Course work: Simulation modeling of economic activity of an enterprise. Simulation modeling of economic systems
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Course project
Subject: “Modeling of production and economic processes»
On the topic: “Simulation modeling of economic processes”
Introduction
1.1 Concept of modeling
1.2 Concept of a model
IV. Practical part
4.1 Problem statement
4.2 Problem solution
Conclusion
Application
Introduction
Simulation modeling, linear programming and regression analysis have long occupied the top three places among all methods of operations research in economics in terms of range and frequency of use. In simulation modeling, the algorithm that implements the model reproduces the process of system functioning in time and space, and the elementary phenomena that make up the process are simulated while preserving its logical time structure.
Currently, modeling has become a fairly effective means of solving complex problems of automation of research, experiments, and design. But to master modeling as a working tool, its wide capabilities and further develop the modeling methodology is possible only with full mastery of the techniques and technology for practical solution of problems of modeling the processes of functioning of systems on a computer. This is the goal of this workshop, which focuses on the methods, principles and main stages of modeling within the framework of the general modeling methodology, and also examines the issues of modeling specific variants of systems and instills skills in using modeling technology in the practical implementation of models of system functioning. The problems of queuing systems are considered, on which simulation models of economic, information, technological, technical and other systems are based. Methods for probabilistic modeling of discrete and random continuous variables are outlined, which make it possible to take into account when modeling economic systems random impacts on the system.
The demands that modern society places on a specialist in the field of economics are steadily growing. Currently, successful activity in almost all spheres of the economy is not possible without modeling the behavior and dynamics of development processes, studying the features of the development of economic objects, and considering their functioning in various conditions. Software and hardware should become the first assistants here. Instead of learning from your own mistakes or from the mistakes of other people, it is advisable to consolidate and test your knowledge of reality with the results obtained on computer models.
Simulation modeling is the most visual and is used in practice for computer modeling of options for resolving situations in order to obtain the most effective solutions to problems. Simulation modeling allows for the study of the analyzed or designed system according to the scheme of operational research, which contains interrelated stages:
· development of a conceptual model;
· development and software implementation of a simulation model;
· checking the correctness and reliability of the model and assessing the accuracy of the modeling results;
· planning and conducting experiments;
· making decisions.
This allows the use of simulation modeling as a universal approach for making decisions under conditions of uncertainty, taking into account factors that are difficult to formalize in models, as well as applying the basic principles of a systems approach to solving practical problems.
The widespread implementation of this method in practice is hampered by the need to create software implementations of simulation models that recreate the dynamics of the functioning of the simulated system in simulated time.
Unlike traditional programming methods, developing a simulation model requires a restructuring of the principles of thinking. It is not without reason that the principles underlying simulation modeling gave impetus to the development of object programming. Therefore, the efforts of simulation software developers are aimed at simplifying software implementations of simulation models: specialized languages and systems are created for these purposes.
Simulation software tools have changed in their development over several generations, from modeling languages and automation tools for model construction to program generators, interactive and intelligent systems, and distributed modeling systems. The main purpose of all these tools is to reduce the labor intensity of creating software implementations of simulation models and experimenting with models.
One of the first modeling languages to facilitate the process of writing simulation programs was the GPSS language, created as a final product by Jeffrey Gordon at IBM in 1962. Currently there are translators for operating systems DOS - GPSS/PC, for OS/2 and DOS - GPSS/H and for Windows - GPSS World. Studying this language and creating models allows you to understand the principles of developing simulation programs and learn how to work with simulation models.
GPSS (General Purpose Simulation System) is a modeling language that is used to build event-driven discrete simulation models and conduct experiments using a personal computer.
The GPSS system is a language and a translator. Like every language, it contains a vocabulary and grammar with the help of which models of systems of a certain type can be developed.
I. Basic concepts of the theory of modeling economic systems and processes
1.1 Concept of modeling
Modeling refers to the process of constructing, studying and applying models. It is closely related to such categories as abstraction, analogy, hypothesis, etc. The modeling process necessarily includes the construction of abstractions, inferences by analogy, and the construction of scientific hypotheses.
The main feature of modeling is that it is a method of indirect cognition using proxy objects. The model acts as a kind of cognition tool that the researcher places between himself and the object, and with the help of which he studies the object of interest to him. Any socio-economic system is a complex system in which dozens and hundreds of economic, technical and social processes, constantly changing under the influence external conditions, including scientific and technological progress. In such conditions, managing socio-economic and production systems turns into a complex task that requires special means and methods. Modeling is one of the main methods of cognition, it is a form of reflection of reality and consists in finding out or reproducing certain properties of real objects, objects and phenomena with the help of other objects, processes, phenomena, or using an abstract description in the form of an image, plan, map , a set of equations, algorithms and programs.
In the most general sense, a model is a logical (verbal) or mathematical description of components and functions that reflect the essential properties of the object or process being modeled, usually considered as systems or elements of a system from a certain point of view. The model is used as a conventional image, designed to simplify the study of the object. In principle, not only mathematical (sign) methods are applicable in economics, but also material models, however, material models have only demonstrative value.
There are two points of view on the essence of modeling:
* this is a study of objects of cognition using models;
* this is the construction and study of models of real-life objects and phenomena, as well as proposed (constructed) objects.
The possibilities of modeling, that is, transferring the results obtained during the construction and research of the model to the original, are based on the fact that the model in a certain sense displays (reproduces, models, describes, imitates) some features of the object that are of interest to the researcher. Modeling as a form of reflection of reality is widespread, and a fairly complete classification of possible types of modeling is extremely difficult, if only because of the polysemy of the concept “model,” which is widely used not only in science and technology, but also in art and in everyday life.
The word “model” comes from the Latin word “modulus”, meaning “measure”, “sample”. Its original meaning was associated with the art of building, and in almost all European languages it was used to denote an image or prototype, or a thing similar in some respect to another thing.
Among socio-economic systems, it is advisable to single out the production system (PS), which, unlike systems of other classes, contains consciously acting person, performing management functions (decision making and control). In accordance with this, various divisions of enterprises, enterprises themselves, research and design organizations, associations, industries and, in some cases, the national economy as a whole can be considered as PS.
The nature of the similarity between the modeled object and the model differs:
* physical - the object and the model have the same or similar physical nature;
* structural - there is a similarity between the structure of the object and the structure of the model; * functional - the object and the model perform similar functions under appropriate influence;
* dynamic - there is a correspondence between the sequentially changing states of the object and the model;
* probabilistic - there is a correspondence between processes of a probabilistic nature in the object and the model;
* geometric - there is a correspondence between the spatial characteristics of the object and the model.
Modeling is one of the most common ways to study processes and phenomena. Modeling is based on the principle of analogy and allows you to study an object under certain conditions and taking into account the inevitable one-sided point of view. An object that is difficult to study is studied not directly, but through the consideration of another, similar to it and more accessible - a model. Based on the properties of the model, it is usually possible to judge the properties of the object being studied. But not about all properties, but only about those that are similar both in the model and in the object and at the same time are important for research.
Such properties are called essential. Is there a need for mathematical modeling of the economy? In order to verify this, it is enough to answer the question: is it possible to complete a technical project without having an action plan, i.e., drawings? The same situation occurs in the economy. Is it necessary to prove the need to use economic and mathematical models for making management decisions in the economic sphere?
Under these conditions, the economic-mathematical model turns out to be the main means of experimental research in economics, since it has the following properties:
* imitates a real economic process (or the behavior of an object);
* has a relatively low cost;
* can be reused;
* takes into account various operating conditions of the object.
The model can and should reflect internal structure economic object from given (certain) points of view, and if it is unknown, then only its behavior, using the “Black Box” principle.
Fundamentally, any model can be formulated in three ways:
* as a result of direct observation and study of the phenomena of reality (phenomenological method);
* isolation from a more general model (deductive method);
* generalizations of more particular models (inductive method, i.e. proof by induction).
Models, endless in their diversity, can be classified according to a variety of criteria. First of all, all models can be divided into physical and descriptive. We constantly deal with both of them. In particular, descriptive models include models in which the modeled object is described using words, drawings, mathematical dependencies, etc. Such models include literature, art, music.
Economic and mathematical models are widely used in managing business processes. There is no established definition of an economic-mathematical model in the literature. Let's take the following definition as a basis. An economic-mathematical model is a mathematical description of an economic process or object, carried out for the purpose of their study or management: a mathematical recording of the economic problem being solved (therefore, the terms problem and model are often used as synonyms).
Models can also be classified according to other criteria:
* Models that describe the momentary state of the economy are called static. Models that show the development of the modeled object are called dynamic.
* Models that can be built not only in the form of formulas (analytical representation), but also in the form of numerical examples (numerical representation), in the form of tables (matrix representation), in the form of a special kind of graphs (network representation).
1.2 Concept of a model
At present, it is impossible to name an area of human activity in which modeling methods would not be used to one degree or another. Meanwhile, there is no generally accepted definition of the concept of a model. In our opinion, the following definition deserves preference: a model is an object of any nature that is created by a researcher in order to obtain new knowledge about the original object and reflects only the essential (from the developer’s point of view) properties of the original.
Analyzing the content of this definition, we can draw the following conclusions:
1) any model is subjective, it bears the stamp of the researcher’s individuality;
2) any model is homomorphic, i.e. it does not reflect all, but only the essential properties of the original object;
3) it is possible that there are many models of the same original object, differing in the purposes of the study and the degree of adequacy.
A model is considered adequate to the original object if it, with a sufficient degree of approximation at the level of understanding of the simulated process by the researcher, reflects the patterns of the functioning of a real system in the external environment.
