Introduction

One of important features ACS – the fundamental impossibility of conducting real experiments before the completion of the project. A possible solution is to use simulation models. However, their development and use are extremely complex, and difficulties arise in accurately determining the degree of adequacy of the modeled process. Therefore, it is important to decide which model to create.

Another important aspect is the use of simulation models during the operation of automated control systems for decision making. These models are created during the design process so that they can be continually updated and adjusted to suit changing user environments.

The same models can be used for training personnel before putting the automated control system into operation and for conducting business games.

1. The concept of simulation modeling

Simulation modeling is a research method that involves simulating on a computer, using a set of programs, the process of functioning of a system or its individual parts and elements. The essence of the simulation method is the development of algorithms and programs that simulate the behavior of the system, its properties and characteristics in the composition, volume and area of ​​change of its parameters necessary for studying the system.

The fundamental capabilities of the method are very large; it allows, if necessary, to study systems of any complexity and purpose with any degree of detail. The only limitations are the power of the computer used and the complexity of preparing a complex set of programs.

Unlike mathematical models, which are analytical dependencies that can be studied using a fairly powerful mathematical apparatus, simulation models, as a rule, allow only single tests to be carried out on them, similar to a single experiment on a real object. Therefore, for a more complete study and obtaining required dependencies between parameters, multiple tests of the model are required, the number and duration of which are largely determined by the capabilities of the computer used, as well as the properties of the model itself.

The use of simulation models is justified in cases where the capabilities of methods for studying a system using analytical models are limited, and full-scale experiments are undesirable or impossible for one reason or another.

Even in cases where creating an analytical model for research specific system In principle, it is possible that simulation modeling may be preferable in terms of computer and researcher time spent on conducting research. For many problems that arise during the creation and operation of automated control systems, simulation sometimes turns out to be the only practically feasible research method. This largely explains the continuously growing interest in simulation modeling and the expansion of the class of problems for which it is used.

Simulation modeling methods are developed and used mainly in three directions: development of standard methods and techniques for creating simulation models; study of the degree of similarity of simulation models to real systems; creation of automation programming tools aimed at creating software packages for simulation models.

There are two subclasses of systems focused on system and logical modeling. The subclass of system modeling includes systems with well-developed general algorithmic tools; with a wide range of tools for describing parallel actions, time sequences of process execution; with the ability to collect and process statistical material. In such systems, special programming and modeling languages ​​are used - SIMULA, SIMSCRIPT, GPSS, etc. The first two of these languages ​​are subsets of procedure-oriented programming languages ​​such as FORTRAN, PL/1, advanced means of dynamic data structures, control operators for quasi-parallel processes, by special means collecting statistics and processing lists. These additional capabilities allow statistical studies of models, which is why such systems are sometimes called statistical modeling systems.

A subclass of logical modeling includes systems that allow you to reflect in a convenient and concise form the logical and topological features of the simulated objects, which have the means of working with parts of words, converting formats, and recording microprograms. This subclass of systems includes the programming languages ​​AUTOCODE, LOTIS, etc.

In most cases, when modeling economic, production and other organizational management systems, the study of the model consists of conducting stochastic experiments. Reflecting the properties of the objects being modeled, these models contain random variables that describe both the functioning of the systems themselves and the impacts external environment. Therefore, statistical modeling has become most widespread.

The simulation model is characterized by sets of input variables

observed or manipulated variables

control actions

disturbing influences

System state at any time

and the initial conditions Y(t0), R(t0), W(t0) can be random variables specified by the corresponding probability distribution. The model relations determine the probability distribution of quantities at time t + ∆t:

There are two main ways to construct a modeling algorithm – the ∆t principle and the principle of special states.

∆t principle. The time period (t0, t) in which the behavior of the system is studied is divided into intervals of length ∆t. In accordance with a given probability distribution for initial conditions for a priori reasons or randomly choose one of the possible states z0(t0) for the initial moment t0. For the moment t0 + ∆t, the conditional probability distribution of states is calculated (subject to the state z0(t0)). Then, similarly to the previous one, one of the possible states z0(t0 ​​+ ∆t) is selected, the procedures for calculating the conditional probability distribution of states for the moment t0 + 2∆t are performed, etc.

As a result of repeating this procedure until the moment t0 + n∆t = T, one of the possible implementations of the random process under study is obtained. In the same way, a number of other implementations of the process are obtained. The described method of constructing a modeling algorithm takes a lot of computer time.

The principle of special states. All possible states of the system Z(t) = (zi(t)) are divided into two classes - ordinary and special. In normal states, the characteristics zi(t) change smoothly and continuously. Special states are determined by the presence of input signals or the exit of at least one of the characteristics zi(t) to the boundary of the domain of existence. In this case, the state of the system changes abruptly.

The modeling algorithm must provide procedures for determining the moments of time corresponding to special states and the values ​​of the system characteristics at these moments. Given a known probability distribution for the initial conditions, one of the possible states is selected and, based on the given patterns of changes in characteristics zi(t), their values ​​are found before the first special state. In the same way we proceed to all subsequent special states. Having received one of the possible implementations of a random multidimensional process, other implementations are constructed using similar procedures. The computer time consumption when using a modeling algorithm based on the principle of special states is usually less than when using the ∆t principle.

Simulation modeling is used mainly for the following applications:

1) when studying complex internal and external interactions of dynamic systems with the aim of optimizing them. To do this, study the patterns of interrelationships between variables in the model, make changes to the model and observe their impact on the behavior of the system;

2) to predict the behavior of the system in the future based on modeling the development of the system itself and its external environment;

3) for the purpose of personnel training, which can be of two types: individual training for the operator managing some technological process or device, and training the group of people carrying out collective management complex production or economic facility.

In both types of systems, a set of programs sets a certain situation at the facility, but there is a significant difference between them. In the first case, the software simulates the functioning of objects described by technological algorithms or transfer functions; The model is focused on training the psychophysiological characteristics of a person, which is why such models are called simulators. Models of the second type are much more complex. They describe certain aspects of the functioning of an enterprise or firm and are focused on issuing certain technical and economic characteristics when the inputs are influenced, most often not by an individual, but by a group of people performing various management functions;

4) for prototyping of the designed system and the corresponding part of the controlled object for the purpose of rough verification of the proposed design solutions. This allows the customer to demonstrate the operation of the future system in the most visual and understandable form, which promotes mutual understanding and coordination of design solutions. In addition, such a model makes it possible to identify and eliminate possible inconsistencies and errors at an earlier design stage, which reduces the cost of correcting them by 2–3 orders of magnitude.

