simulation model- a description of the system and its behavior, which can be implemented and studied in the course of operations on a computer.

Simulation modeling is most often used to describe the properties of a large system, provided that the behavior of its constituent objects is very simply and clearly stated. The mathematical description is then reduced to the level of static processing of the simulation results when finding the macroscopic characteristics of the system. Such a computer experiment actually claims to reproduce a full-scale experiment. 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 a method for solving the resulting model has not been developed. In this case, the mathematical model is replaced by a simulator or simulation model. Simulation modeling allows you to test hypotheses, explore the influence of various factors and parameters.

Simulation- This is a method that allows you to build models that describe processes as they would take place in reality.

Such a model can be "played" in 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. Based on these data, fairly stable statistics can be obtained. Experimenting with a model is called imitation.

Imitation– comprehension of the essence of the phenomenon without experiments on the object.

Imitation as a method for solving non-trivial problems was first developed in connection with the creation of computers in 1950-1960. Varieties of simulation: Monte Carlo method (static test method); simulation modeling method (static modeling).

The demand for simulation modeling: 1) experimenting on a real object is expensive and impossible; 2) it is impossible to build an analytical model: the system has time, causal relationships, consequences, non-linearities, random variables; 3) it is necessary to simulate the behavior of the system in time.

The purpose of simulation- reproduction of the behavior of the system under study based on the results of the analysis of the most significant relationships between its elements (development of a simulator of the studied subject area for conducting various experiments).

Types of simulation modeling.

Agent based modeling- a relatively new (1990 - 2000) direction in simulation modeling, which is used to study decentralized systems, the dynamics of which are determined not by global rules and laws (as in other modeling paradigms), but vice versa. When these global rules and laws are the result of the individual activity of group members. The purpose of agent models is to get an idea about these global rules, the general behavior of the system based on assumptions about the individual, particular behavior of its individual active objects and the interactions of these objects in the system. Agent - a certain entity with activity, autonomous behavior; can make decisions in accordance with a certain set of rules, interact with the environment, and also independently change.

Discrete event simulation- 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", "movement with a load", "unloading", etc. Discrete-event modeling is the most developed and has a huge scope of applications - from logistics and queuing systems to transport and production systems. This type of simulation is most suitable for modeling production processes. Founded by Jeffrey Gordon in the 1960s.

System Dynamics- for the system under study, graphic diagrams of causal relationships and global influences of some parameters on others in time are constructed, and then the model created on the basis of these diagrams is simulated on a computer. In essence, 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. With the help of system dynamics, models of business processes, city development, production models, population dynamics, ecology and epidemic development are built. The method was founded by Forrester in 1950.

Some areas of application of simulation are: business processes, combat, population dynamics, traffic, IT infrastructure, project management, ecosystems. Popular computer simulation systems: AnyLogic, Aimsun, Arena, eM-Plant, Powersim, GPSS.

Simulation modeling allows you to simulate the behavior of a system over time. Moreover, the advantage is that the time in the model can be controlled: slow down in the case of fast processes and speed up for modeling systems with slow variability. It is possible to imitate the behavior of those objects with which real experiments are expensive, impossible and dangerous.

Model An object is any other object whose individual properties completely or partially coincide with the properties of the original one.

It should be clearly understood that an exhaustively complete model cannot be. She always limited and should only correspond to the goals of modeling, reflecting exactly as many properties of the original object and in such completeness as is necessary for a particular study.

Source object can be either real, or imaginary. We deal with imaginary objects in engineering practice at the early stages of designing technical systems. Models of objects not yet embodied in real developments are called anticipatory.

Modeling Goals

The model is created for the sake of research, which is either impossible, or expensive, or simply inconvenient to carry out on a real object. There are several goals for which models and a number of main types of studies are created:

1. Model as a means of understanding helps to identify:

• interdependencies of variables;
• the nature of their change over time;
• existing patterns.

When compiling the model, the structure of the object under study becomes more understandable, important cause-and-effect relationships are revealed. In the process of modeling, the properties of the original object are gradually divided into essential and secondary from the point of view of the formulated requirements for the model. We are trying to find in the original object only those features that are directly related to the side of its functioning that interests us. In a sense, all scientific activity is reduced to the construction and study of models of natural phenomena.