Mathematical models can be divided into analytical, algorithmic (simulation) and combined. Analytical modeling is characterized by the fact that systems of algebraic, differential, integral or finite-difference equations are used to describe the processes of system functioning. The analytical model can be studied using the following methods:
a) analytical, when they strive to obtain, in a general form, explicit dependencies for the desired characteristics;
b) numerical, when, not being able to solve equations in general form, they strive to obtain numerical results with specific initial data;
c) qualitative, when, without having an explicit solution, one can find some properties of the solution (for example, assess the stability of the solution). In algorithmic (simulation) modeling, the process of system functioning over time is described, and the elementary phenomena that make up the process are simulated, preserving their logical structure and sequence of occurrence over time. Simulation models can also be deterministic and statistical.
The general goal of modeling in the decision-making process was formulated earlier - this is the determination (calculation) of the values of the selected performance indicator for various strategies for conducting an operation (or options for implementing the designed system). When developing a specific model, the purpose of the modeling should be clarified taking into account the effectiveness criterion used. Thus, the purpose of modeling is determined both by the purpose of the operation being studied and by the planned method of using the research results.
For example, a problem situation that requires a decision is formulated as follows: find an option for building a computer network that would have the minimum cost while meeting the performance and reliability requirements. In this case, the goal of modeling is to find network parameters that provide the minimum PE value, which is represented by cost.
The task can be formulated differently: from several options for computer network configuration, select the most reliable one. Here, one of the reliability indicators (mean time between failures, probability of failure-free operation, etc.) is selected as the PE, and the purpose of the modeling is a comparative assessment of network options according to this indicator.
The above examples allow us to recall that the choice of performance indicator itself does not yet determine the “architecture” of the future model, since at this stage its concept has not been formulated, or, as they say, the conceptual model of the system under study has not been defined.
II. Basic concepts of the theory of modeling economic systems and processes
2.1 Improvement and development of economic systems
Simulation modeling is the most powerful and universal method for studying and assessing the effectiveness of systems whose behavior depends on the influence of random factors. Such systems include an aircraft, a population of animals, and an enterprise operating in conditions of poorly regulated market relations.
Simulation modeling is based on a statistical experiment (Monte Carlo method), the implementation of which is practically impossible without the use of computer technology. Therefore, any simulation model is ultimately a more or less complex software product.
Of course, like any other program, a simulation model can be developed in any universal programming language, even in Assembly language. However, in this case the following problems arise on the developer's path:
* knowledge is required not only of the subject area to which the system under study belongs, but also of the programming language, and at a fairly high level;
* developing specific procedures for ensuring a statistical experiment (generating random influences, planning an experiment, processing results) can take no less time and effort than developing the system model itself.
And finally, one more, perhaps the most important problem. In many practical problems, interest is not only (and not so much) in the quantitative assessment of the effectiveness of the system, but in its behavior in a given situation. For such observation, the researcher must have appropriate “observation windows” that could, if necessary, be closed, moved to another place, changed the scale and form of presentation of the observed characteristics, etc., without waiting for the end of the current model experiment. In this case, the simulation model acts as a source of answer to the question: “what will happen if...”.
Implementing such capabilities in a universal programming language is very difficult. Currently, there are quite a lot of software products that allow you to simulate processes. Such packages include: Pilgrim, GPSS, Simplex and a number of others.
At the same time, there is currently a product on the Russian computer technology market that allows one to very effectively solve these problems - the MATLAB package, which contains the visual modeling tool Simulink.
Simulink is a tool that allows you to quickly simulate a system and obtain indicators of the expected effect and compare them with the effort required to achieve them.
There are many various types models: physical, analog, intuitive, etc. A special place among them is occupied by mathematical models, which, according to Academician A.A. Samarsky, “are the greatest achievement of the scientific and technological revolution of the 20th century.” Mathematical models are divided into two groups: analytical and algorithmic (sometimes called simulation).
Currently, it is impossible to name an area of human activity in which modeling methods would not be used to one degree or another. Economic activity is no exception. However, in the field of simulation modeling of economic processes, some difficulties are still observed.
In our opinion, this circumstance is explained by the following reasons.
1. Economic processes occur largely spontaneously and uncontrollably. They do not respond well to attempts at strong-willed control on the part of political, government and economic leaders of individual industries and the country’s economy as a whole. For this reason, economic systems are difficult to study and formally describe.
2. Specialists in the field of economics, as a rule, have insufficient mathematical training in general and in mathematical modeling in particular. Most of them do not know how to formally describe (formalize) observed economic processes. This, in turn, does not allow us to establish whether this or that mathematical model is adequate for the economic system under consideration.
3. Specialists in the field of mathematical modeling, without having at their disposal a formalized description of the economic process, cannot create a mathematical model adequate to it.
Existing mathematical models, which are commonly called models of economic systems, can be divided into three groups.
The first group includes models that quite accurately reflect one aspect of a certain economic process occurring in a system of a relatively small scale. From a mathematical point of view, they represent very simple relationships between two or three variables. Usually these are algebraic equations of the 2nd or 3rd degree, in extreme cases a system of algebraic equations that requires the use of the iteration method (successive approximations) to solve. They find application in practice, but are not of interest from the point of view of specialists in the field of mathematical modeling.
The second group includes models that describe real processes occurring in small and medium-sized economic systems, subject to the influence of random and uncertain factors. The development of such models requires making assumptions to resolve uncertainties. For example, you need to specify distributions of random variables related to input variables. This artificial operation to a certain extent raises doubts about the reliability of the modeling results. However, there is no other way to create a mathematical model.
Among the models of this group, the most widely used models are those of the so-called queuing systems. There are two varieties of these models: analytical and algorithmic. Analytical models do not take into account the effect of random factors and therefore can only be used as first approximation models. Using algorithmic models, the process under study can be described with any degree of accuracy at the level of its understanding by the problem maker.
The third group includes models of large and very large (macroeconomic) systems: large commercial and industrial enterprises and associations, industries National economy and the country's economy as a whole. Creating a mathematical model of an economic system of this scale is a complex scientific problem, the solution of which can only be solved by a large research institution.
2.2 Simulation model components
Numerical modeling deals with three types of values: input data, calculated variable values, and parameter values. On an Excel sheet, arrays with these values occupy separate areas.
Initial real data, samples or series of numbers, are obtained through direct field observation or in experiments. Within the framework of the modeling procedure, they remain unchanged (it is clear that, if necessary, the sets of values can be supplemented or reduced) and play a dual role. Some of them (independent environmental variables, X) serve as the basis for calculating model variables; most often these are characteristics of natural factors (the passage of time, photoperiod, temperature, abundance of food, dose of toxicant, volumes of pollutants discharged, etc.). The other part of the data (dependent variables of the object, Y) is a quantitative characteristic of the state, reactions or behavior of the research object, which was obtained in certain conditions, under the influence of registered environmental factors. In a biological sense, the first group of meanings does not depend on the second; on the contrary, object variables depend on environment variables. Data is entered into an Excel sheet from the keyboard or from a file in the usual spreadsheet mode.
Model calculation data reproduce the theoretically conceivable state of the object, which is determined by the previous state, the level of observed environmental factors and is characterized by the key parameters of the process being studied. In the ordinary case, when calculating model values (Y M i) for each time step (i), parameters (A), characteristics of the previous state (Y M i -1) and current levels of environmental factors (X i) are used:
Y M i = f(A, Y M i-1, X i, i),
f() - the accepted form of the relationship between parameters and environmental variables, the type of model,
i = 1, 2, … T or i =1, 2, … n.
Calculations of system characteristics using model formulas for each time step (for each state) make it possible to generate an array of model explicit variables (Y M), which must exactly repeat the structure of the array of real dependent variables (Y), which is necessary for subsequent adjustment of model parameters. Formulas for calculating model variables are entered into the cells of the Excel sheet manually (see the section Useful techniques).
The model parameters (A) constitute the third group of values. All parameters can be represented as a set:
A = (a 1, a 2,…, a j,…, a m),
where j is the parameter number,
m? total number of parameters,
and placed in a separate block. It is clear that the number of parameters is determined by the structure of the adopted model formulas.
Occupying a separate position on the Excel sheet, they play the most significant role in modeling. The parameters are designed to characterize the very essence, the mechanism for the implementation of the observed phenomena. The parameters must have a biological (physical) meaning. For some tasks, it is necessary that parameters calculated for different data sets can be compared. This means that they must sometimes be accompanied by their own statistical errors.
The relationships between the components of the simulation system form a functional unity focused on achieving a common goal - assessing the parameters of the model (Fig. 2.6, Table 2.10). Several elements are simultaneously involved in the implementation of individual functions, indicated by arrows. In order not to clutter the picture, the graphical representation and randomization blocks are not reflected in the diagram. The simulation system is designed to support any changes in model designs that, if necessary, can be made by the researcher. Basic designs of simulation systems, as well as possible ways of their decomposition and integration are presented in the section Frames of simulation systems.
modeling simulation economic series
III. Simulation Basics
3.1 Simulation model and its features
Simulation modeling is a type of analog modeling implemented using a set of mathematical tools, special simulating computer programs and programming technologies that allow, through analogue processes, to conduct a targeted study of the structure and functions of a real complex process in computer memory in the “simulation” mode, and to perform optimization of some its parameters.