Simulation modeling

Simulation modeling (situational modeling)- a method that allows you to build models that describe processes as they would take place in reality. Such a model can be “played” over time for both one test and a given set of them. In this case, the results will be determined by the random nature of the processes. From these data one can obtain fairly stable statistics.

Simulation modeling is a research method in which the system under study is replaced by a model that describes the real system with sufficient accuracy, with which experiments are carried out in order to obtain information about this system. Experimenting with a model is called imitation (imitation is understanding the essence of a phenomenon without resorting to experiments on a real object).

Simulation modeling is a special case of mathematical modeling. There is a class of objects for which, for various reasons, analytical models have not been developed, or methods for solving the resulting model have not been developed. In this case, the analytical model is replaced by a simulator or simulation model.

Simulation modeling is sometimes referred to as obtaining partial numerical solutions to a formulated problem based on analytical solutions or using numerical methods.

A simulation model is a logical and mathematical description of an object that can be used for experimentation on a computer for the purpose of designing, analyzing and evaluating the functioning of the object.

Application of simulation modeling

Simulation modeling is used when:

• it is expensive or impossible to experiment on a real object;
• it is impossible to build an analytical model: the system has time, causal relationships, consequences, nonlinearities, stochastic (random) variables;
• it is necessary to simulate the behavior of the system over time.

The purpose of simulation modeling is to reproduce the behavior of the system under study based on the results of the analysis of the most significant relationships between its elements or, in other words, to develop a simulator. simulation modeling) of the subject area under study to conduct various experiments.

Simulation modeling allows you to simulate the behavior of a system over time. Moreover, the advantage is that time in the model can be controlled: slowed down in the case of fast processes and accelerated for modeling systems with slow variability. It is possible to imitate the behavior of those objects with which real experiments are expensive, impossible or dangerous. With the advent of the era of personal computers, the production of complex and unique products is usually accompanied by computer three-dimensional simulation modeling. This is accurate and relatively fast technology allows you to accumulate everything necessary knowledge, equipment and semi-finished products for the future product before production begins. Computer 3D modeling is now not uncommon even for small companies.

Imitation, as a method for solving non-trivial problems, has received initial development in connection with the creation of computers in the 1950s - 1960s.

There are two types of imitation:

• Monte Carlo method (statistical test method);
• Simulation modeling method (statistical modeling).

Types of simulation

Three Simulation Approaches

Simulation approaches on the scale of abstraction

• Agent-based modeling is a relatively new (1990s-2000s) direction in simulation modeling, which is used for research decentralized systems, the dynamics of whose functioning is determined not by global rules and laws (as in other modeling paradigms), but on the contrary, when these global rules and laws are the result of the individual activity of group members. The purpose of agent-based models is to gain an understanding of these global rules, the general behavior of the system, based on assumptions about the individual, private behavior of its individual active objects and the interaction of these objects in the system. An agent is a certain entity that has activity, autonomous behavior, can make decisions in accordance with a certain set of rules, interact with the environment, and also change independently.

• Discrete-event modeling is an approach to modeling that proposes to abstract from the continuous nature of events and consider only the main events of the simulated system, such as “waiting”, “order processing”, “moving with cargo”, “unloading” and others. Discrete event modeling is the most developed and has a huge range of applications - from logistics and queuing systems to transport and production systems. This type of modeling is most suitable for modeling production processes. Founded by Jeffrey Gordon in the 1960s.

• System dynamics is a modeling paradigm where graphical diagrams of causal relationships and global influences of some parameters on others over time are constructed for the system under study, and then the model created on the basis of these diagrams is simulated on a computer. In fact, this type of modeling, more than all other paradigms, helps to understand the essence of the ongoing identification of cause-and-effect relationships between objects and phenomena. Using system dynamics, models of business processes, city development, production models, population dynamics, ecology and epidemic development are built. The method was founded by Jay Forrester in 1950.

Areas of use

• Population dynamics
• IT infrastructure
• Mathematical modeling of historical processes
• Pedestrian dynamics
• Market and competition
• Service centers
• Supply chains
• Traffic
• Health Economics

Free simulation systems

see also

• Network modeling

Notes

Literature

• Hemdi A. Taha Chapter 18. Simulation Modeling// Introduction to Operations Research = Operations Research: An Introduction. - 7th ed. - M.: “Williams”, 2007. - pp. 697-737. - ISBN 0-13-032374-8

• Strogalev V.P., Tolkacheva I.O. Simulation modeling. - MSTU im. Bauman, 2008. - pp. 697-737. - ISBN 978-5-7038-3021-5

Links

• Computer and static simulation modeling on Intuit.ru
• Simulation modeling in technological engineering problems Makarov V. M., Lukina S. V., Lebed P. A.

Wikimedia Foundation. 2010.

See what “Simulation Modeling” is in other dictionaries:

simulation- (ITIL Continual Service Improvement) (ITIL Service Design) A technique that creates a detailed model to predict the behavior of a configuration item or IT service. Simulation models can be implemented with very high accuracy, but this... ... Technical Translator's Guide

Simulation modeling- Simulation modeling: modeling (symbolic, subject) of technical objects, based on the reproduction of the processes accompanying their existence... Source: INFORMATION SUPPORT OF EQUIPMENT AND OPERATOR ACTIVITY. LANGUAGE… … Official terminology

Simulation modeling- see Machine imitation, Bench experimentation... Economic and mathematical dictionary

Development, construction of a model of some object for its research Dictionary of business terms. Akademik.ru. 2001 ... Dictionary of business terms

simulation- 3.9 simulation modeling: Modeling (symbolic, subject) of technical objects, based on the reproduction of the processes accompanying their existence. Source … Dictionary-reference book of terms of normative and technical documentation

