of the behavioral side of an object is carried out under various environmental influences. Thus, cybernetic models are based on the reflection of some information management processes, which makes it possible to evaluate the behavior of a real object. To build a simulation model in this case, it is necessary to select the investigated function of a real object, try to formalize this function in the form of some communication operators between the input and output, and reproduce it on the simulation model this function, and on the basis of completely different mathematical relationships and, of course, a different physical implementation of the process.

LECTURE 5

"CAPABILITIES AND EFFICIENCY OF SIMULATION OF SYSTEMS ON SVM"

Ensuring the required quality indicators for the functioning of large systems, associated with the need to study the flow of stochastic processes in the studied and designed systems S, makes it possible to carry out a complex of theoretical and experimental studies that complement each other. The efficiency of experimental studies of complex systems turns out to be extremely low, since full-scale experiments with a real system either require large material costs and significant time, or are practically impossible at all (for example, at the design stage, when there is no real system). Efficiency theoretical research from a practical point of view, it fully manifests itself only when their results with the required degree of accuracy and reliability can be represented in the form of analytical relationships or modeling algorithms suitable for obtaining relevant characteristics the process of functioning of the systems under study.

1.System modeling tools.

The advent of modern computers was a decisive condition for the widespread introduction of analytical methods in the study of complex systems. It began to seem that models and methods, for example, mathematical programming, would become a practical tool for solving control problems in large systems. Indeed, significant progress has been made in the creation of new mathematical methods for solving these problems, but mathematical programming has not become a practical tool for studying the process of functioning of complex systems, since mathematical programming models turned out to be too crude and imperfect for their effective use. The need to take into account the stochastic properties of the system, the indeterminacy of the initial information, the presence of correlations between a large number variables and parameters that characterize processes in systems lead to the construction of complex mathematical models that cannot be applied in engineering practice when studying such systems by an analytical method. Analytical relations suitable for practical calculations can be obtained only under simplifying assumptions, which usually significantly distort the actual picture of the process under study. Therefore, in recent years, there has been an increasingly tangible need to develop methods that would make it possible to investigate more adequate models already at the stage of system design. These circumstances lead to the fact that simulation methods are increasingly used in the study of large systems.

Computers have now become the most constructive means of solving engineering problems based on modeling. Modern computers can be divided into two groups: universal, primarily designed to perform settlement work, and control, allowing not only settlement work, but primarily adapted to control objects in real time. Control computers can be used both to control the technological process, experiment, and to implement various simulation models.

Depending on whether it is possible to build a sufficiently accurate mathematical model of the real process, or due to the complexity of the object, it is not possible to penetrate into the depths of the functional connections of a real object and describe them with some analytical relations, two main ways of using computers can be considered:

as a means of calculation for the obtained analytical models and

as a simulation tool.

For a well-known analytical model, assuming that it accurately reflects the studied side of the functioning of a real physical object, the computer is faced with the task of calculating the characteristics of the system using some mathematical ratios when substituting numerical values. In this direction, computers have capabilities that practically depend on the order of the equation being solved and on the requirements for the speed of solution, and both computers and AVMs can be used.

When using a computer, an algorithm for calculating the characteristics is developed, in accordance with which programs are compiled (or generated using an application package) that make it possible to carry out calculations according to the required analytical ratios. The main task of the researcher is to try to describe the behavior of a real object using one of the known mathematical models.

The use of AVM, on the one hand, speeds up the process of solving the problem for fairly simple cases, on the other hand, errors may occur due to the presence of a drift in the parameters of individual blocks included in the AVM, limited accuracy with which the parameters entered into the machine can be set, and also malfunctions of technical means, etc.

A combination of computers and AVMs is promising, i.e., the use of hybrid computer technology - hybrid computing systems (HCC), which in a number of cases significantly speeds up the research process.

In GVK, it is possible to combine the high speed of operation of analog means and the high accuracy of calculations based on digital means of computer technology. At the same time, due to the presence of digital devices, it is possible to ensure control over the operations. The experience of using computer technology in modeling problems shows that with the complication of the object, the use of hybrid technology gives greater efficiency in terms of the speed of the solution and the cost of performing operations.

Specific technical means implementations of the simulation model can be a computer, AVM and GVK. If the use of analog technology accelerates the receipt of final results, while maintaining some visibility of the real process, then the use of digital technology allows you to control the implementation of the model, create programs for processing and storing simulation results, and provide an effective dialogue between the researcher and the model.