A simulation model is an economic and mathematical model, the study of which is carried out by experimental methods. The experiment consists of observing the results of calculations for various specified values of the input exogenous variables. The simulation model is a dynamic model due to the fact that it contains such a parameter as time. A simulation model is also called a special software package that allows you to simulate the activities of any complex object. The emergence of simulation modeling was associated with the “new wave” in economics and topic modeling. Problems of economic science and practice in the field of management and economic education, on the one hand, and the growth of computer productivity, on the other, have caused a desire to expand the scope of “classical” economic and mathematical methods. There has been some disappointment in the capabilities of normative, balance sheet, optimization and game-theoretic models, which at first deservedly attracted the attention of the fact that they bring an atmosphere of logical clarity and objectivity to many problems of economic management, and also lead to a “reasonable” (balanced, optimal, compromise) solution . It was not always possible to fully comprehend a priori goals and, even more so, to formalize the optimality criterion and (or) restrictions on admissible solutions. Therefore, many attempts to nevertheless apply such methods began to lead to unacceptable, for example, unrealizable (albeit optimal) solutions. Overcoming the difficulties that arose took the path of abandoning complete formalization (as is done in normative models) of procedures for making socio-economic decisions. Preference began to be given to a reasonable synthesis of the intellectual capabilities of an expert and the information power of a computer, which is usually implemented in dialogue systems. One trend in this direction is the transition to “semi-normative” multi-criteria man-machine models, the second is a shift in the center of gravity from prescriptive models focused on the “conditions - solution” scheme to descriptive models that answer the question “what will happen, If...".
Simulation modeling is usually resorted to in cases where the dependencies between the elements of the systems being modeled are so complex and uncertain that they cannot be formally described in the language of modern mathematics, i.e., using analytical models. Thus, researchers of complex systems are forced to use simulation modeling when purely analytical methods are either inapplicable or unacceptable (due to the complexity of the corresponding models).
In simulation modeling, the dynamic processes of the original system are replaced by processes simulated by a modeling algorithm in an abstract model, but maintaining the same duration ratios, logical and time sequences as in the real system. Therefore, the simulation method could be called algorithmic or operational. By the way, such a name would be more successful, since imitation (translated from Latin as imitation) is the reproduction of something by artificial means, i.e. modeling. In this regard, the currently widely used name “simulation modeling” is tautological. In the process of simulating the functioning of the system under study, as in an experiment with the original itself, certain events and states are recorded, from which the necessary characteristics of the quality of functioning of the system under study are then calculated. For systems, for example, information and computing services, such dynamic characteristics can be defined as:
* performance of data processing devices;
* length of queues for service;
* waiting time for service in queues;
* number of applications that left the system without service.
In simulation modeling, processes of any degree of complexity can be reproduced if there is a description of them, given in any form: formulas, tables, graphs, or even verbally. The main feature of simulation models is that the process under study is, as it were, “copied” on a computer, therefore simulation models, unlike analytical models, allow:
* take into account a huge number of factors in models without gross simplifications and assumptions (and therefore, increase the adequacy of the model to the system under study);
* it is enough to simply take into account the uncertainty factor in the model caused by the random nature of many model variables;
All this allows us to draw a natural conclusion that simulation models can be created for a wider class of objects and processes.
3.2 The essence of simulation modeling
The essence of simulation modeling is targeted experimentation with a simulation model by “playing” on it various options for the functioning of the system with their corresponding economic analysis. Let us immediately note that the results of such experiments and the corresponding economic analysis It is advisable to format them in the form of tables, graphs, nomograms, etc., which greatly simplifies the decision-making process based on the modeling results.
Having listed above a number of advantages of simulation models and simulation, we also note their disadvantages, which must be remembered when using simulation in practice. This:
* lack of well-structured principles for constructing simulation models, which requires significant elaboration of each specific case of its construction;
* methodological difficulties in finding optimal solutions;
* increased requirements for the speed of computers on which simulation models are implemented;
* difficulties associated with the collection and preparation of representative statistics;
* uniqueness of simulation models, which does not allow the use of ready-made ones software products;
* the complexity of analyzing and understanding the results obtained as a result of a computational experiment;
* quite a large investment of time and money, especially when searching for optimal trajectories of behavior of the system under study.
The number and essence of the listed shortcomings is very impressive. However, given the great scientific interest in these methods and their extremely intensive development in recent years, it is safe to assume that many of the above-mentioned shortcomings of simulation modeling can be eliminated, both conceptually and in application terms.
Simulation modeling of a controlled process or controlled object is a high-level information technology that provides two types of actions performed using a computer:
1) work on creating or modifying a simulation model;
2) operation of the simulation model and interpretation of the results.
Simulation modeling of economic processes is usually used in two cases:
* for managing a complex business process, when a simulation model of a managed economic entity is used as a tool%in the circuit adaptive system management created on the basis of information technology;
* when conducting experiments with discrete-continuous models of complex economic objects to obtain and monitor their dynamics in emergency situations associated with risks, the full-scale modeling of which is undesirable or impossible.
The following can be distinguished typical tasks problems solved by means of simulation modeling in the management of economic objects:
* modeling of logistics processes to determine time and cost parameters;
* managing the process of implementing an investment project at various stages of its life cycle, taking into account possible risks and allocation tactics sums of money;
* analysis of clearing processes in the work of a network of credit institutions (including application to mutual settlement processes in the Russian banking system);
* forecasting the financial results of an enterprise for a specific period of time (with analysis of the dynamics of account balances);
* business reengineering of an insolvent enterprise (changing the structure and resources of a bankrupt enterprise, after which, using a simulation model, one can make a forecast of the main financial results and give recommendations on the feasibility of one or another option for reconstruction, investment or lending to production activities);
A simulation system that provides the creation of models to solve the listed problems must have the following properties:
* the possibility of using simulation programs in conjunction with special economic and mathematical models and methods based on control theory;
* instrumental methods of conducting structural analysis of a complex economic process;
* ability to model material, monetary and information processes and flows within a single model, in general, model time;
* the possibility of introducing a mode of constant clarification when receiving output data (main financial indicators, time and spatial characteristics, risk parameters, etc.) and conducting an extreme experiment.
Many economic systems are essentially queuing systems (QS), i.e. systems in which, on the one hand, there are requirements for the performance of any services, and on the other hand, these requirements are satisfied.
IV. Practical part
4.1 Problem statement
Investigate the dynamics of an economic indicator based on the analysis of a one-dimensional time series.
For nine consecutive weeks, demand Y(t) (million rubles) for credit resources of a financial company was recorded. The time series Y(t) of this indicator is given in the table.
Required:
1. Check for anomalous observations.
2. Build linear model Y(t) = a 0 + a 1 t, the parameters of which are estimated by least squares (Y(t)) - calculated, simulated values of the time series).
3. Assess the adequacy of the constructed models using the properties of independence of the residual component, randomness and compliance with the normal distribution law (when using the R/S criterion, take tabulated limits of 2.7-3.7).
4. Assess the accuracy of the models based on the use of the average relative error of approximation.
5. Based on the two constructed models, forecast demand for the next two weeks (calculate the confidence interval of the forecast at a confidence probability of p = 70%)
6. Present the actual values of the indicator, modeling and forecasting results graphically.
4.2 Problem solution
1). The presence of anomalous observations leads to distortion of the modeling results, so it is necessary to ensure the absence of anomalous data. To do this, we will use Irwin’s method and find the characteristic number () (Table 4.1).
The calculated values are compared with the tabulated values of the Irvine criterion, and if they are greater than the tabulated ones, then the corresponding value of the series level is considered anomalous.
Appendix 1 (Table 4.1)
All obtained values were compared with the table values and did not exceed them, that is, there were no anomalous observations.
2) Construct a linear model, the parameters of which can be estimated by least squares methods (calculated, simulated values of the time series).
To do this, we will use Data Analysis in Excel.
Appendix 1 ((Fig. 4.2).Fig. 4.1)
The result of the regression analysis is contained in the table
Appendix 1 (table 4.2 and 4.3.)
In the second column of the table. 4.3 contains the coefficients of the regression equation a 0, a 1, the third column contains the standard errors of the coefficients of the regression equation, and the fourth contains t - statistics used to test the significance of the coefficients of the regression equation.
The regression equation of dependence (demand for credit resources) on (time) has the form.
Appendix 1 (Fig. 4.5)
3) Assess the adequacy of the constructed models.
3.1. Let's check independence (absence of autocorrelation) using the Durbin-Watson d test using the formula:
Appendix 1 (Table 4.4)
Because the calculated value d falls in the range from 0 to d 1, i.e. in the interval from 0 to 1.08, then the property of independence is not satisfied, the levels of a number of residuals contain autocorrelation. Therefore, the model is inadequate according to this criterion.
3.2. We will check the randomness of the levels of a number of residues based on the criterion of turning points. P>
The number of turning points is 6.
Appendix 1 (Fig. 4.5)
The inequality is satisfied (6 > 2). Therefore, the randomness property is satisfied. The model is adequate according to this criterion.
3.3. Let us determine whether a number of residuals correspond to the normal distribution law using the RS criterion:
The maximum level of a number of residues,
The minimum level of a number of residues,
Standard deviation,
The calculated value falls within the interval (2.7-3.7), therefore, the property of normal distribution is satisfied. The model is adequate according to this criterion.
3.4. Checking the equality of the mathematical expectation of the levels of a series of residues to zero.
In our case, therefore, the hypothesis that the mathematical expectation of the values of the residual series is equal to zero is satisfied.
Table 4.3 summarizes the analysis of a number of residues.
Appendix 1 (Table 4.6)
4) Assess the accuracy of the model based on the use of the average relative error of approximation.
To assess the accuracy of the resulting model, we will use the relative approximation error indicator, which is calculated by the formula:
Calculation of relative approximation error
Appendix 1 (Table 4.7)
If the error calculated by the formula does not exceed 15%, the accuracy of the model is considered acceptable.
5) Based on the constructed model, forecast demand for the next two weeks (calculate the confidence interval of the forecast at a confidence level of p = 70%).