SIMULATION MODELING- (...from the French modele sample) a method of studying any phenomena and processes using statistical tests (Monte Carlo method) using a computer. The method is based on drawing (simulating) the influence of random factors on the phenomenon being studied or... ... encyclopedic Dictionary in psychology and pedagogy

Simulation modeling- this is the reproduction of a particular real situation on a model, its study and, ultimately, finding the most good decision. Actually, I.M. consists of constructing a mathematical model of a real system and setting it up... ... Librarian's terminological dictionary on socio-economic topics

This article should be Wikified. Please format it according to the article formatting rules. Simulation models are not associated with an analytical representation, but with the principle of simulation using information and programs... Wikipedia

Monte Carlo Simulation- (Monte Carlo method) An analytical method for solving a problem by performing a large number of test operations, called simulation, and obtaining the required solution from the combined test results. Calculation method... ... Investment Dictionary

Simulation models

Simulation modelreproduces behaviorcreation of a complex system of interacting elementsComrade Simulation modeling is characterized by the presence of the following circumstances (all or some of them simultaneously):

• the object of modeling is a complex heterogeneous system;
• the simulated system contains factors of random behavior;
• it is required to obtain a description of a process developing over time;
• It is fundamentally impossible to obtain simulation results without using a computer.

The state of each element of the simulated system is described by a set of parameters that are stored in the computer memory in the form of tables. The interactions of system elements are described algorithmically. Modeling is carried out in step by step mode. At each modeling step, the values ​​of the system parameters change. The program that implements the simulation model reflects changes in the state of the system, producing the values ​​of its required parameters in the form of tables by time steps or in the sequence of events occurring in the system. To visualize modeling results, graphical representation is often used, incl. animated.

Deterministic Modeling

A simulation model is based on imitation of a real process (imitation). For example, when modeling the change (dynamics) in the number of microorganisms in a colony, you can consider many individual objects and monitor the fate of each of them, setting certain conditions for its survival, reproduction, etc. These conditions are usually specified verbally. For example: after a certain period of time, the microorganism is divided into two parts, and after another (longer) period of time, it dies. The fulfillment of the described conditions is algorithmically implemented in the model.

Another example: modeling the movement of molecules in a gas, when each molecule is represented as a ball with a certain direction and speed of movement. The interaction of two molecules or a molecule with the wall of a vessel occurs according to the laws of absolutely elastic collision and is easily described algorithmically. The integral (general, averaged) characteristics of the system are obtained at the level of statistical processing of modeling results.

Such a computer experiment actually claims to reproduce a full-scale experiment. To the question: “Why do you need to do this?” we can give the following answer: simulation modeling makes it possible to isolate “in its pure form” the consequences of hypotheses embedded in ideas about micro-events (i.e. at the level of system elements), freeing them from the inevitable influence of other factors in a full-scale experiment, which we may not even know about suspect. If such modeling also includes elements of a mathematical description of processes at the micro level, and if the researcher does not set the task of finding a strategy for regulating the results (for example, controlling the number of a colony of microorganisms), then the difference simulation model from the mathematical (descriptive) turns out to be quite conditional.

The above examples of simulation models (evolution of a colony of microorganisms, movement of molecules in a gas) lead to deterministicbathroom description of systems. They lack elements of probability and randomness of events in simulated systems. Let's consider an example of modeling a system that has these qualities.

Models of random processes

Who has not stood in line and impatiently wondered whether he would be able to make a purchase (or pay rent, ride a carousel, etc.) in the time available to him? Or, trying to call the helpline and encountering short beeps several times, you get nervous and evaluate whether I can get through or not? From such “simple” problems, at the beginning of the 20th century, a new branch of mathematics was born - queuing theory, using the apparatus of probability theory and mathematical statistics, differential equations and numerical methods. Subsequently, it turned out that this theory has numerous implications in economics, military affairs, production organization, biology and ecology, etc.

Computer modeling in solving queuing problems, implemented in the form of a statistical test method (Monte Carlo method), plays an important role. The capabilities of analytical methods for solving real-life queuing problems are very limited, while the statistical testing method is universal and relatively simple.

Let's consider the simplest problem of this class. There is a store with one seller, into which customers randomly enter. If the seller is free, then he begins to serve the buyer immediately, if several buyers come in at the same time, a queue forms. There are many other similar situations:

• repair area for motor vehicles and buses that have left the line due to a breakdown;
• emergency room and patients who came for an appointment due to injury (i.e. without an appointment system);
• a telephone exchange with one entrance (or one telephone operator) and subscribers who, when the entrance is busy, are put in a queue (such a system is sometimes
  practiced);
• server local network and personal computers at the workplace that send a message to a server capable of receiving and processing no more than one message at a time.

The process of customers coming to the store is a random process. The time intervals between the arrivals of any consecutive pair of buyers are independent random events distributed according to some law, which can only be established through numerous observations (or some plausible version of it is taken for modeling). The second random process in this problem, which is in no way connected with the first, is the duration of service for each customer.

The purpose of modeling systems of this type is to obtain answers to a number of questions. A relatively simple question - what is the average time you will have to stand and queue for given distribution laws of the above random variables? More complex issue; What is the distribution of waiting times for service in the queue? An equally difficult question: at what ratios of the parameters of the input distributions will a crisis occur, in which the turn of the newly entered buyer will never reach? When you think about this relatively simple task, the possible questions multiply.

The modeling method looks like general outline So. The mathematical formulas used are the laws of distribution of initial random variables; the numerical constants used are the empirical parameters included in these formulas. No equations are solved that would be used in the analytical study of this problem. Instead, a queue is simulated, played out using computer programs that generate random numbers with given distribution laws. Then statistical processing of the set of obtained values ​​of quantities determined by the given modeling goals is carried out. For example, there is optimal quantity sellers for different periods of store opening hours, which will ensure the absence of queues. The mathematical apparatus used here is called methods of mathematical statistics.

Another example is described in the article "Modeling Ecological Systems and Processes" imitationnogo modeling: one of many models of the predator-prey system. Individuals of species that are in the indicated relationships, according to certain rules containing elements of chance, move, predators eat victims, both of them reproduce, etc. Such the model does not contain any mathematical formulas, but requires by the waystical processing the results.

Example of a deterministic algorithm simulation model

Let's consider a simulation model of the evolution of a population of living organisms, known as "Life", which is easy to implement in any programming language.