1. Model as a means of forecasting allows you to learn how to predict behavior and control an object by testing various control options on the model. Experimenting with a real object is often, at best, inconvenient, and sometimes simply dangerous or even impossible due to a number of reasons: the long duration of the experiment, the risk of damaging or destroying the object, the absence of a real object in the case when it is still being designed.
2. The built models can be used to finding optimal ratios of parameters, studies of special (critical) modes of operation.
3. The model may also in some cases replace the original object when training, for example, be used as a simulator in training personnel for subsequent work in a real environment, or act as an object of study in a virtual laboratory. Models implemented in the form of executable modules are also used as simulators of control objects in bench tests of control systems, and, at the early stages of design, replace future hardware-based control systems themselves.

Simulation

In Russian, the adjective "imitation" is often used as a synonym for the adjectives "similar", "similar". Among the phrases "mathematical model", "analog model", "statistical model", a pair - "simulation model", which appeared in the Russian language, probably as a result of inaccurate translation, gradually acquired a new meaning different from its original one.

Indicating that this model is a simulation model, we usually emphasize that, unlike other types of abstract models, this model retains and easily recognizes such features of the modeled object as structure, connections between components way of transmitting information. Simulation models are also usually associated with the requirement illustrations of their behavior with the help of graphic images accepted in this application area. It is not without reason that imitative models are usually called enterprise models, environmental and social models.

Simulation = computer simulation (synonyms). Currently, for this type of modeling, the synonym "computer modeling" is used, thereby emphasizing that the tasks being solved cannot be solved using standard means of performing computational calculations (calculator, tables or computer programs, replacing these means).

A simulation model is a special software package that allows you to simulate the activity of any complex object, in which:

• the structure of the object is reflected (and presented graphically) with links;
• running parallel processes.

To describe the behavior, both global laws and local laws obtained on the basis of field experiments can be used.

Thus, simulation modeling involves the use computer technology to simulate various processes or operations (i.e., their simulation) performed by real devices. Device or process commonly referred to system . For scientific research system, we resort to certain assumptions regarding its functioning. These assumptions, usually in the form of mathematical or logical relationships, constitute a model from which one can get an idea of ​​the behavior of the corresponding system.

If the relationships that form the model are simple enough to obtain accurate information on the issues of interest to us, then mathematical methods can be used. This kind of solution is called analytical. However, most existing systems are very complex, and it is impossible to create a real model for them, described analytically. Such models should be studied by simulation. In modeling, a computer is used to numerically evaluate the model, and with the help of the obtained data, its real characteristics are calculated.

From the point of view of a specialist (informatics-economist, mathematician-programmer or economist-mathematician), simulation modeling of a controlled process or controlled object is a high-level information technology, which provides two kinds of actions performed using the computer:

• work on the creation or modification of a simulation model;
• operation of the simulation model and interpretation of the results.

Simulation (computer) modeling of economic processes is usually used in two cases:

• to manage a complex business process, when the simulation model of a managed economic object is used as a tool in the contour of an adaptive control system created on the basis of information (computer) technologies;
• when conducting experiments with discrete-continuous models of complex economic objects to obtain and track their dynamics in emergency situations associated with risks, the full-scale modeling of which is undesirable or impossible.

Typical simulation tasks

Simulation modeling can be applied in the most various fields activities. Below is a list of tasks for which modeling is especially effective:

• design and analysis of production systems;
• determination of requirements for equipment and protocols of communication networks;
• determination of equipment requirements and software various computer systems;
• design and analysis of the operation of transport systems, such as airports, highways, ports and subways;
• evaluation of projects for the creation of various queuing organizations, such as order processing centers, fast food establishments, hospitals, post offices;
• modernization of various business processes;
• defining policies in inventory management systems;
• analysis of financial and economic systems;
• assessment of various weapons systems and requirements for their logistics.

Model classification

The following were chosen as the basis for classification:

• a functional feature that characterizes the purpose, purpose of building a model;
• the way the model is presented;
• time factor reflecting the dynamics of the model.

Function	Model class	Example
Descriptions Explanations		Demo Models Educational posters
Predictions	Scientific and technical Economic	Mathematical models of processes Models of developed technical devices
measurements Processing of empirical data		Model ship in the pool Aircraft model in a wind tunnel
Interpreting		Military, economic, sports, business games
criterial	Exemplary (reference)	shoe model clothing model

In accordance with it, the models are divided into two large groups: material and abstract (non-material). Both material and abstract models contain information about the original object. Only for a material model, this information has a material embodiment, and in an intangible model, the same information is presented in abstract form(thought, formula, drawing, scheme).