Usually, the model is built according to the hierarchical principle, when certain aspects of the object's functioning are sequentially analyzed, and when the researcher's focus shifts, the previously considered subsystems pass into the external environment. The hierarchical structure of models can also reveal the sequence in which the real object is studied, namely the sequence of transition from the structural (topological) level to the functional (algorithmic) and from the functional to the parametric.

The modeling result largely depends on the adequacy of the initial conceptual (descriptive) model, on the obtained degree of similarity of the description of a real object, the number of model implementations, and many other factors. In some cases, the complexity of an object does not allow not only to build a mathematical model of the object, but also to give a sufficiently close cybernetic description, and it is promising here to single out the most difficult part of the object to be mathematically described and include this real part of the physical object in the simulation model. Then the model is implemented, on the one hand, on the basis of computer technology, and on the other hand, there is a real part of the object. This greatly expands the possibilities and increases the reliability of the simulation results.

The modeling system is implemented on a computer and allows you to explore the model M , given in the form of a certain set of individual block models and links between them in their interaction in space and time during the implementation of any process. There are three main groups of blocks:

blocks characterizing the simulated process of functioning of the system S;

blocks displaying the external environment E and its impact on the process being implemented;

blocks that play a service auxiliary role, ensuring the interaction of the first two, as well as performing additional functions for obtaining and processing simulation results.

In addition, the modeling system is characterized by a set of variables, with the help of which it is possible to control the process under study, and a set of initial conditions, when it is possible to change the conditions for conducting a machine experiment.

Thus, the modeling system is a means of conducting a computer experiment, and the experiment can be repeated many times, planned in advance, and the conditions for its implementation can be determined. At the same time, it is necessary to choose a methodology for assessing the adequacy of the results obtained and to automate both the processes of obtaining and processing the results in the course of a computer experiment.

2. Providing simulation.

The modeling system is characterized by the presence of mathematical, software, information, technical, ergonomic and other types of support.

Mathematical support of the modeling system includes a set of mathematical relationships that describe the behavior of a real object, a set of algorithms that provide both training and work with the model. This may include algorithms: input of initial data, simulation, output, processing.

Software in its content, it includes a set of programs: experiment planning, system model, experiment, processing and interpretation of results. In addition, the software must ensure the synchronization of processes in the model, i.e., a block is needed that organizes the pseudo-parallel execution of processes in the model. Machine experiments with models cannot take place without well-designed and implemented information support.

Information Support includes tools and technology for organizing and reorganizing the modeling database, methods for logical and physical organization arrays, forms of documents describing the modeling process and its results. Information support is the least developed part, since only now there is a transition to the creation of complex models and a methodology is being developed for their use in the analysis and synthesis of complex systems using the concept of a database and knowledge.

Technical support includes, first of all, means of computer technology, communication and exchange between the operator and the computer network, input and output of information, control of the experiment.

Ergonomic support is a set of scientific and applied techniques and methods, as well as normative-technical and organizational-methodical documents used at all stages of the interaction of a human experimenter with tools (computers, hybrid complexes, etc.). These documents, used at all stages of development and operation of modeling systems and their elements, are intended to form and maintain ergonomic quality by substantiating and choosing organizational and design solutions that create optimal conditions for highly efficient human activity in interaction with the modeling complex.

Thus, the modeling system can be considered as a machine analogue of a complex real process. It allows to replace an experiment with a real process of system operation by an experiment with a mathematical model of this process in a computer. Currently, simulation experiments are widely used in the practice of designing complex systems, when a real experiment is impossible.

Possibilities and efficiency of computer systems modeling

Despite the fact that computer simulation is a powerful tool for studying systems, its use is not rational in all cases. There are many problems that can be solved more efficiently by other methods. At the same time, for a large class of research and system design problems, the simulation method is the most appropriate. Its correct use is possible only in the case of a clear understanding of the essence of the simulation method and the conditions for its use in the practice of studying real systems, taking into account the features of specific systems and the possibilities of their study by various methods.

As the main criteria for the expediency of using the method of simulation modeling on a computer, the following can be indicated: the absence or unacceptability of analytical, numerical and qualitative methods for solving the problem; the presence of a sufficient amount of initial information about the simulated system S to ensure the possibility of building an adequate simulation model; the need to carry out on the basis of other possible methods of solving a very a large number calculations that are difficult to implement even with the use of a computer; the possibility of searching for the optimal variant of the system when it is simulated on a computer.