Let's use the Excel function STUDYDISTRIBUTE.
Appendix 1 (Table 4.8)
To build an interval forecast, we calculate the confidence interval. Let us accept the significance level, therefore, the confidence probability is equal to 70%, and the Student’s test at is equal to 1.12.
We calculate the width of the confidence interval using the formula:
(we find from table 4.1)
We calculate the upper and lower limits of the forecast (Table 4.11).
Appendix 1 (Table 4.9)
6) Present the actual values of the indicator, modeling and forecasting results graphically.
Let's transform the selection schedule, supplementing it with forecast data.
Appendix 1 (Table 4.10)
Conclusion
An economic model is defined as a system of interrelated economic phenomena expressed in quantitative characteristics and presented in a system of equations, i.e. is a system of formalized mathematical description. For a targeted study of economic phenomena and processes and the formulation of economic conclusions - both theoretical and practical, it is advisable to use the method of mathematical modeling. Particular interest is shown in methods and means of simulation modeling, which is associated with the improvement of information technologies used in simulation modeling systems: the development of graphical shells for constructing models and interpreting the output results of modeling, the use of multimedia tools, Internet solutions, etc. In economic analysis, simulation modeling is the most universal tool in the field of financial, strategic planning, business planning, production management and design. Mathematical modeling of economic systems The most important property of mathematical modeling is its universality. This method allows, at the stages of design and development of an economic system, to form various variants of its model, to conduct repeated experiments with the resulting variants of the model in order to determine (based on specified criteria for the functioning of the system) the parameters of the created system necessary to ensure its efficiency and reliability. In this case, there is no need to purchase or produce any equipment or hardware to perform the next calculation: you just need to change the numerical values of the parameters, initial conditions and operating modes of the complex economic systems under study.
Methodologically, mathematical modeling includes three main types: analytical, simulation and combined (analytical-simulation) modeling. An analytical solution, if possible, provides a more complete and clear picture, allowing one to obtain the dependence of the modeling results on the totality of the initial data. In this situation, one should move to the use of simulation models. A simulation model, in principle, allows one to reproduce the entire process of functioning of an economic system while preserving the logical structure, connections between phenomena and the sequence of their occurrence over time. Simulation modeling allows you to take into account a large number of real details of the functioning of the simulated object and is indispensable in the final stages of creating a system, when all strategic issues have already been resolved. It can be noted that simulation is intended to solve problems of calculating system characteristics. The number of options to be evaluated should be relatively small, since the implementation of simulation modeling for each option for constructing an economic system requires significant computing resources. The fact is that a fundamental feature of simulation modeling is the fact that in order to obtain meaningful results it is necessary to use statistical methods. This approach requires repeated repetition of the simulated process with changing values of random factors, followed by statistical averaging (processing) of the results of individual single calculations. The use of statistical methods, inevitable in simulation modeling, requires a lot of computer time and computing resources.
Another disadvantage of the simulation modeling method is the fact that to create sufficiently meaningful models of an economic system (and at those stages of creating an economic system when simulation modeling is used, very detailed and meaningful models are needed) significant conceptual and programming efforts are required. Combined modeling allows you to combine the advantages of analytical and simulation modeling. To increase the reliability of the results, you should use combined approach, based on a combination of analytical and simulation modeling methods. In this case, analytical methods should be used at the stages of analyzing the properties and synthesizing the optimal system. Thus, from our point of view, a system of comprehensive training of students in the means and methods of both analytical and simulation modeling is necessary. Organization of practical classes Students study ways to solve optimization problems that can be reduced to linear programming problems. The choice of this modeling method is due to the simplicity and clarity of both the substantive formulation of the relevant problems and the methods for solving them. In the process of performing laboratory work, students solve the following typical problems: transport problem; the task of allocating enterprise resources; the problem of equipment placement, etc. 2) Studying the basics of simulation modeling of production and non-production queuing systems in the GPSS World (General Purpose System Simulation World) environment. Methodological and practical questions creation and use of simulation models in the analysis and design of complex economic systems and decision-making in commercial and marketing activities. Methods for describing and formalizing simulated systems, stages and technology for constructing and using simulation models, and issues of organizing targeted experimental studies using simulation models are studied.
List of used literature
Basic
1. Akulich I.L. Mathematical programming in examples and problems. - M.: Higher School, 1986.
2. Vlasov M.P., Shimko P.D. Modeling of economic processes. - Rostov-on-Don, Phoenix - 2005 (electronic textbook)
3. Yavorsky V.V., Amirov A.Zh. Economic informatics and information systems (laboratory workshop) - Astana, Foliant, 2008.
4. Simonovich S.V. Informatics, St. Petersburg, 2003
5. Vorobyov N.N. Game theory for economists - cyberneticists. - M.: Nauka, 1985 (electronic textbook)
6. Alesinskaya T.V. Economic and mathematical methods and models. - Tagan Rog, 2002 (electronic textbook)
7. Gershgorn A.S. Mathematical programming and its application in economic calculations. -M. Economics, 1968
Additionally
1. Darbinyan M.M. Inventories in trade and their optimization. - M. Economics, 1978
2. Johnston D.J. Economic methods. - M.: Finance and Statistics, 1960.
3. Epishin Yu.G. Economic and mathematical methods and planning of consumer cooperation. - M.: Economics, 1975
4. Zhitnikov S.A., Birzhanova Z.N., Ashirbekova B.M. Economic and mathematical methods and models: Textbook. - Karaganda, KEU publishing house, 1998
5. Zamkov O.O., Tolstopyatenko A.V., Cheremnykh Yu.N. Mathematical methods in economics. - M.: DIS, 1997.
6. Ivanilov Yu.P., Lotov A.V. Mathematical methods in economics. - M.: Science, 1979
7. Kalinina V.N., Pankin A.V. Math statistics. M.: 1998
8. Kolemaev V.A. Mathematical Economics. M., 1998
9. Kremer N.Sh., Putko B.A., Trishin I.M., Fridman M.N. Operations research in economics. Textbook - M.: Banks and exchanges, UNITY, 1997
10. Spirin A.A., Fomin G.P. Economic and mathematical methods and models in trade. - M.: Economics, 1998
Annex 1
Table 4.1
Table 4.2
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Simulation modeling is a method that allows you to build models that describe processes as they would occur 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 you can obtain fairly stable statistics.
The relevance of this topic lies in the fact that simulation modeling on digital computers is one of the most powerful means of studying, in particular, complex dynamic systems. Like any computer modeling, it makes it possible to conduct computational experiments with systems that are still being designed and to study systems with which full-scale experiments, due to safety considerations or high cost, are not advisable. At the same time, due to its closeness in form to physical modeling, this research method is accessible to a wider range of users.
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 and experiments are carried out with it in order to obtain information about this system.
The goals of conducting such experiments can be very different - from identifying the properties and patterns of the system under study to solving specific practical problems. With the development of computer technology and software, the range of applications of simulation in economics has expanded significantly. Currently, it is used both to solve problems of intra-company management and to model management at the macroeconomic level. Let's consider the main advantages of using simulation modeling in the process of solving problems of financial analysis.
In the simulation process, the researcher deals with four main elements:
Real system;
Logical-mathematical model of the simulated object;
Simulation (machine) model;
The computer on which the simulation is carried out is a directed computational experiment.
To describe the dynamics of the simulated processes in simulation, a mechanism for specifying model time is implemented. These mechanisms are built into the control programs of any modeling system.
If the behavior of one component of the system were simulated on a computer, then the execution of actions in the simulation model could be carried out sequentially, by recalculating the time coordinate.
To ensure the simulation of parallel events of a real system, a certain global variable (ensuring the synchronization of all events in the system) t0 is introduced, which is called model (or system) time.
There are two main ways to change t0:
Step-by-step (fixed change intervals are used)
model time);
Event-based (variable change intervals are used
model time, while the step size is measured by the interval
until the next event).
In the case of the step-by-step method, time advances with the smallest possible constant step length (t principle). These algorithms are not very efficient in terms of using computer time for their implementation.
Event-based method (principle of “special states”). In it, time coordinates change only when the state of the system changes. In event-based methods, the length of the time shift step is the maximum possible. Model time changes from the current moment to the nearest moment of the next event. The use of the event-by-event method is preferable if the frequency of occurrence of events is low, then a large step length will speed up the progress of model time.
When solving many problems of financial analysis, models containing random variables, whose behavior cannot be controlled by decision makers. Such models are called stochastic. The use of simulation allows one to draw conclusions about possible results based on the probability distributions of random factors (variables). Stochastic simulation is often called the Monte Carlo method.
From all of the above, we can conclude that simulation allows us to take into account the maximum possible number of environmental factors to support management decision-making and is the most powerful tool for analyzing investment risks. The need for its application in domestic financial practice is due to the peculiarities of the Russian market, characterized by subjectivity, dependence on non-economic factors and a high degree of uncertainty.
The simulation results can be supplemented with probabilistic and statistical analysis and, in general, provide the manager with the most complete information about the degree of influence of key factors on the expected results and possible scenarios for the development of events.
A.A.Emelyanov
E.A.Vlasova R.V.Duma
IMITATION
MODELING
ECONOMIC
PROCESSES
Edited by Dr. economic sciences YES. Emelyanova
on education in the field of applied computer science as a teaching aid for students,
students majoring in “Applied Informatics (by area)”,
A also in other computer specialties
and directions
MOSCOW "FINANCE AND STATISTICS" 2002
UDC 330.45:004.942(075.8) BBK 65v6ya73
REVIEWERS:
Department of Information Systems in Economics, Ural State University State Economic University (head of department A.F. Shorikov,
Doctor of Physical and Mathematical Sciences, Professor);
V.N. Volkova,
Doctor of Economics, Professor of St. Petersburg State University
Technical University, Academician of the International Academy of Sciences of Higher School
Emelyanov A.A. and etc.