To build the game algorithm, consider square field from n -\- 1 columns and rows with regular numbering from 0 to P. For convenience, we define the extreme boundary columns and rows as the “dead zone”; they play only an auxiliary role.

For any internal cell of the field with coordinates (i,j), 8 neighbors can be defined. If the cell is “live”, we paint it over; if the cell is “dead”, it empty.

Let's set the rules of the game. If cell (i,j) is “live” and is surrounded by more than three “live” cells, it dies (from overcrowding). A “living” cell also dies if there are less than two “living” cells in its environment (from loneliness). A “dead” cell comes to life if three “live” cells appear around it.

For convenience, we introduce a two-dimensional array A, whose elements take the value 0 if the corresponding cell is empty, and 1 if the cell is “live”. Then the algorithm for determining the state of a cell with coordinate (i, j) can be defined as follows:

S:=A+A+A+A+A+A+A+A;
If (A = 1) And (S > 3) Or (S< 2)) Then B: =0;
If (A = 0) And (S = 3)
Then B: = 1;

Here the array defines the coordinates of the field on " next stage. For all internal cells from i = 1 to n - 1 and j = 1 to n - 1, the above is true. Note that subsequent generations are defined similarly, you just need to carry out the reassignment procedure:

For I: = 1 Then N - 1 Do
For J: = 1 Then N - 1 Do
A:=B;

It is more convenient to display the field status on the display screen not in a matrix form, but in a graphical form.
All that remains is to determine the procedure for setting the initial configuration of the playing field. When randomly determining the initial state of cells, an algorithm is suitable

For I: = 1 To K Do
Begin K1: = Random(N-1);
K2:= Random (N-1)+1;
End;

It is more interesting for the user to set the initial configuration himself, which is easy to implement. As a result of experiments with this model, one can find, for example, stable settlements of living organisms that never die, remaining unchanged or changing their configuration over a certain period. Absolutely unstable (perishing in the second generation) is “cross” settlement.

In a basic computer science course, students can implement the Life simulation model as part of the Introduction to Programming section. A more thorough mastery of simulation modeling can occur in high school in a specialized or elective course in computer science. This option will be discussed below.

The beginning of the study is a lecture on simulation modeling of random processes. In Russian schools, the concepts of probability theory and mathematical statistics are just beginning to be introduced into mathematics courses, and the teacher should be prepared to make an introduction to this material, which is essential for the formation of a worldview and mathematical culture. Let us emphasize that we're talking about about an elementary introduction to the range of concepts discussed; this can be done in 1-2 hours.

Then we discuss technical issues related to the computer generation of sequences of random numbers with a given distribution law. In this case, we can rely on the fact that every universal programming language has a sensor of random numbers uniformly distributed on the interval from 0 to 1. At this stage it is inappropriate to go into the complex question of the principles of its implementation. Based on existing random number sensors, we show how to arrange

a) a generator of uniformly distributed random numbers on any segment [a, b];

b) a random number generator under almost any distribution law (for example, using the intuitively clear “selection-rejection” method).

It is advisable to begin considering the queuing problem described above with a discussion of the history of solving queuing problems (Erlang problem of servicing requests at a telephone exchange). This is followed by a consideration of the simplest problem, which can be formulated using the example of forming and examining a queue in a store with one seller. Note that at the first stage of modeling, the distributions of random variables at the input can be assumed to be equally probable, which, although not realistic, removes a number of difficulties (to generate random numbers, you can simply use the sensor built into the programming language).

We draw students' attention to what questions are posed first when modeling systems of this type. First, it is the calculation of average values ​​(mathematical expectations) of some random variables. For example, what is the average time you have to wait in line at the counter? Or: find the average time spent by the seller waiting for the buyer.

The teacher's task, in particular, is to explain that sample means themselves are random variables; in another sample of the same size they will have different values ​​(with large sample sizes - not too different from each other). Further options are possible: in a more prepared audience, you can show a method for estimating confidence intervals in which the mathematical expectations of the corresponding random variables are located at given confidence probabilities (using methods known from mathematical statistics without attempting to justify them). For a less prepared audience, we can limit ourselves to a purely empirical statement: if in several samples of equal size the average values ​​coincide at a certain decimal place, then this sign is most likely correct. If the simulation fails to achieve the desired accuracy, the sample size should be increased.

For an even more mathematically prepared audience, one can pose the question: what is the distribution of random variables that are the results of statistical modeling, given the given distributions of random variables that are its input parameters? Since the presentation of the corresponding mathematical theory in this case is impossible, we should limit ourselves to empirical techniques: constructing histograms of the final distributions and comparing them with several typical distribution functions.

After practicing the primary skills of the above modeling, we move on to a more realistic model in which the input flows random events distributed, for example, by Poisson. This will require students to additionally master the method of generating sequences of random numbers with the specified distribution law.

In the problem considered, as in any more difficult task about queues, a critical situation may arise when the queue grows without limit over time. Modeling the approach to a critical situation as one of the parameters increases is an interesting research task for the most prepared students.

Using the queue problem as an example, several new concepts and skills are practiced at once:

• concepts of random processes;
• concepts and basic skills of simulation modeling;
• construction of optimization simulation models;
• building multi-criteria models (by solving problems about the most rational customer service in combination with the interests of
  store owner).

Exercise :

• Make a diagram key concepts;
• Select practical tasks with solutions for basic and specialized computer science courses.

This process consists of two large stages: model development and analysis of the developed model. Simulation allows you to explore the essence complex processes and phenomena through experiments not with a real system but with its model. In the field of creating new systems, modeling is a research tool important characteristics future system at the earliest stages of its development.

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Simulation modeling

Modeling

Modeling is a generally accepted means of understanding reality. This process consists of two large stages: model development and analysis of the developed model. Modeling allows you to explore the essence of complex processes and phenomena through experiments not with a real system, but with its model. It is known that in order to make a reasonable decision on organizing the operation of a system, it is not necessary to know all the characteristics of the system; an analysis of its simplified, approximate representation is always sufficient.