Material and abstract models can reflect the same prototype and complement each other.

Models can be roughly divided into two groups: material And ideal, and, accordingly, to distinguish between subject and abstract modeling. The main varieties of subject modeling are physical and analog modeling.

Physical it is customary to call such modeling (prototyping), in which a real object is associated with its enlarged or reduced copy. This copy is created on the basis of the theory of similarity, which allows us to assert that the required properties are preserved in the model.

In physical models, in addition to geometric proportions, for example, the material or color scheme of the original object, as well as other properties necessary for a particular study, can be saved.

analog modeling is based on replacing the original object with another object physical nature with similar behavior.

Both physical and analog modeling as the main method of research involves natural experiment with the model, but this experiment turns out to be in some sense more attractive than the experiment with the original object.

Ideal models are abstract images of real or imaginary objects. There are two types of ideal modeling: intuitive and iconic.

About intuitive modeling is said when they cannot even describe the model used, although it exists, but they are taken to predict or explain the world around us with its help. We know that living beings can explain and predict phenomena without the visible presence of a physical or abstract model. In this sense, for example, the life experience of each person can be considered his intuitive model of the world around him. When you are about to cross a street, you look to the right, to the left, and intuitively decide (usually correctly) whether you can go. How the brain copes with this task, we simply do not yet know.

Iconic called modeling, using signs or symbols as models: diagrams, graphs, drawings, texts in various languages, including formal, mathematical formulas and theories. An obligatory participant in sign modeling is an interpreter of a sign model, most often a person, but a computer can also cope with the interpretation. Drawings, texts, formulas in themselves have no meaning without someone who understands them and uses them in their daily activities.

The most important type of sign modeling is math modeling. Abstracting from the physical (economic) nature of objects, mathematics studies ideal objects. For example, using the theory differential equations you can study the already mentioned electrical and mechanical vibrations in the most general view and then apply the acquired knowledge to study objects of a specific physical nature.

Types of mathematical models:

Computer model - this is a software implementation of a mathematical model, supplemented by various utility programs (for example, those that draw and change graphic images in time). The computer model has two components - software and hardware. The software component is also an abstract sign model. This is just another form of an abstract model, which, however, can be interpreted not only by mathematicians and programmers, but also by a technical device - a computer processor.

A computer model exhibits the properties of a physical model when it, or rather its abstract components - programs, are interpreted by a physical device, a computer. The combination of a computer and a simulation program is called " electronic equivalent of the object under study". A computer model as a physical device can be part of test benches, simulators and virtual laboratories.

Static model describes the immutable parameters of an object or a one-time slice of information on a given object. Dynamic Model describes and investigates time-varying parameters.

The simplest dynamic model can be described as a system of linear differential equations:

all modeled parameters are functions of time.

Deterministic Models

There is no place for chance.

All events in the system occur in a strict sequence, exactly in accordance with the mathematical formulas that describe the laws of behavior. Therefore, the result is precisely defined. And the same result will be obtained, no matter how many experiments we conduct.

Probabilistic models

Events in the system do not occur in an exact sequence, but randomly. But the probability of occurrence of this or that event is known. The result is not known in advance. When conducting an experiment, different results can be obtained. These models accumulate statistics over many experiments. Based on these statistics, conclusions are drawn about the functioning of the system.

Stochastic Models

When solving many problems of financial analysis, models are used that contain random variables whose behavior cannot be controlled by decision makers. Such models are called stochastic. The use of simulation allows you to draw conclusions about the possible results based on the probability distributions of random factors (values). Stochastic simulation often called the Monte Carlo method.

Stages of computer simulation
(computational experiment)

It can be represented as a sequence of the following basic steps:

1. STATEMENT OF THE PROBLEM.

Description of the task. The purpose of the simulation. Formalization of the task: structural analysis of the system and processes occurring in the system; building a structural and functional model of the system (graphic); highlighting the properties of the original object that are essential for this study

2. DEVELOPMENT OF THE MODEL.

Construction of a mathematical model. Choice of modeling software. Design and debugging of a computer model (technological implementation of the model in the environment)

3. COMPUTER EXPERIMENT.

Assessment of the adequacy of the constructed computer model (satisfaction of the model with the goals of modeling). Drawing up a plan of experiments. Conducting experiments (studying the model). Analysis of the results of the experiment.