E60 Simulation modeling of economic processes: Textbook. allowance / A.A. Emelyanov, E.A. Vlasova, R.V. Thought; Ed. A.A. Emelyanova. - M.: Finance and Statistics, 2002. - 368 p.: ill.
ISBN 5-279-02572-0
Modern concepts for constructing a modeling system, formalized objects such as material, information and monetary resources, as well as language tools for creating simulation models, techniques for their creation, debugging and operation using CASE technology for constructing models “without programming” are presented. The features of modeling in geospace are shown - with reference to maps or plans. The planning of extreme experiments is described.
For university students studying in the specialties “Applied Informatics (by area)”, “Mathematical support and administration of information systems”, as well as for other computer specialties and areas of higher professional education
PREFACE
More than 25 years have passed since the publication of T. Naylor’s book “Machine Simulation Experiments with Models of Economic Systems” in Russian. Since then, methods of simulation modeling of economic processes have undergone significant changes. Their use in economic activity has changed. Some books published in recent years (for example, on the use of GPSS in engineering and technology, on algorithmic modeling of elements of economic systems in Visual Basic) repeat the concepts of simulation modeling 30 years ago using new software tools, but do not reflect what has happened changes.
The purpose of this book is a comprehensive coverage of the approaches and methods of applying simulation modeling in project economic activity that have appeared in recent years, and new tools that provide the economist with a variety of opportunities.
The tutorial begins with a description of the theoretical foundations of simulation modeling. Next, we consider one of the modern concepts for constructing a modeling system. Language tools for describing models are provided. The technique of creating, debugging and operating models using CASE technology for constructing models “without programming” - using an interactive graphical designer is described. There is a special chapter devoted to simulation modeling in geospace with reference to the territories of economic regions. The issues of planning optimization experiments are considered - finding rational parameters of processes using simulation models. The last chapter contains a set of well-debugged simulation models for various purposes, which can be a good help for various categories of readers. They will help teachers develop laboratory work and assignments. For university students, as well as graduate students and specialists who independently study this type of computer modeling, they
will allow you to quickly move on to practical modeling in your subject area.
At the end of each chapter there are brief conclusions and a checklist for self-assessment. A brief glossary of terms and a subject index also make it easier to understand the book's material.
The textbook was written using the work experience accumulated by the authors in the process of teaching academic disciplines related to simulation modeling, risk management, management systems research, during preparation and publication in universities teaching aids And educational materials. The book reflects the results of the author's scientific research and development.
A.A. Emelyanov, Doctor of Economics, Head of the Department of General Theory of Systems and System Analysis at MESI - chapters 1 - 3, 6, 7, 8 (sections 8.1 - 8.3, 8.6, 8.7) and general editing of the book.
E.A. Vlasova, senior lecturer at the Department of General Theory of Systems and System Analysis at MESI - chapters 4 and 8 (sections 8.4 and 8.5).
R.V. Duma, Candidate of Economic Sciences, leading specialist at Business Consol - Chapter 5.
The textbook can be recommended to students studying in computer specialties and areas. It can be useful in training specialist managers and masters in the Master of Business Administration (MBA) programs.
To independently study the book, the reader must first be familiar with computer science, with the basics of programming, higher mathematics, probability theory, mathematical statistics, linear algebra, economic theory and accounting.
INTRODUCTION
Simulation modeling(from the English simulation) is a common type of analog simulation, implemented using a set of mathematical tools, special simulating computer programs and programming technologies that allow, through analogue processes, to conduct a targeted study of the structure and functions of a real complex process in computer memory in “simulation” mode, optimize some of its parameters.
Simulation model is called a special software package that allows you to simulate the activity of any complex object. It launches parallel interacting computational processes in the computer, which are, in their time parameters (with an accuracy of time and space scales), analogues of the processes under study. In countries that occupy a leading position in the creation of new computer systems and technologies, scientific direction Computer Science uses exactly this interpretation of simulation modeling, and master's programs in this area have a corresponding academic discipline.
It should be noted that any modeling has in its methodological basis elements of simulating reality using some kind of symbolism (mathematics) or analogues. Therefore, sometimes in Russian universities, simulation modeling began to be called a targeted series of multivariate calculations performed on a computer using economic and mathematical models and methods. However, from the point of view of computer technology, such modeling is ordinary calculations performed using calculation programs or an Excel spreadsheet processor.
Mathematical calculations (including tabular calculations) can be performed without a computer: using a calculator, a logarithmic ruler, rules of arithmetic operations and auxiliary tables. But simulation modeling is a purely computer work that cannot be done with improvised means.
Therefore, the synonym is often used for this type of modeling
computer modelling.
A simulation model needs to be created. This requires special software - modeling system(simulation system). The specifics of such a system are determined by the technology of operation, a set of language tools, service programs and modeling techniques.
The simulation model must reflect a large number of parameters, logic and patterns of behavior of the simulated object over time (time dynamics) and in space (spatial dynamics). Modeling economic objects is associated with the concept
financial dynamics of the object.
From the point of view of a specialist (computer scientist-economist, mathematician-programmer or economist-mathematician), simulation modeling controlled process or controlled object is a high-level information technology that provides two types of actions performed using a computer:
1) work on creating or modifying a simulation model;
2) operation of the simulation model and interpretation of the results.
Simulation (computer) modeling of economic processes is usually used in two cases:
to manage complex a business process, when a simulation model of a managed economic entity is used as a tool in the contour of an adaptive management 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.
It is possible to identify the following typical tasks that can be solved by means of simulation modeling in the management of economic objects:
modeling of logistics processes to determine time and cost parameters;
managing the process of implementing an investment project at various stages of its life cycle, taking into account possible risks and tactics for raising funds;
analysis of clearing processes in the work of a network of credit institutions (including application to the processes of mutual settlements in the Russian banking system);
forecasting the financial results of an enterprise for a specific period of time (with analysis of the dynamics of the balance in the accounts);
business reengineering insolvent enterprise (change in the structure and resources of a bankrupt enterprise, after which, using a simulation model, one can make a forecast of the main financial results and give recommendations on the feasibility of one or another option for reconstruction, investment or lending to production activities);
analysis of the adaptive properties and survivability of a computer regional banking information system (for example, partially failed as a result of natural disaster the system of electronic payments and payments after the catastrophic earthquake of 1995 on the central islands of Japan demonstrated high survivability: operations resumed within a few days);
assessment of reliability parameters and delays in a centralized economic information system with collective access (using the example of an air ticket sales system, taking into account the imperfection of the physical organization of databases and equipment failures);
analysis of operational parameters of a distributed multi-level departmental information management system, taking into account the heterogeneous structure, bandwidth communication channels and imperfections in the physical organization of the distributed database in regional centers;
modeling the actions of a courier (courier) helicopter flight group in a region affected by a natural disaster or a major industrial accident;
analysis of the PERT (Program Evaluation and Review Technique) network model for projects of replacement and adjustment of production equipment, taking into account the occurrence of faults;
analysis of the work of a motor transport enterprise engaged in commercial transportation of goods, taking into account the specifics of commodity and cash flows in the region;
calculation of reliability parameters and information processing delays in the banking information system.
The given list is incomplete and covers those examples of the use of simulation models that are described in the literature or used by the authors in practice. The actual scope of application of the simulation modeling apparatus has no visible limitations. For example, the rescue of American astronauts in the event of an emergency on the APOLLO spacecraft became possible only thanks to the “playing out” of various rescue options on models of the space complex.
A simulation system that provides the creation of models to solve the listed problems must have the following properties:
The possibility of using simulation programs in conjunction with special economic and mathematical models and methods based on control theory; "
instrumental methods for conducting structural analysis of a complex economic process;
the ability to model material, monetary and information processes and flows within a single model, in a common model time;
the possibility of introducing a regime of constant clarification when receiving output data (main financial indicators, time and space characteristics, risk parameters
And etc.) and conducting an extreme experiment.
Historical reference. Simulation modeling of economic processes is a type of economic and mathematical modeling. However, this type of modeling is largely based on computer technology. Many modeling systems, ideologically developed in the 1970-1980s, have undergone evolution along with computer technology and operating systems (for example, GPSS - General Purpose Simulation System) and are now effectively used on new computer platforms. In addition, at the end of the 1990s. Fundamentally new modeling systems appeared, the concepts of which could not have arisen before - with the use of computers and operating systems of the 1970-1980s.
1. Period 1970-1980s. T. Naylor was the first to use simulation modeling methods to analyze economic processes. For two decades, attempts to use this type of modeling in real economic management
processes were episodic in nature due to the complexity of formalizing economic processes:
in the computer software there was no formal language support for the description of elementary processes and their functions in the nodes of a complex stochastic network of economic processes
With taking into account their hierarchical structure;
There were no formalized methods of structural system analysis necessary for the hierarchical (multilayer) decomposition of the real simulated process into elementary components in the model.
The algorithmic methods proposed during these years for simulation modeling have been used sporadically for the following reasons:
they were labor-intensive to create models of complex processes (requiring very significant programming costs);
when modeling simple component processes they were inferior mathematical solutions in analytical form, obtained by methods of queuing theory. Analytical models were much simpler to implement in the form of computer programs.
The algorithmic approach is still used in some universities to study the basics of modeling elements of economic systems.