In the field of creating new systems, modeling is a means of exploring the important characteristics of a future system at the earliest stages of its development. Using simulation it is possible to explore narrow places future system, evaluate performance, cost, throughput all its main characteristics even before the system is created. Using models, optimal operating plans and schedules for the functioning of existing complex systems. In organizational systems, simulation becomes the main tool for comparison various options management decisions and searching for the most effective of them both for decisions within a workshop, organization, company, and at the macroeconomic level.

Models of complex systems are built in the form of programs executed on a computer. Computer modeling has been around for almost 50 years, originating with the advent of the first computers. Since then, two overlapping fields of computer modeling have emerged, which can be characterized as mathematical modeling and simulation.

Math modelingassociated mainly with the development of mathematical models physical phenomena, with the creation and justification of numerical methods. There is an academic interpretation of modeling as a field of computational mathematics, which is traditional for the activity of applied mathematicians. In Russia, a strong school has developed in this area: the Research Institute of Mathematical Modeling of the Russian Academy of Sciences the parent organization, the Scientific Council of the Russian Academy of Sciences on the problem of "Mathematical Modeling", publishes the journal "Mathematical Modeling" ( www.imamod.ru).

Simulation modelingthis is the development and execution on a computer of a software system that reflects the behavior and structure of the modeled object. A computer experiment with a model consists of executing this program on a computer with different meanings parameters (initial data) and analysis of the results of these executions.

Problems of developing simulation models

Simulation modeling is a very broad field. You can take different approaches to the classification of problems solved in it. In accordance with one of the classifications, this area currently has four main areas:

1. modeling dynamic systems,
2. discrete-event modeling,
3. system dynamics
4. agent-based modeling.

Each of these areas is developing its own tools that simplify the development of models and their analysis. These areas (except for agent-based modeling) are based on concepts and paradigms that appeared and were recorded in modeling tool packages several decades ago and have not changed since then.

Aimed at studying complex objects whose behavior is described by systems of algebraic-differential equations. The engineering approach to modeling such objects 40 years ago was to assemble block diagrams from the decisive blocks of analog computers: integrators, amplifiers and adders, in which the currents and voltages represented the variables and parameters of the simulated system. This approach is still the main one in modeling dynamic systems, only the decision blocks are not hardware, but software. It is implemented, for example, in the tool environment Simulink.

Discrete-event modeling

In him systems with discrete events are considered. To create a simulation model of such a system, the simulated system is reduced to a flow of requests that are processed by active devices. For example, to model the process of servicing individuals in a bank, individuals are represented as a flow of applications, and the bank employees serving them are represented as active devices. Ideologydiscrete eventmodeling was formulated more than 40 years ago and implemented in the modeling environment GPSS , which, with some modifications, is still used for teaching simulation.

System dynamics.

System dynamicsthis is a direction in the study of complex systems that studies their behavior in time and depending on the structure of the system elements and the interaction between them. Including: cause-and-effect relationships, loops feedback , reaction delays, environmental influences and others. The founder of system dynamics is the American scientist Jay Forrester. J. Forrester applied the principles of feedback existing in systems automatic regulation, to demonstrate that the dynamics of the functioning of complex systems, primarily industrial and social, significantly depend on the structure of connections and time delays in decision-making and actions that exist in the system. In 1958, he proposed the use of flow diagrams for computer modeling of complex systems, reflecting cause-and-effect relationships in a complex system,

Currently, system dynamics has become a mature science. The System Dynamics Society www.systemdynamics.org ) is the official forum of systems analysts around the world. The journal System Dynamics Review is published quarterly, and several international conferences on these issues are convened annually. System dynamics as a methodology and tool for studying complex economic and social processes is studied in many business schools around the world.

Agent-based modeling

Agent-based model (ABM) methodsimulation modeling, which studies the behavior of decentralized agents and how such behavior determines the behavior of the entire system as a whole. Unlikesystem dynamicsthe analyst determines the behavior of agents at the individual level, and global behavior arises as a result of the activities of many agents (bottom-up modeling).

Agent-based modeling includes elements of game theory, complex systems, multi-agent systems and evolutionary programming, Monte Carlo methods, and uses random numbers.

There are many definitions of the concept of agent. What all these definitions have in common is that an agent is some entity that has activity, autonomous behavior, can make decisions in accordance with a certain set of rules, can interact with the environment and other agents, and can also change (evolve). Multi-agent (or simply agent-based) models are used to study decentralized systems, the dynamics of which are not determined by global rules and laws, but, on the contrary, these global rules and laws are the result of the individual activity of group members. The goal of agent-based models is to gain an understanding of these global rules, the general behavior of the system, based on assumptions about the individual, private behavior of its individual active objects and the interaction of these objects in the system.

When creating an agent model, the logic of agent behavior and their interaction cannot always be expressed purely graphically; here it is often necessary to use program code. For agent-based modeling, the Swarm and RePast packages are used. An example of an agent-based model is a city development model.

IN modern world information technology, a decade is comparable to a century of progress in traditional technologies, But in simulation modeling, the ideas and solutions of the 60s of the last century are applied almost unchanged. On the basis of these ideas, software tools were developed back in the last century, which are still used with minor changes. Developing simulation models using these programs is a very complex and time-consuming task, accessible only to highly qualified specialists and requiring a lot of time. One of the developers of simulation models is Robert. Shannon wrote: “the development of even simple models requires 5 x 6 man-months and costs about 30,000 dollars, and complex ones cost two orders of magnitude more.” In other words, the complexity of building a complex simulation model traditional methods is estimated at one hundred person-years.

Simulation modeling using traditional methods is actually used by a narrow circle of professionals who must have not only deep knowledge in the application area for which the model is being built, but also deep knowledge in programming, probability theory and statistics.

In addition, problems in the analysis of modern real systems often require the development of models that do not fit into the framework of a single modeling paradigm. For example, when modeling a system with a predominant discrete type of events, it may be necessary to introduce variables that describe continuous characteristics of the environment. Discrete-event systems do not fit into the paradigm of a block model of data flows. In a system-dynamic model, there is often a need to take into account discrete events or model the individual properties of objects from heterogeneous groups. Therefore, the use of the above software does not meet modern requirements.

AnyLogic new generation simulation tool

AnyLogic - software For simulation modelingnew generation, developed Russian by The AnyLogic Company (formerly AJ Technologies, - English XJ Technologies). This tool greatly simplifies model development and analysis.