Simulation modeling on a computer, like any research method, has advantages and disadvantages that are manifested in specific applications. The main advantages of the simulation modeling method in the study of complex systems include the following: a computer experiment with a simulation model makes it possible to investigate the features of the process of functioning of the system S under any conditions; the use of computers in a simulation experiment significantly reduces the duration of testing compared to a full-scale experiment; the simulation model allows you to include the results of full-scale tests of a real system or its parts for further research; the simulation model has a certain flexibility of varying the structure, algorithms and parameters of the simulated system, which is important from the point of view of finding the optimal system option; Simulation modeling of complex systems is often the only practical method for studying the process of functioning of such systems at the stage of their design.

The main disadvantage that manifests itself in the machine implementation of the simulation method is that the solution obtained in the analysis of the simulation model M is always of a particular nature, since it corresponds to fixed elements of the structure, behavior algorithms and values ​​of the system parameters S, initial conditions and external influences. environment E. Therefore, for a complete analysis of the characteristics of the process of functioning of systems, and not for obtaining only a single point, it is necessary to repeatedly reproduce the simulation experiment, varying the initial data of the problem. In this case, as a consequence, there is an increase in the cost of computer time for conducting an experiment with a simulation model of the process of functioning of the system under study S.

Efficiency of machine simulation. In simulation modeling, as well as in any other method of analysis and synthesis of the system S, the question of its effectiveness is very significant. The efficiency of simulation modeling can be evaluated by a number of criteria, including the accuracy and reliability of simulation results, the time of building and working with the model M, the cost of machine resources (time and memory), the cost of developing and operating the model. Obviously, the best estimate of efficiency is a comparison of the results obtained with a real study, i.e. with simulation on a real object during a full-scale experiment. Since it is not always possible to do this, the statistical approach makes it possible to obtain, with a certain degree of accuracy, with the repetition of a computer experiment, some average characteristics of the system behavior. The number of realizations has a significant impact on the accuracy of modeling, and depending on the required reliability, it is possible to estimate the required number of realizations of a reproducible random process.

A significant indicator of efficiency is the cost of machine time. In connection with the use of computers of various types, the total costs are the sum of the time for input and output of data for each modeling algorithm, the time for performing computational operations, taking into account access to RAM and external devices, as well as the complexity of each modeling algorithm. Calculations of the computer time costs are approximate and can be refined as the programs are debugged and the researcher gains experience when working with the simulation model. Big influence the cost of computer time during simulation experiments is rendered by the rational planning of such experiments. The procedures for processing simulation results, as well as the form of their presentation, can have a certain impact on the costs of computer time.

At present, the concept of “system” in science is not completely defined. Scientists have begun to study complex systems (SS).
Numerous literature on systems analysis and systems engineering note the following main properties of complex systems:

Property 1. Integrity and articulation.

A complex system is considered as an integral set of elements, characterized by the presence of a large number of interconnected and interacting elements.
The researcher has a subjective possibility of dividing the system into subsystems, the goals of functioning of which are subordinate to the general goal of the functioning of the entire system (the purposefulness of systems). Purposefulness is interpreted as the ability of a system to carry out, under conditions of uncertainty and the influence of random factors, behavior (choice of behavior) that pursues the achievement of a certain goal.

Property 2. Connections.

The presence of significant stable connections (relations) between elements or (and) their properties, exceeding in power (strength) the connections (relationships) of these elements with elements that are not included in this system (external environment).
By “connections” is meant some virtual channel through which the exchange between elements and the external environment of matter, energy, information is carried out.

Property 3. Organization.

The property is characterized by the presence of a certain organization - the formation of significant links between elements, an ordered distribution of links and elements in time and space. During the formation of links, a certain structure of the system is formed, and the properties of the elements are transformed into functions (actions, behavior).

In the study of complex systems, it is usually noted:

• the complexity of the function performed by the system and aimed at achieving a given goal of functioning;
• the presence of management, an extensive information network and intensive information flows;
• the presence of interaction with the external environment and functioning under conditions of uncertainty and the impact of random factors of various nature.

Property 4. Integrative qualities.

The existence of integrative qualities (properties), i.e. such qualities that are inherent in the system as a whole, but are not characteristic of any of its elements separately. The presence of integrative qualities shows that the properties of the system, although they depend on the properties of the elements, are not completely determined by them.
Examples of SS in the economic sphere are numerous: organizational - production system, enterprise; socio-economic system, such as a region; and etc.
The research methodology for SS is system analysis. One of the most important tools for applied systems analysis is computer modelling.
Simulation is the most effective and universal version of computer simulation in the field of research and control of complex systems.

Model is an abstract description of a system (object, process, problem, concept) in some form different from the form of their real existence.