4. ANALYSIS OF SIMULATION RESULTS.

Generalization of the results of experiments and conclusion about the further use of the model.

According to the nature of the formulation, all tasks can be divided into two main groups.

TO first group include tasks that require explore how the characteristics of an object will change with some impact on it. This kind of problem statement is called "what happens if…?" For example, what happens if you double your utility bills?

Some tasks are formulated somewhat more broadly. What happens if you change the characteristics of an object in a given range with a certain step? Such a study helps to trace the dependence of the object parameters on the initial data. Very often it is required to trace the development of the process in time. This extended problem statement is called sensitivity analysis.

Second group tasks has the following generalized formulation: what effect should be made on the object so that its parameters satisfy some given condition? This problem statement is often referred to as "How do you make...?"

How to make sure that "both the wolves are fed and the sheep are safe."

The largest number of modeling tasks, as a rule, is complex. In such problems, a model is first built for one set of initial data. In other words, the problem “what happens if ...?” is solved first. Then the study of the object is carried out while changing the parameters in a certain range. And, finally, according to the results of the study, the parameters are selected so that the model satisfies some of the designed properties.

It follows from the above description that modeling is a cyclic process in which the same operations are repeated many times.

This cyclicity is due to two circumstances: technological, associated with "unfortunate" mistakes made at each of the considered stages of modeling, and "ideological", associated with the refinement of the model, and even with its rejection, and the transition to another model. Another additional "outer" loop can appear if we want to expand the scope of the model, and change the inputs that it must correctly account for, or the assumptions under which it must be fair.

Summing up the results of the simulation may lead to the conclusion that the planned experiments are not enough to complete the work, and possibly to the need to refine the mathematical model again.

Planning a computer experiment

In experiment design terminology, the input variables and structural assumptions that make up the model are called factors, and the output performance measures are called responses. The decision about which parameters and structural assumptions to consider as fixed indicators, and which as experimental factors, depends more on the purpose of the study, and not on the internal form of the model.

More about planning computer experiment read for yourself (pp. 707–724; pp. 240–246).

Practical methods of planning and conducting a computer experiment are considered in practical classes.

Limits of possibilities of classical mathematical methods in economics

Ways to study the system

Experiment with a real system or with a model system? If it is possible to physically change the system (if it is cost-effective) and put it into operation in new conditions, it is best to do just that, since in this case the question of the adequacy of the result obtained disappears by itself. However, such an approach is often not feasible, either because it is too costly to implement or because it has a devastating effect on the system itself. For example, the bank is looking for ways to reduce costs, and for this purpose it is proposed to reduce the number of tellers. If you try it in action new system– with fewer cashiers, this can lead to long delays in serving customers and their abandonment of the bank. Moreover, the system may not actually exist, but we want to explore its various configurations in order to choose the most effective method execution. Communication networks or strategic nuclear weapons systems are examples of such systems. Therefore, it is necessary to create a model representing the system and examine it as a substitute for the real system. When using a model, the question always arises - whether it really accurately reflects the system itself to such an extent that it is possible to make a decision based on the results of the study.

Physical model or mathematical model? When we hear the word "model," most of us think of cockpits set up outside the planes on training grounds and used for pilot training, or miniature supertankers moving around in a pool. These are all examples of physical models (also called iconic or figurative). They are rarely used in operations research or systems analysis. But in some cases, the creation of physical models can be very effective in the study of technical systems or control systems. Examples include scale tabletop models of loading and unloading systems and at least one full-scale physical model of a fast food restaurant in a large store that involved real customers. However, the vast majority of created models are mathematical. They represent the system through logical and quantitative relationships, which are then processed and modified to determine how the system responds to change, more precisely, how it would respond if it actually existed. Probably the most simple example mathematical model is the known relation S=V/t, Where S- distance; V– movement speed; t- travel time. Sometimes such a model may be adequate (for example, in the case of a space probe directed to another planet, when it reaches the flight speed), but in other situations it may not correspond to reality (for example, transport connection during rush hours on an urban congested freeway).

Analytical solution or simulation? To answer questions about the system that a mathematical model represents, it is necessary to establish how this model can be built. When the model is simple enough, it is possible to calculate its relations and parameters and obtain an accurate analytical solution. However, some analytical solutions can be extremely complex and require huge computer resources. The inversion of a large nonsparse matrix is ​​a familiar example of a situation where there is a known analytical formula in principle, but in this case it is not so easy to obtain a numerical result. If, in the case of a mathematical model, an analytical solution is possible and its calculation seems to be effective, it is better to study the model in this way, without resorting to simulation. However, many systems are extremely complex; they almost completely exclude the possibility of an analytical solution. In this case, the model should be studied using simulation, i.e. repeated testing of the model with the desired input data to determine their impact on the output criteria for evaluating the performance of the system.