The AnyLogic package was created using the latest advances in information technology: object-oriented approach, standard elements UML Java programming language, etc. The first version of the package (Anylogic 4.0) was released in 2000. To date, Anylogic 6.9 version has been released.

The package supports everything known methods simulation modeling:

• Modeling of dynamic systems
• system dynamics;
• discrete event simulation;
• agent-based modeling.

Increases in computer performance and advances in information technology used in AnyLogic have made it possible to implement agent-based models containing tens and even hundreds of thousands of active agents

With AnyLogic it is possible to develop models in the following areas:

• production;
• logistics and supply chain;
• market and competition;
• business processes and service sector;
• healthcare and pharmaceuticals;
• asset and project management;
• telecommunications and information systems;
• social and ecological systems;
• pedestrian dynamics;
• defense.

Models. The Science and Art of Modeling

Modeling consists of three stages:

1. analysis of a real phenomenon and construction of its simplified model,
2. analysis of the constructed model by formal means (for example, with using a computer),
3. interpretation of the results obtained from the model in terms of the real phenomenon.

The first and third stages cannot be formalized; their implementation requires intuition, creative imagination and understanding of the essence of the phenomenon being studied, i.e., the qualities inherent in artists.

1.1. Process and system models

Modern concept scientific research consists in the fact that real objects are replaced by their simplified representations, abstractions chosen in such a way that they reflect the essence of the phenomenon, those properties of the original objects that are essential for solving the problem posed. The object constructed as a result of simplification is called a model.

Model this is a simplified analogue of a real object or phenomenon, representing the laws of behavior of the parts included in the object and their connections. Building a model and analyzing it is called modeling. IN scientific work modeling is one of the main elements of scientific knowledge.

IN practical activities The purpose of building a model is to solve some real world problem that is expensive or impossible to solve by experimenting with a real object.

Typically, the initial problem is to analyze an existing or proposed facility to make management decisions. For example, such an object may be a geographically distributed system of suppliers of raw materials, factories, warehouses of finished products and their transport connections. Another example is a port for unloading tankers with several terminals, tanks for loading oil, and a pool of oil tanks for exporting oil.

When constructing a model as a substitute for a real system, those aspects that are essential to solving a problem are highlighted, and those aspects that complicate the problem, make analysis very difficult or even impossible, are ignored. The problem of analysis is always posed in the world of real objects. In the example of a port, this may be the problem of optimal use of existing resources (organizing the movement of tankers in the port waters and the use of railway oil tanks) to organize the pumping of oil from tankers and sending it to consumers.

Making decisions on resource management by rebuilding a real system is not economically feasible. Another way to solve this problem is to formulate this problem for a model that includes the port layout, the volume of oil tanks, unloading speeds, the average intensity of tanker arrivals, the average tank turnaround time, etc.

Real objects and situations are usually complex, and models are needed in order to limit this complexity, make it possible to understand the situation, understand trends in the situation (predict the future behavior of the analyzed system), make a decision on changing the future behavior of the system and check it. If a model reflects the properties of a system that are essential for solving a specific problem, then analysis of the model allows one to derive characteristics that will explain the known and predict new properties of the real system under study without experiments with the system itself. Simulation has produced many impressive results in science, technology, and manufacturing.

1.2. Modeling to support adoption management decisions

Making smart decisions on rational organization and management modern systems becomes impossible on the basis of usual common sense or intuition due to the increasing complexity of systems. Back in 1969, the famous scientist, the founder of system dynamics, Jay Forrester, noted that on the basis of intuition, to control complex systems, incorrect decisions are more often chosen than correct ones, and this happens because in a complex system the cause-and-effect relationships of its parameters are not simple and clear. There are a large number of examples in the literature showing that people are unable to foresee the outcome of their actions in complex systems. An example is the cascading development of accidents in the power systems of the Northwestern United States on August 16, 2003 and in the Moscow region on May 25, 2005, which led to billions of losses and affected millions of people.

Increasing productivity and reliability, reducing costs and risks, assessing the sensitivity of the system to changes in parameters, optimizing the structure - all these problems arise both when operating existing and when designing new technical and organizational systems. The difficulty of understanding cause-and-effect relationships in a complex system leads to ineffective organization of systems, errors in their design, and high costs for eliminating errors. Today modeling is becoming the only practical effective means finding ways of optimal (or acceptable) solutions to problems in complex systems, a means of supporting responsible decision-making.

Modeling is especially important precisely when the system consists of many subsystems operating in parallel and interacting in time. Such systems are most often encountered in life. Every person thinks consistently, even very clever man can usually think about only one thing at a time. Therefore, understanding the simultaneous development over time of many processes influencing each other is a difficult task for humans. A simulation model helps to understand complex systems, predict their behavior and the development of processes in different situations and, finally, it makes it possible to change the parameters and even the structure of the model in order to direct these processes in the desired direction. Models allow you to evaluate the effect of planned changes, implement comparative analysis quality of possible solutions. Such modeling can be carried out in real time, which allows its results to be used in various technologies(from operational management to personnel training).

1.3. Levels of abstraction and model adequacy

The main paradox of modeling is that a simplified model of the system is studied, and the conclusions obtained are applied to the original real system with all its complexities. Is such a substitution legal?

When studying natural objects, the researcher abstracts from unimportant, random details that not only complicate, but can also obscure the phenomenon itself. For example, when analyzing an oil loading port, it is convenient to talk about tankers as containers from which a certain volume of oil is pumped at a certain speed, and not as ships with cabins, a certain number of crew, etc. Since all abstractions are incomplete and imprecise, we can say only about the approximate correspondence to the reality of the results obtained by studying the models. The correspondence of a model to the simulated object or phenomenon when solving a specific problem is called adequacy. Adequacy determines the possibility of using approximate results obtained from the model to solve a practical problem in the real world. Often the adequacy of a model is determined by a number of conditions and restrictions on the entities of the real world, and in order to use the analysis results obtained from the model, it is necessary to carefully check (or even ensure) these restrictions and conditions during the functioning of the real system (for example, to make processes in society manageable , a vertical of power is created). Since the adequacy of a model is determined only by the ability to use the model to solve a specific problem, an adequate model does not necessarily have to thoroughly reflect the processes occurring in the system being modeled (or, which is the same thing, the model does not have to display a “physically correct” picture of the world).