Modeling is one of the main methods of cognition, is a form of reflection of reality and consists in clarifying or reproducing certain properties of real objects, objects and phenomena with the help of other objects, processes, phenomena, or with the help of an abstract description in the form of an image, plan, map, sets of equations, algorithms and programs.

During simulation, there is always original(object) and model, which reproduces (models, describes, imitates) some features of the object.

Modeling is based on the presence of a variety of natural and artificial systems that differ both in purpose and physical embodiment, similarity or similarity of some properties: geometric, structural, functional, behavioral. This resemblance may be complete. (isomorphism) and partial (homomorphism).

The study of modern SS suggests various model classes. Development information technologies can be interpreted as the possibility of implementing models of various types within information systems for various purposes, for example, Information Systems, image recognition systems, artificial intelligence systems, decision support systems. These systems are based on models of various types: semantic, logical, mathematical, etc.

Here is a general classification of the main types of modeling:

• conceptual modeling- representation of the system with the help of special signs, symbols, operations on them or with the help of natural or artificial languages;
• physical modeling- the simulated object or process is reproduced based on the similarity ratio arising from the similarity of physical processes and phenomena;
• structural - functional modeling– models are diagrams (graphs, block diagrams), graphs, charts, tables, drawings with special rules for their combination and transformation;
• mathematical (logical-mathematical) modeling- the construction of the model is carried out by means of mathematics and logic;
• simulation (software) modeling- in this case, the logical-mathematical model of the system under study is an algorithm for the functioning of the system, software-implemented on a computer.

These types of modeling can be used independently or simultaneously, in some combination (for example, in simulation modeling, almost all of the listed types of modeling or individual techniques are used). So, for example, simulation modeling includes a conceptual (on early stages simulation model formation) and logical-mathematical (including artificial intelligence methods) modeling to describe individual subsystems of the model, as well as in the procedures for processing and analyzing the results of a computational experiment and decision-making. The technology of conducting and planning a computational experiment with appropriate mathematical methods was introduced into simulation modeling from physical (experimental full-scale or laboratory) modeling. Finally, structural-functional modeling is used both to create a stratified description of multi-model complexes and to form various diagrammatic representations when creating simulation models.

The concept of computer modeling is interpreted more widely than the traditional concept of “computer modeling”. Let's bring him.

Computer modelling is a method for solving problems of analysis or synthesis of a complex system based on the use of its computer model.

Computer simulation can be viewed as:

• math modeling;
• simulation modeling;
• stochastic modeling.

Under the term "computer model" understand the conditional image of an object or some system of objects (or processes) described using equations, inequalities, logical relationships, interconnected computer tables, graphs, diagrams, graphs, drawings, animation fragments, hypertexts, etc. and displaying the structure and relationships between the elements of the object. Computer models described using equations, inequalities, logical relationships, interconnected computer tables, graphs, diagrams, graphs, we will call mathematical. Computer models described using interconnected computer tables, graphs, charts, graphs, drawings, animation fragments, hypertexts, etc. and displaying the structure and relationships between the elements of the object, we will call structural and functional;

Computer models (a separate program, a set of programs, a software package) that allow, with the help of a sequence of calculations and a graphical display of the results of its work, to reproduce (simulate) the processes of the functioning of an object (system of objects) subject to the impact on the object of various, as a rule, random factors, we will call imitation.

The essence of computer modeling lies in obtaining quantitative and qualitative results on the existing model. Qualitative Results analysis reveal previously unknown properties of a complex system: its structure, development dynamics, stability, integrity, etc. Quantitative Conclusions are mainly in the nature of an analysis of the existing SS or a forecast of the future values ​​of some variables. The possibility of obtaining not only qualitative, but also quantitative results is a significant difference between simulation modeling and structural-functional modeling.. Simulation modeling has a number of specific features.

The methodology of computer modeling is system analysis(direction of cybernetics, general systems theory), in which the dominant role is given to system analysts. Unlike mathematical modeling on a computer, where methodological basis are: operations research, theory of mathematical models, decision theory, game theory, etc.

The central procedure of system analysis is the construction of a generalized model that reflects all the factors and relationships of a real system. The subject of computer simulation can be any complex system, any object or process. The categories of goals in this case can be very different. A computer model should reflect all the properties, main factors and relationships of a real complex system, criteria, limitations.

Computer modelling offers a set of methodological approaches and technological tools used to prepare and make decisions in various areas of research.

The choice of a modeling method for solving a given problem or studying a system is an urgent task that a system analyst must be able to cope with.