Simulation is perceived as a "method of last resort", and there is a grain of truth in this. However, in most situations, we quickly realize the need to resort to this particular tool, since the systems and models under study are quite complex and need to be represented in an accessible way.

Suppose we have a mathematical model that needs to be investigated using simulation (hereinafter referred to as the simulation model). First of all, we need to come to a conclusion about the means of its study. In this regard, simulation models should be classified according to three aspects.

Static or dynamic? A static simulation model is a system at a certain point in time, or a system in which time simply does not play any role. Examples of a static simulation model are Monte Carlo models. A dynamic simulation model represents a system that changes over time, such as a conveyor system in a factory. Having built a mathematical model, it is necessary to decide how it can be used to obtain data about the system it represents.

Deterministic or stochastic? If the simulation model does not contain probabilistic (random) components, it is called deterministic. In a deterministic model, the result can be obtained when all input quantities and dependencies are given for it, even if in this case a large amount of computer time is required. However, many systems are modeled with multiple random component inputs, resulting in a stochastic simulation model. Most queuing and inventory management systems are modeled this way. Stochastic simulation models produce a result that is random in itself and therefore can only be considered as an estimate of the true characteristics of the model. This is one of the main disadvantages of modeling.

Continuous or discrete? Generally speaking, we define discrete and continuous models in a similar way to the previously described discrete and continuous systems. It should be noted that a discrete model is not always used to model a discrete system, and vice versa. Whether it is necessary to use a discrete or continuous model for a particular system depends on the objectives of the study. Thus, a traffic flow model on a highway will be discrete if you need to take into account the characteristics and movement of individual cars. However, if the vehicles can be considered collectively, the traffic flow can be described using differential equations in a continuous model.

The simulation models that we will consider next will be discrete, dynamic, and stochastic. In what follows, we will refer to them as discrete-event simulation models. Since deterministic models are a special kind of stochastic models, the fact that we limit ourselves to such models does not introduce any generalization errors.

Existing approaches to visual modeling of complex dynamic systems.
Typical simulation systems

Simulation modeling on digital computers is one of the most powerful means of research, in particular, complex dynamic systems. Like any computer simulation, it makes it possible to carry out computational experiments with systems that are still being designed and to study systems with which full-scale experiments, due to safety or high cost reasons, are not appropriate. At the same time, due to its closeness in form to physical modeling, this research method is accessible to a wider range of users.

At present, when the computer industry offers a variety of modeling tools, any qualified engineer, technologist or manager should be able to not only model complex objects, but to model them using modern technologies implemented in the form of graphical environments or visual modeling packages.

“The complexity of the systems being studied and designed leads to the need to create a special, high-quality new technology research using the apparatus of imitation - reproduction on a computer by specially organized systems of mathematical models of the functioning of the designed or studied complex ”(N.N. Moiseev. Math problems system analysis. M.: Nauka, 1981, p. 182).

Currently, there is a great variety of visual modeling tools. We will agree not to consider in this work packages oriented to narrow applied areas (electronics, electromechanics, etc.), since, as noted above, the elements complex systems usually belong to different application areas. Among the remaining universal packages (oriented to a certain mathematical model), we will not pay attention to packages oriented to mathematical models other than a simple dynamical system (partial differential equations, statistical models), as well as purely discrete and purely continuous. Thus, the subject of consideration will be universal packages that allow modeling structurally complex hybrid systems.

They can be roughly divided into three groups:

• "block modeling" packages;
• "physical modeling" packages;
• packages focused on the scheme of a hybrid machine.

This division is conditional, primarily because all these packages have much in common: they allow you to build multi-level hierarchical functional diagrams, support OOM technology to one degree or another, and provide similar visualization and animation capabilities. The differences are due to which of the aspects of a complex dynamical system is considered the most important.

"block modeling" packages focused on the graphic language of hierarchical block diagrams. Elementary blocks are either predefined or can be constructed using some special lower level auxiliary language. A new block can be assembled from existing blocks using oriented links and parametric tuning. The predefined elementary blocks include purely continuous, purely discrete, and hybrid blocks.