In Fig. Figure 1.3 presents a scale of levels of abstraction and examples of modeling problems in specific areas, approximately placed on this scale. On lower level abstractions solve problems in which individual physical objects, their individual behavior and physical connections are important, exact dimensions, distances, times. Examples of models belonging to this level of abstraction are models of pedestrian movement, models of movement of mechanical systems and their control systems. On average level problems of mass production and service are usually solved; individual objects are presented here, but their physical dimensions neglected; the values ​​of velocities and times are averaged or their stochastic values ​​are used. Examples of models at this level of abstraction are queuing models, traffic models, and resource management models. High level abstraction is used in developing models of complex systems in which the researcher abstracts from individual objects and their behaviors, considering only collections of objects and their integral, aggregated characteristics, trends in changes in values, and the influence on the dynamics of the system of causal feedbacks. Market and population dynamics models, environmental models and classic models epidemic spreads are built on this level of abstraction.

For each research goal, even for the same real-world object, its own model must be built that corresponds to this goal. To solve a specific problem, a model that adequately reflects the structure of the object and the laws by which it functions at the selected level of abstraction will be convenient. For example, it is obvious that planets are not material points, but with such an abstraction within the framework of Newton’s theory of gravity, it is possible to predict quite accurately the characteristics of the movement of planets. However, this model requires refinement to calculate the trajectories of satellites and rockets. To solve the problem of optimal use of transport, it is necessary detailed maps, distances and times. The fact that the Earth appears flat on the map is not essential for solving transport problems.

Although there are well-established approaches to choosing the level of abstraction and reasonable explanations given choice to build sufficiently adequate models for solving many types of problems, yet there is no general methodology for constructing a model with the required level of adequacy. As a recommendation for choosing an abstraction level, we can only say the following. It is necessary to start with the simplest model, reflecting only the most significant (from the researcher’s point of view) aspects of the system being modeled. After discovering the inadequacy of the model, i.e., its inapplicability to solving the problem posed, individual substructures and processes of the model should be implemented in more detail, at a lower level of abstraction. One can be confident that the development of a sequence of increasingly complex and detailed models can lead to acceptable adequacy for solving any specific problem.

about the modeled object. For example, no model can represent all the characteristics of planet Earth. On the other hand, it is also obvious that any specific task will not require knowledge of all these characteristics for its solution.

Of course, it is possible to build models that abstract from essential aspects of reality. Such models will be inadequate and the conclusions drawn from these models will be incorrect.

Obviously, no model ever provides complete knowledge

1.4. Modeling as science and art

Modeling as a type of professional activity is associated with the analysis of real systems and processes of a very different nature. When developing a model in a specific area, a modeling specialist must connect the vocabulary of this area with modeling terminology, identify subsystems and their connections in a real system, determine the parameters of subsystems and their dependencies, and select the appropriate level of abstraction when building a model of each subsystem. He must correctly select the appropriate mathematical apparatus and use it correctly, be able to implement model elements, their connections and logical relationships using suitable means in the modeling environment, understand the limitations when interpreting modeling results, and master methods of verification and calibration of models. All this makes modeling a serious scientific activity.

But modeling is also an art, and to a much greater extent than, for example, programming. There is no universal general method for constructing adequate models. Although adequate models have long been developed for many physical phenomena, sufficient for solving a wide class of problems in the analysis of dynamic systems (for example, the relationship between speed, distance and time when analyzing the free movement of objects in space), however, for industrial, social, biological systems, as well as many technical systems when constructing a model, you need to show ingenuity, knowledge of mathematics, understanding of the processes in the system, the essence of abstraction, etc. Building a model creative creative activity is akin to art, it requires intuition, deep penetration into the nature of the phenomenon and the problem being solved.

Types of models

Models can be classified according to various criteria: static and dynamic, continuous and discrete, deterministic and stochastic, analytical and simulation, etc.

2.1. Static and dynamic models

Static models operate with characteristics and objects that do not change over time. IN dynamic In models that are usually more complex, the change in parameters over time is significant. The model of an oil loading port is dynamic: it models the time behavior of individual system objects: the movement of tankers in the port water area, the movement of tanks at the berth, the oil level in storage tanks.

Static models usually deal with steady-state processes, balance-type equations, and limit stationary characteristics. Modeling dynamic systems consists of simulating the rules for a system's transition from one state to another over time. The state of the system is understood as a set of values ​​of essential parameters and system variables. A change in the state of a system over time in dynamic systems is a change in the values ​​of system variables in accordance with the laws that determine the relationships of variables and their dependence on each other in time.

AnyLogic package supports the development and analysis of dynamic models. This tool contains tools for analytically specifying equations that describe the change in variables over time, makes it possible to take into account model time and contains means for its promotion, there is also a language for expressing logic and describing the progress of systems under the influence of any type of event, in particular, the exhaustion of a given timeout time interval.

2.2. Continuous, discrete and hybrid models

Real physical objects operate in continuous time, and to study many problems of physical systems, their models must be continuous. The state of such models changes continuously over time. These are models of movement in real coordinates, models of chemical production, etc. The processes of movement of objects and the processes of pumping oil in the model of an oil loading port are continuous.

At a higher level of abstraction, for many systems, models in which transitions of the system from one state to another can be considered instantaneous, occurring at discrete moments in time, are adequate. Such systems are called discrete. An example of an instantaneous transition is a change in the number of bank customers or the number of customers in a store. It is obvious that discrete systems are an abstraction; processes in nature do not occur instantly. In a real store, a real customer enters for some time, he may be stuck in the door, hesitating whether to enter or not, and there is always a continuous sequence of his position while passing the store doors. However, when constructing models store to estimate, for example, the average length of the queue at the cash register for a given flow of customers and known characteristics of customer service by the cashier, you can abstract from these secondary phenomena and consider the system discrete: the results of the analysis of the resulting discrete model are usually quite accurate for making informed management decisions for similar systems. In the model of an oil loading port, for example, transitions of traffic lights at the entrance to the harbor from the “prohibited” state to the “allowed” state can be considered instantaneous. At an even higher level of abstraction, systems analysis also uses continuous models, as is typical for system dynamics. Traffic flows on highways, consumer demand, and the spread of infection among the population are often conveniently described using the interdependencies of continuous variables that describe quantities, the intensity of changes in these quantities, and the degree of influence of some quantities on others. The relationships between such variables are usually expressed by differential equations.