To this end, we clarify the place of simulation models and their specificity among models of other classes. In addition, we will clarify some concepts and definitions that a system analyst deals with in the modeling process. To this end, consider procedural and technological scheme for constructing and researching models of complex systems. This scheme (given on page 6) includes, characteristic of any modeling method, the following stages of determination:

1. Systems (subject, problem area);
2. Simulation object;
3. Purpose of models;
4. Requirements for models;
5. Presentation Forms;
6. Model description type;
7. The nature of the implementation of the model;
8. Model research method.

The first three stages characterize the object and purpose of the study and practically determine the next stages of modeling. Wherein great importance acquires a correct description of the object and the formulation of the modeling goal from the subject area of ​​the study.

Subject (problem) area. The study of various systems: mathematical, economic, industrial, social, queuing systems, computing, information and many others.

The model must be built purposefully. A goal-oriented model is a replacement for reality with the degree of abstraction that is necessary for the goal. That is, the model, first of all, should reflect those essential properties and those aspects of the modeled object that are determined by the task. At the same time, it is important to correctly identify and formulate the problem, to clearly define the purpose of the study conducted with the help of modeling.

Model Requirements. Simulation is related to the solution of real problems and it is necessary to be sure that the simulation results reflect the true state of affairs with a sufficient degree of accuracy, i.e. model is adequate to reality.

A good model should satisfy some generally accepted requirements. Such a model should be:

• adequate;
• reliable;
• simple and understandable to the user;
• purposeful;
• easy to manage and handle;
• functionally complete in terms of the possibilities of solving the main tasks;
• adaptive, allowing you to easily switch to other modifications or update data;
• subject to change (in the process of operation, it can become more complicated).

Depending on the target orientation of the model, special requirements are set for it. The most characteristic are: integrity, reflection of information properties, multi-level, multiplicity (multi-model), extensibility, universality, feasibility (the real possibility of building the model itself and its study), feasibility (for example, on a computer, the possibility of materializing the model in the form of a real system in design tasks ), efficiency (expenses of time, labor, material and other types of resources for building models and conducting experiments are within acceptable limits or justified). The significance or priority of the requirements for the model follows directly from the purpose of the model. For example, in research tasks, tasks of management, planning and description, an important requirement is the adequacy of the model of objective reality. In the tasks of designing and synthesizing unique systems, an important requirement is the feasibility of the model, for example, in CAD or a decision support system (DSS).

The purpose of the simulation and the specification of the requirements for the model determine model presentation form.

Any model (before becoming an objectively existing object) must exist in a mental form, be constructively developed, translated into a symbolic form and materialized. Thus, there are three forms of representation of models:

• mental(images);
• iconic(structural diagrams, descriptions in the form of oral and written statement, logical, mathematical, logical-mathematical constructions);
• material(laboratory and operating layouts, prototypes).

A special place in modeling is occupied by iconic, in particular, logical, mathematical, logical-mathematical models, as well as models recreated on the basis of a description compiled by experts. Sign models are used to model a variety of systems. This direction is associated with the development of computing systems. We will restrict ourselves to them in further consideration.

The next step in the process flow is choice of type of description and
model building. For sign forms, such descriptions can be:

• relation and predicate calculus, semantic networks, frames, artificial intelligence methods, etc. - for logical forms.
• algebraic, differential, integral, integral-differential equations, etc. - for mathematical forms.

Nature of implementationiconic models happen:

• a nalitic(for example, a system of differential equations can be solved by a mathematician on a piece of paper);
• machine(analogue or digital);
• physical(automatic).

In each of them, depending on the complexity of the model, the purpose of modeling, the degree of uncertainty of the characteristics of the model, there may be different ways of conducting research (experiments), i.e., research methods. For example, in analytical research, various mathematical methods. In physical or full-scale modeling, an experimental research method is used.

An analysis of the applied and promising methods of machine experimentation allows us to identify calculation, statistical, simulation and self-organizing research methods.

Computational (mathematical) modeling used in research mathematical models and is reduced to their machine implementation with different numerical initial data. The results of these implementations (calculations) are given in graphical or tabular form. For example, a classical scheme is a machine implementation of a mathematical model, presented as a system of differential equations, based on the use of numerical methods, with the help of which the mathematical model is reduced to an algorithmic form, is programmatically implemented on a computer, and a calculation is carried out to obtain the results.

simulation modeling is distinguished by a high degree of generality, creates the prerequisites for the creation of a unified model that is easily adaptable to a wide class of tasks, and acts as a means for integrating models of various classes.