The advantages of this approach include, first of all, the extreme simplicity of creating not very complex models, even by a not very trained user. Another advantage is the efficiency of the implementation of elementary blocks and the simplicity of constructing an equivalent system. At the same time, when creating complex models, one has to build rather cumbersome multilevel block diagrams that do not reflect the natural structure of the system being modeled. In other words, this approach works well when there are suitable building blocks.

Most well-known representatives"block modeling" packages are:

• SIMULINK subsystem of the MATLAB package (MathWorks, Inc.; http://www.mathworks.com);
• EASY5 (Boeing)
• SystemBuild subsystem of the MATRIXX package (Integrated Systems, Inc.);
• VisSim (Visual Solution; http://www.vissim.com).

"Physical Simulation" packages allow the use of undirected and streaming relationships. The user can define new block classes himself. The continuous component of the behavior of an elementary block is given by a system of algebraic differential equations and formulas. The discrete component is specified by the description of discrete events (events are specified by a logical condition or are periodic), upon occurrence of which instantaneous assignments of new values ​​to variables can be performed. Discrete events can propagate through special links. Changing the structure of equations is possible only indirectly through the coefficients on the right-hand sides (this is due to the need for symbolic transformations when passing to an equivalent system).

The approach is very convenient and natural for describing typical blocks of physical systems. The disadvantages are the need for symbolic transformations, which sharply narrows the possibilities of describing hybrid behavior, as well as the need to numerically solve a large number algebraic equations, which greatly complicates the task of automatically obtaining a reliable solution.

Physical modeling packages include:

• 20 SIM(Controllab Products B.V; http://www.rt.el.utwente.nl/20sim/);
• Dymola(Dymasim; http://www.dynasim.se);
• Omola, OmSim(Lund University; http://www.control.lth.se/~case/omsim.html);

As a generalization of the experience of developing systems in this direction, an international group of scientists developed a language Modelica(The Modelica Design Group; http://www.dynasim.se/modelica) offered as a standard for exchanging model descriptions between different packages.

Packages based on the use of the hybrid machine scheme, make it possible to describe hybrid systems with complex switching logic very clearly and naturally. The need to determine an equivalent system at each switch makes it necessary to use only oriented connections. The user can define new block classes himself. The continuous component of the behavior of an elementary block is given by a system of algebraic differential equations and formulas. The redundancy of the description when modeling purely continuous systems should also be attributed to the disadvantages.

This package includes Shift(California PATH: http://www.path.berkeley.edu/shift) as well as the native package Model Vision Studio. The Shift package is more focused on describing complex dynamic structures, while the MVS package is more focused on describing complex behaviors.

Note that there is no insurmountable gap between the second and third directions. In the end, the impossibility of sharing them is due only to today's computing capabilities. At the same time, the general ideology of building models is practically the same. In principle, a combined approach is possible, when in the structure of the model the constituent blocks, the elements of which have a purely continuous behavior, should be singled out and transformed once to an equivalent elementary one. Further, the cumulative behavior of this equivalent block should be used in the analysis of the hybrid system.

When creating a technique for simulation modeling, I needed to understand the terms. The problem was that conventional terms were not suitable for describing the statistical data collected during the simulation. Terms: process And process instances were unacceptable because I could not work in the Aristotelian paradigm. Aristotle's paradigm doesn't fit with the hardware I used. At the same time, the practical application of this technique was simple - modeling and imitation of business objects in order to adopt management decisions. The program created a virtual object, the description of which consisted of a description of scenarios and their interaction. Scenarios were run inside the program, and resources and their interactions were modeled.

Let me remind you that:

Simulation- a method of studying objects, based on the fact that the object under study is replaced by a simulating object. Experiments are carried out with a simulating object (without resorting to experiments on a real object) and as a result, information about the object under study is obtained. The imitating object in this case is an information object.

The purpose of simulation- obtaining approximate knowledge about a certain parameter of an object without directly measuring its values. It is clear that this is necessary if and only if the measurement is impossible, or it costs more than simulation. At the same time, to study this parameter, we can use other known parameters of the object and the model of its design. Assuming that the design model accurately describes the object, it is assumed that the statistical distributions of the parameter values ​​of the modeling object obtained during the simulation will coincide to some extent with the distribution of the parameter values ​​of the real object.