In many cases, both types of processes are present in real systems, and if both of them are essential for the analysis of the system, then in the model some processes should be represented as continuous, others as discrete. Such models with mixed type processes are called hybrid. For example, if when analyzing the functioning of a store, not only the number of customers is significant, but also their spatial position and the movement of customers, then the model in this case should represent a mixture of continuous and discrete processes, i.e. it is a hybrid model. Another example is the operating model of a large bank. The flow of investments, receipt and issuance of loans in normal mode is described by a set of differential and algebraic equations, i.e. the model is continuous. However, there are situations, such as default (a discrete event), which results in panic among the population, and from that moment on the system is described by a completely different continuous model. Model this process at the level of abstraction at which we want to adequately describe both modes of bank operation and the transition between modes, it must include both a description of continuous processes and discrete events, as well as their interdependencies.

AnyLogic package supports the description of both continuous and discrete processes, as well as the construction of hybrid models. AnyLogic allows you to implement the model, in fact, at any level of abstraction (detail). Executing hybrid models in AnyLogic based on modern results of the theory of hybrid dynamic systems.

2.3. Deterministic and stochastic models

When modeling complex real systems, the researcher often encounters situations in which random influences play a significant role. Stochastic models, unlikedeterministic,take into account the probabilistic nature of the parameters of the modeled object. For example, in a model of an oil loading port, the exact moments when tankers arrive at the port cannot be determined. These moments are random variables, therefore this model is stochastic: the values ​​of the model variables, which depend on the implementation of random variables, themselves become random variables. Analysis similar models is performed on a computer based on statistics collected during simulation experiments during repeated runs of the model for different values ​​of the initial random variables, selected in accordance with their statistical characteristics.

AnyLogic contains tools for generating random variables and statistical processing of the results of computer experiments. AnyLogic includes random number generators for a variety of distributions. The model developer can also use his own random variable generator, built in accordance with observational data on the real system.

2.4. Analytical and simulation models

The use of abstractions when solving problems using models often involves the use of one or another mathematical apparatus. The simplest mathematical models are algebraic relations, and the analysis of the model often comes down to the analytical solution of these equations. Some dynamic systems can be described in a closed form, for example, in the form of systems of linear differential and algebraic equations and the solution can be obtained analytically. This kind of modeling is called analytical. In analytical modeling, the functioning processes of the system under study are written in the form of algebraic, integral, differential equations and logical relations, and in some cases the analysis of these relations can be performed using analytical transformations. Modern means analytical modeling support are spreadsheet type MS Excel.

However, the use of purely analytical methods when modeling real systems faces serious difficulties: classical mathematical models that allow analytical solutions are in most cases inapplicable to real problems. For example, in a model of an oil loading port, it is impossible to construct an analytical formula for estimating the equipment utilization rate, if only because there are stochastic processes in the system, there are priorities for processing requests for the use of resources, internal parallelism in processing subsystems, work interruptions, etc. Even if the analytical the model can be constructed, for real systems they are often significantly nonlinear, and purely mathematical relations in them are usually supplemented by logical-semantic operations, and for them there is no analytical solution. Therefore, when analyzing systems, there is often a choice between a model that is a realistic analogue of the real situation, but cannot be solved analytically, and a simpler, but inadequate model, the mathematical analysis of which is possible.

With imitation In modeling, the structure of the modeled system - its subsystems and connections - is directly represented by the structure of the model, and the process of functioning of the subsystems, expressed in the form of rules and equations connecting variables, is simulated on a computer. AnyLogic is a framework simulation modeling. Various means of specification and analysis of results available in AnyLogic , allow you to build models that simulate the operation of the simulated system with virtually any desired degree of adequacy, and analyze the model on a computer without carrying out analytical transformations.

Simulation modeling

3.1. What is simulation modeling

Simulation modeling — This is the development and execution on a computer of a software system that reflects the structure and functioning (behavior) of a simulated object or phenomenon over time. like this software system called a simulation model of this object or phenomenon. Objects and entities of the simulation model represent objects and entities of the real world, and the connections of the structural units of the modeling object are reflected in the interface connections of the corresponding model objects. Thus,simulation model — it is a simplified likeness of a real system, either existing or one that is supposed to be created in the future. A simulation model is usually represented by a computer program; the execution of the program can be considered an imitation of the behavior of the original system over time.

In Russian-language literature the term"modeling" corresponds to American"modeling" and it makes sense to create model and its analysis, and under the term"model" is understood as an object of any nature that simplifies the system under study. Words"simulation modeling" And "computational (computer) experiment" withcorrespond to the English term"simulation". These terms imply the development of a model exactly how computer program and execution of this program on a computer.

So, simulationthis is the activity of developing software models of real or hypothetical systems, executing these programs on a computer and analyzing the results of computer experiments to study the behavior of models. Simulation modeling has significant advantages over analytical modeling in cases where:

• the relationships between the variables in the model are nonlinear and therefore analytical models are difficult or impossible to construct;
• the model contains stochastic components;
• to understand the behavior of the system, visualization of the dynamics of the processes occurring in it is required;
• the model contains many parallel functioning interacting components.

In many cases, simulation is the only way to gain insight into and analyze the behavior of a complex system.

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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.

A system is viewed as consisting of many interrelated elements combined to perform a 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. Estimates alternative solutions according to 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(V 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 limitations) 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 finds wide application in the study and management of complex discrete systems (CDS) and the processes occurring in them. Such systems include economic and industrial facilities, seaports, 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 the numerical method of conducting computer experiments with mathematical models that describe the behavior of complex systems over a long period 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, testing effective strategies control, 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.

Simulation means that successive moments in time are specified and the state of the model is calculated by the computer sequentially at each of these points 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 - 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 in next moment time according to the current state, control vectors and 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 easier implementation, but the accuracy is less and there may be empty (that is, redundant) 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 currently the 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.