The complexity of real economic processes and the abundance of contradictory conditions for the existence of these processes (from hundreds to thousands) lead to the following result. If you use an algorithmic approach when creating a simulation model using conventional programming languages (BASIC, Fortran
And etc.), then the complexity and volume of modeling programs will be very large, and the logic of the model will be too confusing. Creating such a simulation model requires a significant period of time (sometimes many years). Therefore, simulation modeling was mainly used only in scientific activities.
However, in the mid-1970s. The first fairly technological tools for simulation modeling appeared, having their own language tools. The most powerful of them is the GPSS system. It made it possible to create models of controlled processes and objects mainly for technical or technological purposes.
2. Period 1980-1990s. Simulation modeling systems began to be used more actively in the 80s, when more than 20 various systems. The most common systems were GASP-IV, SIMULA-67, GPSS-V and SLAM-II, which, however, had many disadvantages.
The GASP-IV system provided the user with a structured programming language similar to Fortran, a set of methods for event-based modeling of discrete model subsystems and modeling of continuous subsystems using state variable equations, and pseudo-random number sensors.
The SIMULA-67 system is similar in its capabilities to GASP-IV, but provides the user with a structured programming language similar to ALGOL-60.
The effectiveness of the models created using the GASP-IV and SIMULA-67 systems depended to a large extent on the skill of the model developer. For example, the responsibility for creating independent simulated processes rested entirely with the developer, a specialist with high mathematical training. According to this this system mainly^ used only in scientific organizations.
The GASP-IV and SIMULA-67 systems did not have tools suitable for simulating the spatial dynamics of the modeled process.
The GPSS-V system provided the user with a complete, high-level information technology for creating simulation models. This system has means of formalized description of parallel discrete processes in the form of conventional graphic images or using native language operators. Process coordination is carried out automatically in a single model time. The user, if necessary, can enter his own synchronization rules for data. There are tools for model management, dynamic debugging, and automation of results processing. However, this system had three main disadvantages:
the developer could not include continuous dynamic components in the model, even using his own external routines written in PL/1, Fortran or Assembly language;
there were no means of simulating spatial processes
the system was purely interpretive, which significantly reduced the performance of the models.
If 1 hour is selected and the scale is set to 7200, then the model will run slower than the real process. Moreover, 1 hour of a real process will be simulated on a computer for 2 hours, i.e. about 2 times slower. The relative scale in this case is 2:1
(see time scale).
Simulation model(simulation model) is a special software package that allows you to simulate the activity of any complex object. It launches parallel interacting computational processes in the computer, which are, in their time parameters (accurate to time and space scales), analogues of the processes under study. In countries that occupy a leading position in the creation of new computer systems and technologies, the scientific direction of Computer Science is focused on precisely this interpretation of simulation modeling, and master’s programs in this area have a corresponding academic discipline.
Simulation modeling(simulation) is a common type of analog simulation, implemented using a set of mathematical tools, special simulating computer programs and programming technologies that allow, through analog processes, to conduct a targeted study of the structure and functions of a real complex process in computer memory in the “simulation” mode , optimize some of its parameters.
Simulation (computer) modeling of economic processes - usually used in two cases:
1) to manage a complex business process, when a simulation model of a managed economic entity is used as a tool in the contour of an adaptive management system created on the basis of information (computer) technologies;
2) when conducting experiments with discrete-continuous models of complex economic objects to obtain and “observe” their dynamics in emergency situations associated with risks, the natural modeling of which is undesirable or impossible.
Valve blocking the path of transactions - type of node of the simulation model. It is named key. If the valve is influenced by the hold signal from any node, the valve closes and transactions cannot pass through it. A rels signal from another node opens the valve.
Collective management of the modeling process - a special type of experiment with a simulation model, used in business games and educational and training companies
Computer modelling simulation modeling.
Maximum accelerated time scale - scale specified by the number “zero”. The simulation time is determined purely by the processor execution time of the model. The relative scale in this case has a very small value; it is almost impossible to determine(see time scale).
Time scale is a number that specifies the duration of simulation of one unit of model time, converted into seconds, in seconds of astronomical real time when the model is executed. The relative time scale is a fraction that shows how many units of model time fit into one unit of processor time when executing a model on a computer.
Manager (or manager) of resources - type of node of the simulation model. It is named manage. Controls the operation of attach type nodes. For the model to work correctly, it is enough to have one node manager: it will serve all warehouses without violating the logic of the model. To distinguish statistics for different warehouses of transported resources, you can use several manager nodes.
The Monte Carlo method is a method of statistical tests carried out using a computer and programs - sensors of pseudo-random values. Sometimes the name of this method is mistakenly used as a synonym simulation modeling.
Simulation system (simulation system - simulation system) is a special software designed for creating simulation models and having the following properties:
the possibility of using simulation programs in conjunction with special economic and mathematical models and methods based on management theory;
instrumental methods for conducting structural analysis of a complex economic process;
the ability to model material, monetary and information processes and flows within a single model, in a common model time;
the possibility of introducing a regime of constant clarification when receiving output data (main financial indicators, time and spatial characteristics, risk parameters, etc.) and conducting an extreme experiment.
Normal Law- the law of distribution of random variables, which has a symmetrical form (Gauss function). In simulation models of economic processes, it is used to model complex multi-stage work.
Generalized Erlang's law- the law of distribution of random variables, which has an asymmetric form. Occupies an intermediate position between exponential and normal. In simulation models of economic processes, it is used to model complex group flows of applications (requirements, orders).
Queue (with or without relative priorities) - type of node of the simulation model. It is called queue. If priorities are not taken into account, then transactions are ordered in the queue in the order they were received. When priorities are taken into account, the transaction does not end up at the “tail” of the queue, but at the end of its priority group. When priority groups are ordered from the “head” of the queue to the “tail” in order of decreasing priority. If a transaction gets into the queue and does not have its own priority group, then a group with such a priority will immediately appear: there will be one newly arrived transaction in it.
Space-based priority queue - type of node of the simulation model. It is called dynam. Transactions that fall into such a queue are tied to points in space. The queue is serviced by a special rgos unit operating in the spatial movement mode. The point of servicing transactions: it is necessary to visit all points in space with which transactions are connected (or from which they came). When each new transaction arrives, if it is not the only one in the queue, the queue is reordered in such a way that the total path of visiting points is minimal (one should not assume that this is solving the “traveling salesman problem”). The considered rule for the operation of the dynam node is called the “first aid algorithm” in the literature.
Free structural node - type of node of the simulation model. Has the name down. It is necessary to simplify a very complex layer of the model - to “untie” a confusing circuit located on one layer into two different levels (or layers).
Proportionally accelerated time scale - scale given by a number expressed in seconds. This number is less than the selected model time unit. For example, if you choose 1 hour as the unit of model time, and set the number 0.1 as the scale, then the model will run faster than the real process. Moreover, 1 hour of a real process will be simulated on a computer for 0.1 s (taking into account errors), i.e. approximately 36,000 times faster. The relative scale is 1:36,000(see time scale).
Spatial dynamics- a type of dynamics of process development that allows one to observe spatial movements of resources over time. It is studied in simulation models of economic (logistics) processes, as well as transport systems.
Space is a model object that simulates geographic space (the surface of the Earth), a Cartesian plane (you can enter others). Nodes, transactions and resources can be linked to points in space or migrate within it.
Uniform law- the law of distribution of random variables, which has a symmetrical form (rectangle). In simulation models of economic processes, it is sometimes used to model simple (single-stage) work; in military affairs, to model the timing of travel by units, the time of digging trenches and the construction of fortifications.
Finance Manager- type of node of the simulation model “chief accountant”. It is called direct. Controls the operation of send type nodes. For the model to work correctly, one direct node is enough: it will service all accounts without violating the logic of the model. To distinguish statistics for different parts of the modeled accounting department, you can use several direct nodes.
Real time- scale specified by a number expressed in seconds. For example, if you choose 1 hour as the unit of model time, and set the number 3600 as the scale, then the model will be executed at the speed of the real process, and the time intervals between events in the model will be equal to the time intervals between real events in the simulated object (with accuracy up to corrections for errors when specifying the initial data). The relative time scale in this case is 1:1 (see time scale).
A resource is a typical object of a simulation model. Regardless of its nature, during the modeling process it can be characterized by three general parameters: capacity, remainder and deficit. Types of resources: material (based, transportable), informational and monetary.
A signal is a special function performed by a transaction located in one node in relation to another node to change the operating mode of the latter.
Simulation system - sometimes used as an analogue of the termmodeling system(not a very successful translation into Russian of the term simulation system).
Warehouse of transportable resources- type of node of the simulation model. It is called attach. Represents the storage of any number of
quality of the same type of resource. Resource units in the required quantity are allocated to transactions arriving at the attach node if the balance allows such servicing. Otherwise, a queue occurs. Transactions that receive resource units migrate along the graph along with them and return them as necessary in different ways: either all together, or in small batches, or in bulk. The correct operation of the warehouse is ensured by a special unit - the manager.
An event is a dynamic model object that represents the fact that one transaction exits a node. Events always occur at certain points in time. They can also be connected to a point in space. The intervals between two neighboring events in the model are, as a rule, random variables. It is practically impossible for the model developer to control events manually (for example, from a program). Therefore, the event management function is given to a special control program - a coordinator, which is automatically integrated into the model.
Process structural analysis- formalization of the structure of a complex real process by decomposing it into subprocesses that perform certain functions and have mutual functional connections according to the legend developed by the working expert group. The identified subprocesses, in turn, can be divided into other functional subprocesses. The structure of the general modeled process can be represented in the form of a graph with a hierarchical multilayer structure. As a result, a formalized image of the simulation model appears in graphical form.