It is clear that the mathematical apparatus that was applied is statistical mathematics. It is clear that mathematical statistics does not use the terms instances and types. It works with objects and sets. As a result, to write the methodology, I was forced to use the logical paradigm on the basis of which the ISO 15926 standard was created. Its basis is the presence of objects, classes and classes of classes.

Definition examples:

Operation

Event

The figure shows the relationship between entities: events are grouped into event classes. The event class is described using the "Events" directory object. Events of one class are depicted on process diagrams using graphic elements. Based on the "Events" directory object, the simulation engine creates simulation events.

Process

1. Simulated process: The sequence of simulated operations. It is convenient to present the description of this sequence in the form of a Gantt chart. Description contains events. For example, events: “process start” and “process end”.
2. Simulating process: An object created to simulate a simulated process. This object is created in the computer's memory during the simulation.
3. Class of simulated processes: A set of simulated processes, united by some feature. The most common union is the union of processes that have a common model. A process diagram made in any modeling notation can be used as a model: Process, Procedure, EPC, BPMN.
4. Class of simulating processes: A set of mock processes created within the mock to mimic the activity.
5. Process ( as an object in a directory): Directory object “Processes.
6. Process ( process diagram): Model of processes of one class, made in the form of a diagram. Simulating processes are created on the basis of this model.

Conclusion

Thank you for your attention. I sincerely hope that my experience will be useful to those who wish to distinguish between the above objects. The problem of the current state of the industry is such that entities named by the same term cease to differ in the minds of analysts. I tried to give you an example of how you can think, and how you can introduce terms to distinguish between different entities. I hope the reading was interesting.

Simulation

Simulation modeling (situational modeling)- a method that allows you to build models that describe the processes as they would take place in reality. Such a model can be "played" in 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. Based on 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 the comprehension of 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 called obtaining particular numerical solutions of the 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 in order to design, analyze and evaluate the functioning of an object.

Application of simulation modeling

Simulation 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, non-linearities, stochastic (random) variables;
• it is necessary to simulate the behavior of the system in 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 - the development of a simulator (eng. simulation modeling) of the subject area under study for conducting various experiments.

Simulation modeling allows you to simulate the behavior of a system over time. Moreover, the advantage is that the time in the model can be controlled: slow down in the case of fast processes and speed up 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, as a rule, is accompanied by computer three-dimensional simulation. This precise and relatively fast technology allows you to accumulate all the necessary knowledge, equipment and semi-finished products for a future product before the start of production. Computer 3D modeling is now not uncommon even for small companies.

Imitation, as a method for solving non-trivial problems, was first developed in connection with the creation of computers in the 1950s and 1960s.

There are two types of imitation:

• Monte Carlo method (method of statistical tests);
• Method of simulation modeling (statistical modeling).

Types of simulation modeling

Three Simulation Approaches

Simulation modeling approaches on the scale of abstraction

• Agent-based modeling is a relatively new (1990s-2000s) direction in simulation modeling, which is used to study decentralized systems, the dynamics of which are determined not by global rules and laws (as in other modeling paradigms), but vice versa, when these global rules and laws are the result of the individual activity of group members. The purpose of agent models is to get an idea about these global rules, the general behavior of the system, based on assumptions about the individual, particular 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 independently change.

• 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”, “movement with a load”, “unloading” and others. Discrete event modeling is the most developed and has a huge scope of applications - from logistics and queuing systems to transport and production systems. This type of simulation is most suitable for modeling production processes. Founded by Jeffrey Gordon in the 1960s.

• System dynamics is a modeling paradigm, where graphic diagrams of causal relationships and global influences of some parameters on others in 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. With the help of 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 the 1950s.

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

• Hemdy A. Taha Chapter 18// Introduction to Operations Research = Operations Research: An Introduction. - 7th ed. - M .: "Williams", 2007. - S. 697-737. - ISBN 0-13-032374-8

• Strogalev V. P., Tolkacheva I. O. Simulation modeling. - MSTU im. Bauman, 2008. - S. 697-737. -

In connection with the listed difficulties arising in the study of complex systems analytical methods, the practice required a more flexible and powerful method. As a result, in the early 1960s of the last century, simulation modeling (Modeling & Simulation) appeared.

As already mentioned, under simulation modeling We

we will understand not just the development of the model, but the complex process of IISS. This is the formulation of the research problem, the formalization of the functioning of the system, its individual elements and the rules of interaction between them, the development of a model, the accumulation and filling of the model with data, the conduct of research and the development guidelines on the existence and modernization of the system.