Structural resource allocation unit - type of node of the simulation model. It is called rent. Designed to simplify that part of the simulation model that is associated with the operation of the warehouse. The warehouse operation is modeled on a separate structural layer of the model. Calls to this layer at the required inputs occur from other layers from the rent node without merging them.
Structural unit of financial and economic payments - type of node of the simulation model. It has the name pay. Designed to simplify that part of the simulation model that is associated with the work of accounting. The work of the accounting department is modeled on a separate structural layer of the model. Calls to this layer to the required inputs occur from other layers from the pay node, without combining these layers.
Accounting account- type of node of the simulation model. It is called send. The transaction that enters such a node is a request to transfer money from account to account or to accounting entry. The correctness of working with accounts is regulated by a special
direct node, which simulates the work of the accounting department. If the balance of money in the send node is sufficient to transfer to another account, then the transfer is carried out. Otherwise, a queue of unserviced transactions forms in the send node.
Terminator is a type of node in the simulation model. It has the name term. A transaction entering the terminator is destroyed. The terminator records the lifetime of the transaction.
A transaction is a dynamic object of a simulation model that represents a formal request for some service. Unlike ordinary requests, which are considered when analyzing queuing models, it has a set of dynamically changing special properties and parameters. The migration paths of transactions along the model graph are determined by the logic of the functioning of the model components in the network nodes.
Triangular law- the law of distribution of random variables, having a symmetrical form (isosceles triangle) or non-symmetrical form (triangle general view). In simulation models of information processes, it is sometimes used to model the access time to databases.
Service node with many parallel channels - type of node of the simulation model. It is named serv. Service can be in the order in which a transaction enters the free channel or according to the rule of absolute priorities (with interruption of service).
Nodes are objects of the simulation model that represent transaction service centers in the graph of the simulation model (but not necessarily queuing). At nodes, transactions can be delayed, serviced, generate families of new transactions, and destroy other transactions. An independent process is spawned at each node. Computing processes run in parallel and coordinate each other. They are performed in a single model time, in one space, and take into account temporal, spatial and financial dynamics.
Managed transaction generator (or multiplier) - type of node of the simulation model. Has the name creat. Allows you to create new families of transactions.
Controlled process (continuous or spatial) - type of node of the simulation model. It has the name rgos. This node operates in three mutually exclusive modes:
modeling a controlled continuous process (for example,
in the reactor);
access to operational information resources;
spatial movements (for example, a helicopter).
Managed transaction terminator - type of simulation node
models. It is called delet. It destroys (or absorbs) a specified number of transactions belonging to a specific family. The requirement for such an action is contained in the destroying transaction received at the input of the delet node. It waits for transactions of the specified family to arrive at the node and destroys them. After absorption, the destructive transaction leaves the node.
Financial dynamics- a type of dynamics of the development of a process that allows one to observe changes in resources, funds, and the main results of the activity of an economic entity over time, and the parameters are measured in monetary units. It is studied in simulation models of economic processes.
The exponential law is the law of the distribution of random variables, which has a pronounced asymmetrical appearance (decaying exponential). In simulation models of economic processes, it is used to model the intervals of receipt of orders (applications) coming to the company from numerous market clients. In reliability theory, it is used to model the time interval between two successive faults. In communications and computer science - for modeling information flows (Poisson flows).
LITERATURE
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pp. 9-86.
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^. Emelyanov A. A. Simulation modeling in risk management. - St. Petersburg: Inzhekon, 2000. - 376 p.
9. Emelyanov A. A., Vlasova E. A. Simulation modeling in economic information systems. - M.: Publishing house MESI, 1998.-108 p.
10. Emelyanov A. A., Moshkina N. L., Snykov V. P.Automated compilation of operational schedules for surveying areas of extremely high pollution // Soil pollution and adjacent environments. W.T. 7. - St. Petersburg: Gidrometeoizdat, 1991. - P. 46-57.
11. Kalyanoe G. N. CASE structural system analysis(automation and application). - M.: Lori, 1996. - 241 p.
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14. Kuzin L. T., Pluzhnikov L. K., Belov B. N.Mathematical methods in economics and production organization. - M.: Publishing House MEPhI, 1968.-220 p.
15. Nalimov V. D., Chernova I. A. Statistical methods for planning extreme experiments. - M.: Nauka, 1965. - 366 p.
16. Naylor T. Machine simulation experiments with models of economic systems. - M.: Mir, 1975. - 392 p.
17. Oykhman E. G., Popov E. V. Business reengineering. - M.: Finance and Statistics, 1997. - 336 p.
18. Pritzker A. Introduction to simulation modeling and the SLAM-P language. - M.: Mir, 1987. - 544 p.
19. Saati T. Elements of queuing theory and its applications. - M.: Sov. radio, 1970. - 377 p.
20. Cheremnykh S.V., Semenov I.O., Ruchkin V.S.Structural analysis systems: GOER-technology.- M.: Finance and Statistics, 2001. - 208 p.
21. Chicherin I. N. Cost of the right to lease a land plot and interaction with investors // Economic information systems on threshold of XXI century. - M.: Publishing house MESI, 1999. - P. 229232.
22. Shannon R. E. Simulation modeling of systems: science and art. - M: Mir, 1978. - 420 p.
23. Schreiber T. J. Modeling on GPSS. - M.: Machine Building, 1979. - 592 p.
PREFACE | |
INTRODUCTION |
Chapter 1 THEORETICAL FOUNDATIONS OF SIMULATION
1.3. Using the laws of distribution of random variables when simulating economic
processes | ||
1.4. Non-traditional network models and temporary | ||
activity interval charts |
||
Self-test questions | ||
CONCEPT AND CAPABILITIES | ||
OBJECT-ORIENTED | ||
MODELING SYSTEM |
||
Main objects of the model | ||
2.2. Modeling of work with material resources | ||
11imitation of information resources | ||
Monetary resources | ||
Simulation of spatial dynamics... | ||
2.6. Model time management | ||
Self-test questions | ||
Although classical optimization methods and mathematical programming methods are powerful analytical tools, the number of real-world problems that can be formulated in a way that does not conflict with the assumptions underlying these methods is relatively small. In this regard, analytical models and, first of all, mathematical programming models have not yet become a practical tool for management activities.
The development of computer technology has given rise to a new direction in the study of complex processes - simulation modeling. Simulation methods, which are a special class of mathematical models, are fundamentally different from analytical ones in that computers play a major role in their implementation. Computers of the third and even more so the fourth generation have not only colossal speed and memory, but also developed external devices and advanced software. All this makes it possible to effectively organize a dialogue between man and machine within the framework of a simulation system.
The idea of the simulation modeling method is that instead of an analytical description of the relationships between inputs, states and outputs, an algorithm is built that displays the sequence of development of processes within the object under study, and then the behavior of the object is “played out” on a computer. It should be noted that since simulation often requires powerful computers and large samples of statistical data, the costs associated with simulation are almost always high compared to the costs required to solve the problem using a small analytical model. Therefore, in all cases, the cost and time required for simulation should be compared with the value of the information expected to be obtained.
Simulation system – a computational procedure that formally describes the object being studied and imitates its behavior. When compiling it, there is no need to simplify the description of the phenomenon, sometimes discarding even essential details in order to squeeze it into the framework of a model convenient for the application of certain known mathematical methods of analysis. Simulation modeling is characterized by the imitation of elementary phenomena that make up the process under study, preserving their logical structure, the sequence of events in time, the nature and composition of information about the states of the process. The model is logical-mathematical (algorithmic) in form.
Simulation models as a subclass of mathematical models can be classified into: static and dynamic; deterministic and stochastic; discrete and continuous.
The task class imposes certain requirements on the simulation model. So, for example, in static simulation, the calculation is repeated several times under different experimental conditions - a study of behavior “in a certain short period of time.” Dynamic simulation simulates the behavior of a system “over an extended period of time” without changing conditions. In stochastic simulation, random variables with known distribution laws are included in the model; with deterministic simulation, these disturbances are absent, i.e. their influence is not taken into account.
The procedure for constructing a simulation model and its research generally corresponds to the scheme for constructing and researching analytical models. However, the specifics of simulation modeling lead to a number of specific features in the implementation of certain stages. The literature provides the following list of the main stages of simulation:
System Definition – Establishing the boundaries, limitations, and performance measures of the system to be studied.
Formulating a model is a transition from a real system to some logical scheme (abstraction).
Data preparation is the selection of data necessary to build a model and present it in the appropriate form.
Model translation is a description of the model in the language used for the computer being used.
Adequacy assessment is an increase to an acceptable level of the degree of confidence with which one can judge the correctness of conclusions about a real system obtained based on access to the model.
Strategic planning is the planning of an experiment that should provide the necessary information.
Tactical planning - determining how to conduct each series of tests provided for in the experimental plan.
Experimentation is the process of performing simulations to obtain desired data and perform sensitivity analyses.
Interpretation - drawing conclusions from data obtained through simulation.
Implementation – practical use of the model and (or) modeling results.
Documentation – recording the progress of the project and its results, as well as documenting the process of creating and using the model
Documentation is closely related to implementation. Careful and complete documentation of the development and experimentation processes with a model can significantly increase its lifespan and the likelihood of successful implementation, facilitates modification of the model and ensures that it can be used even if the departments involved in developing the model no longer exist, and can help the model developer learn from his mistakes .
As can be seen from the list above, the stages of planning experiments on the model are especially highlighted. And this is not surprising. After all, computer simulation is an experiment. The analysis and search for optimal solutions to algorithmic models (and all simulation models belong to this class) is carried out by one or another method of experimental optimization on a computer. The only difference between a simulation experiment and an experiment with a real object is that a simulation experiment is performed with a model of a real system, and not with the system itself.