Usage random variables makes it necessary to repeatedly conduct experiments with the simulation system (on a computer) and subsequent statistical analysis the results obtained. In general, simulation modeling implies the execution of the processes of creating a software model and carrying out consistent and targeted experiments with this program, carried out by the user on the computer. It should be noted that the simulation model is a software representation of the formal description of the system. It reflects only a part of the system that was formalized and described using the program. In this case, the user can include in the model (and most often this happens) only a part of the formal description. This happens primarily due to the computational capabilities of a computer available for use, the complexity of software implementation, the need for a detailed study of only some parts of the system, the lack of the necessary initial data for modeling, etc.

We confirm once again that when creating a simulation model, the researcher performs all the procedures inherent in system analysis - formulates the purpose of the study, creates a formal description of the functioning of the system using one of the approaches (composition, structure, operation algorithms, indicators), programs the model in one of the languages simulation model, conducts experiments with the model, formulates conclusions and recommendations.

In the most general form, the level of detail of the simulation model, in projection on its existing formal description, is shown in Fig. 1.8.

The advantages of simulation modeling over other methods of system analysis are as follows:

Possibility to create a greater proximity to the real system than with the use of analytical models - detailing,

Rice. 1.8.

terminology, user interface, presentation of initial data and results;

• - block principle of building and debugging the model. This approach makes it possible to verify each block of the model before it is included in the overall system model and implement the stage-by-stage creation and execution of the model;
• - the use in the model of dependencies of a more complex nature (including random ones), which are not described by simple mathematical relationships, through the use of numerical methods;
• - Unlimited level of system detail. It is limited only by the needs of the task, the capabilities of the computer and the simulation system, and the ability of the user to describe the system;
• - the possibility of conducting experiments with a software model, and not with the system, which saves us from many mistakes and saves real money;
• - verification of force majeure circumstances, which are difficult to check on a real system, and most often impossible;
• - modeling allows you to study a system that does not yet exist. For example, the feasibility of upgrading (either expanding or reducing the existing system).

The listed advantages determine the disadvantages and some additional difficulties inherent in any processes, including when using a simulation model. It must be admitted that such shortcomings and difficulties do exist. The main disadvantages of the simulation model include:

• - to build a simulation model in comparison with the analytical model is longer, more difficult and more expensive;
• - to work with the simulation system, it is necessary to have a computer suitable for the class and a simulation language corresponding to the task;
• - the complexity of building a dialogue between the user and the model. The interaction between the user and the simulation model (interface) should be simple, convenient and consistent with the subject area, and this requires an additional amount of programming;
• - building a simulation model requires a deeper, longer and more detailed study of the real process (since the model is more detailed) than mathematical modeling.

When using a simulation model, absolutely any subject of the economy can act as a system under study - a specific enterprise (or its component), a large infrastructure project, a branch of production, technology, etc. By means of a simulation model, any queuing system can be analyzed, as well as any other system that has a certain number of discrete states and the logic of their relationship. The transition in time from one state to another is provided due to a number of conditions and reasons (deterministic and random). The main difference between the simulation modeling method and other methods lies in the almost unlimited degree of detailing of systems and, as a result, in the ability to present the system for the researcher as it “looks” in real life.

When using simulation modeling, you can check and get an answer to many questions such as: what will happen if:

• - build a new system in one way or another;
• - to carry out this or that reorganization of the system;
• - change suppliers of raw materials, materials and components;
• - to modernize the logistics chains of their supply;
• - increase (decrease) the volume of resources, the number of personnel and equipment;
• - change processing or maintenance technology?

From point of view practical application The most important thing is that as a result of modeling it is possible to:

• - reduce economic and organizational costs of enterprises and projects;
• - detect system bottlenecks and test various options for their elimination;
• - increase the throughput of the system;
• - reduce economic, organizational, technological and other risks of enterprises and projects.

Note that all this can be achieved without conducting experiments on the real system itself, but by studying only its program model. This makes it possible to avoid many systemic errors, social problems, and conduct experiments that could be detrimental to a real system.

Of course, the use of a simulation model in everyday practice is not necessary, and in Russia it is not regulated by any norms and laws. Although certain efforts are being made to create a regulatory framework for the simulation model.

Now, unfortunately, in many cases, systems are created, upgraded and operated without using the simulation model method. Each developer or owner of the system has the right to independently decide on the use of a simulation model.