The concept of a modeling algorithm and formalized
process diagrams
To simulate a process on a computer, it is necessary to transform its mathematical model into a special modeling algorithm, according to which the computer will generate information describing the elementary phenomena of the process under study, taking into account their connections and mutual influences. A certain part of the circulating information is printed out and used to determine those process characteristics that need to be obtained as a result of modeling (Fig. 4.1).
The central link of the modeling algorithm is the simulation model itself - the generated process diagram. A formalized scheme is a formal description of the procedure for the functioning of a complex object in the operation under study and allows for any specified values of the input factors of the model (variables - , deterministic - 
, random – 
) calculate the corresponding numerical values of the output characteristics 
.
The remaining models (Fig. 4.1) represent external mathematical support for the simulation process.
Input models provide specification of certain values of input factors. Static models of deterministic inputs are elementary: they are arrays of constant values corresponding to certain factors of the model. Dynamic input models provide changes in the values of deterministic factors over time according to a known law 
.
Random input models (otherwise known as random number sensors) simulate the arrival at the input of the object under study of random influences with given (known) distribution laws 
. Dynamic models of random inputs take into account that the laws of distribution of random variables are functions of time, i.e. for each time period, either the form or characteristic of the distribution law (for example, mathematical expectation, dispersion, etc.) will be different.
Rice. 4.1. Structure of the modeling algorithm for an optimization model with random factors
Due to the fact that the result obtained by reproducing a single implementation due to the presence of random factors cannot characterize the process under study as a whole, it is necessary to analyze a large number of such implementations, since only then, according to the law of large numbers, the resulting estimates acquire statistical stability and can be accepted with a certain accuracy as estimates of the desired quantities. The output model provides accumulation, accumulation, processing and analysis of the resulting set of random results. To do this, it is used to organize multiple calculations of the values of output characteristics at constant values of factors 
and various values of random factors 
(in accordance with the given distribution laws) – “cycle according y" In this regard, the output model includes programs for tactical experiment planning on a computer - determining the method of conducting each series of runs corresponding to specific values 
And 
. In addition, the model solves the problem of processing random values of output characteristics, as a result of which they are “cleaned” from the influence of random factors and are fed to the input of the model feedback, i.e. The output model implements the reduction of a stochastic problem to a deterministic one using the “averaging over the result” method.
The feedback model allows, based on the analysis of the obtained modeling results, to change the values of control variables, implementing the function of strategic planning of a simulation experiment. When using methods of the theory of optimal experimental planning, one of the functions of the feedback model is to present the simulation results in analytical form - determining the levels of the response function (or characteristic surface). During optimization, the output model calculates based on the values of the output characteristics??? objective function value 
and, using one or another numerical optimization method, changes the values of the control variables to select the values that are best from the point of view of the objective function.
Procedure for developing a formalized process diagram
The procedure for developing a formalized scheme consists of structuring the object into modules; choosing a mathematical scheme for a formalized description of the operation of each module; generating input and output information for each module; development of a control block diagram of the model to display the interaction of individual modules in it.
When structuring an object, a complex object is divided into relatively autonomous parts - modules - and the connections between them are fixed. It is advisable to structurize an object during modeling in such a way that the solution to a complex problem is divided into a number of simpler ones based on the capabilities of the mathematical description of individual modules and the practical implementation of the model on existing computer equipment in a given time. The selection of elements (subsystems of an object) from the object under study and their combination into a relatively autonomous block (module) is carried out on the basis of functional and information-procedural models of the object only when it has been established that it is fundamentally possible to construct mathematical relationships between the parameters of these elements and the intermediate or output characteristics of the object. In this regard, neither the functions nor the inputs and outputs of individual real elements necessarily determine the boundaries of the module, although in general these are the most important factors. The resulting scheme for structuring an object can be adjusted from the point of view of experience or the convenience of transmitting information in an algorithm implemented on a computer.
Next, for each module corresponding to the elementary process occurring in the object, an approximate selection of a mathematical description method is made, on the basis of which the corresponding operation model will be built. The basis for choosing a method of mathematical description is knowledge of the physical nature of the functioning of the element being described and the features of the computer on which the simulation is planned. When developing original dependencies, the developer's practical experience, intuition, and ingenuity play a significant role.
For each selected module, a list of information, both available and necessary for the implementation of the proposed method of mathematical description of information, its sources and recipients is determined.
The modules are combined into a single model based on the operation models and information-procedural models given in the substantive description of the task. In practice, this issue is solved by constructing a control block diagram of the model, which provides an ordered sequence of operations associated with solving the problem. In it, individual modules are designated by rectangles, inside of which the names of the problems solved in it are written. At this level, the flowchart shows “what needs to be done”, but without any details, i.e. does not indicate "how to execute". The sequence of solution and the interdependence of individual elementary problems is indicated by directed arrows, including logical conditions that determine the procedure for control transfers. Such a flowchart makes it possible to cover the entire process in its dynamics and the interconnection of individual phenomena, being a work plan along which the efforts of a team of performers are directed to construct the model as a whole.
In the process of constructing a control block diagram, the inputs and outputs of individual modules are coordinated with each other, their information linkage is carried out using the previously obtained tree of goals-parameters. The practical method of designing a control block diagram follows directly from the purpose for which it is designed, i.e. to sufficiently fully and clearly imagine the functioning of a real complex system in all the variety of interactions of its component phenomena. It is advisable to record the control block diagram in operator form.
After constructing the control block diagram, the contents of the individual modules are detailed. The detailed flowchart contains clarifications that are not present in the generalized flowchart. It already shows not only what should be done, but also how it should be done, gives detailed and unambiguous instructions on how this or that procedure should be performed, how a process should be carried out or a given function should be implemented.
When constructing a formalized diagram, the following should be taken into account. In any operating model there may be following processes: obtaining information necessary for management, movement, “production”, i.e. the main simulated process and support (material and technical, energy, repair, transport, etc.).
Considering this entire set is an extremely difficult matter. Therefore, when constructing a model of an object, it is “production”, i.e. the purpose for which the research task is set is described quite fully. To take into account the influence of non-core processes, the main process model is supplemented with input models that simulate the impact of the processes of movement, support, etc., and various random factors on the process under study. The outputs of these fairly simple models are the values of the environmental characteristics, which are the inputs to the “production” model.
Thus, the resulting formalized diagram contains a control block diagram of the process, a description of each module (the name of the elementary problem being solved, a mathematical method of description, the composition of input and output information, numerical data), a description of the rules for transferring control from one module to another and a final list of the required quantities and studied dependencies. The formalized process diagram serves as the basis for further formalization of the simulation model and the compilation of a computer calculation program that allows one to calculate the values of the output characteristics of the object for any given values of the controlled parameters, initial conditions and characteristics of the environment.
Principles of constructing simulation models
algorithms
A simulation model is, as a rule, a dynamic model that reflects the sequence of elementary processes and the interaction of individual elements along the “model” time axis t M .
The process of functioning of an object over a certain period of time T can be represented as a random sequence of discrete moments in time 
. At each of these moments, changes in the states of the object’s elements occur, and in the interval between them no changes in state occur.
When constructing a formalized process diagram, the following recurrent rule must be fulfilled: an event occurring at a point in time 
, can be simulated only after all events that occurred at the moment in time have been simulated 
. Otherwise, the simulation result may be incorrect.
This rule can be implemented in various ways.
1. Time-based modeling with a deterministic step (“principle 
") in time-based modeling with a deterministic step, the algorithm simultaneously views all elements of the system at sufficiently small intervals of time (simulation step) and analyzes all possible interactions between the elements. To do this, the minimum time interval is determined during which the state of none of the system elements can change; detailed value 
is taken as a modeling step.
The modeling method with a deterministic step consists of a set of repeatedly repeated actions:
"Principle 
"is the most universal principle for constructing modeling algorithms, covering a very wide class of real complex objects and their elements of a discrete and continuous nature. At the same time, this principle is very uneconomical from the point of view of computer time consumption - for a long period, none of the elements of the system can change their state and runs of the model will be in vain.
2. Modern modeling with a random step (simulation based on “special” states). When considering most complex systems, two types of system states can be found: 1) ordinary (non-special) states in which the system is most of the time, and 2) special states characteristic of the system at some points in time, coinciding with the moments of input into the system of influences from environment, the exit of one of the characteristics of the system to the boundary of the domain of existence, etc. For example, a machine is working - a normal state, a machine is broken - a special state. Any abrupt change in the state of an object can be considered during modeling as a transition to a new “special” state.
Time-based modeling with a random step (from event to event) is that the modeling algorithm examines models of system elements only at such moments in time when the state of the system under study changes. At those moments in time when the model of any element of the system must change state, the model of this particular element is inspected and, taking into account the interrelations of the elements, the state of the model of the entire system is adjusted. Step duration 
– random value. This method differs from the "principle 
» in that it includes a procedure for determining the moment of time corresponding to the nearest special state based on the known characteristics of previous states.
3. Application method. When modeling the processing of sequential requests, it is sometimes convenient to build modeling algorithms in a request-by-request way, in which the passage of each request (part, information carrier) is traced from its entry into the system to its exit from the system. After this, the algorithm provides for the transition to consideration of the next application. This kind of modeling algorithms is very economical and does not require special measures to take into account special states of the system. However, this method can only be used in simple models in cases of sequential applications that are not ahead of each other, because otherwise, it becomes very difficult to take into account the interaction of requests entering the system.
Modeling algorithms can be built on several principles simultaneously. For example, general structure The modeling algorithm is based on the principle of special states, and between special states, a per-application method is implemented for all applications.
The structure of the modeling algorithm, as practice shows, has specifics associated with narrow classes of specific types of systems and problems for which the model is intended.
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