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At the second stage of modeling - the stage of algorithmization of the model and its machine implementation, the mathematical model formed in the first stage is embodied in a specific machine model. This stage is a stage of practical activity aimed at implementing ideas and mathematical schemes in the form of a machine model of the process of functioning S. Before considering the elements of algorithmization and machine implementation of the model, we will discuss the basic principles of building modeling algorithms and the forms of their presentation.

Principles of constructing modeling algorithms.

The process of functioning system S can be considered as a sequential change of its states in-dimensional space. It is obvious that the task of simulating the compounding process of the system S system is to build functions based on which it is possible to calculate the characteristics of the system of functioning of the system. To do this, there should be a relationship that bind functions with variables, parameters and time, as well as the initial conditions at the time of time.

Consider the process of functioning of some deterministic system in which there are no random factors, i.e. the status vector of such a system can be determined from (2.3) as. Then the state of the process at the time of time

it can be uniquely determined from the ratios of the mathematical model according to the well-known initial conditions. This allows you to build a modeling system of the system of the system. To do this, we transform the ratio of the model to this species to make a convenient calculation by the values \u200b\u200bwhere we organize the system time counter, which in the initial moment shows the time. To do this moment, we add the time interval Then the counter will show the values \u200b\u200bto be calculated then by turning to the time if the step is small enough, then this way you can get approximate values

Consider the process of functioning the stochastic system that is, the systems that are affected by random factors, i.e., the status vector is determined by relation (2.3). For such a system, the function of the process states at the time of time the ratio of the model is determined only by the distribution of probabilities for at the time of time. In general, the initial conditions may be random specified by the corresponding probability distribution. At the same time, the structure of the modeling algorithm for stochastic systems is mainly the same. Only instead of the state now it is necessary to calculate the distribution of probabilities for possible states. Let the system time counter shows the time. In accordance with the specified probability distribution, it is chosen further, based on the distribution, the state is obtained until one of the possible implementations of the random multidimensional process will be built at a specified time interval.

The considered principle of constructing modeling algorithms is called the principle of the most universal principle, which allows to determine the consistent states of the process of operation of the system S at a given time intervals, but from the point of view of machine time costs it is sometimes not economical.

When considering the operation of some systems, some systems can be found that two types of states are characterized: 1) Special inherent in the functioning of the system only at some time of time (moments of entering input or control effects, perturbations of the external environment, etc. Non-singular in which the process is All the rest of the time. Special conditions are also characteristic of the fact that the function of the states in these moments of time are changed by a jump, and between special states, the change in coordinate occurs smoothly and continuously or does not occur at all. Thus, by simulating the system model, only its special

states in those moments of time when these states occur, you can obtain the information necessary to build functions. Obviously, modeling algorithms on the "principle of special states" can be constructed for the described type of systems. Denote by the hopping (relay) change of state as a "principle of special states" - as a principle

For example, for a mass service system (-sham), states can be selected as a special states in the moments of receipt of applications for service in the device P and at the time of the end of servicing applications by channels to when the state of the system, estimated by the number of applications in it, changes the jump.

Note that the characteristics of the functioning process of such systems with special states are evaluated according to information about special states, and non-singular states during modeling are not considered. "The principle makes it possible for radical systems to significantly reduce the cost of machine time for the implementation of modeling algorithms compared with the" principle of the logic of constructing a modeling algorithm that implements "the principle differs from the considered for the" principle only in what includes the procedure for determining the time of the time corresponding to the following special state S. Systems S. To study the process of functioning of large systems rationally, the use of a combined principle of constructing modeling algorithms that combines the benefits of each of the considered principles.

Forms of representation of modeling algorithms.

A convenient form of representing the logical structure of models of the operation of systems and machine programs is a scheme. At various stages of modeling, generalized and detailed logic schemes of modeling algorithms are compiled, as well as program schemes.

The generalized (enlarged) scheme of the simulator algorithm sets the overall procedure for modeling the system without any refineering parts. The generalized scheme indicates that it is necessary to perform at the next modeling step, for example, to refer to the random number sensor.

A detailed scheme of the simulator algorithm contains clarifications that are absent in the generalized scheme. A detailed diagram shows not only what should be performed at the next step modeling system, but also how to execute it.

The logic diagram of the simulator algorithm is the logical structure of the model of the system of the system S. The logic circuit indicates the time-ordered sequence of logical operations associated with the solution of the modeling problem.

The program scheme displays the order of the program implementation of the simulator algorithm using a specific mathematical support. The program scheme is the interpretation of the logical scheme of the simulated algorithm by the developer of the program based on a specific algorithmic language. The difference between these schemes is that the logic circuit reflects the logical structure of the model of the system of the system, and the program scheme is the logic of the machine implementing the model using specific software and technical modeling.

The logical scheme of the algorithm and the program scheme can be made both in the enlarged and in detailed form. To draw these schemes, a set of characters defined by GOST 19,701 - 90 (ISO 5807 - 85) "Unified System Documentation System is used.

Schemes of algorithms, programs, data and systems.

Conditional designations and rules of execution. " Some most commonly used in the practice of modeling on computer symbols are shown in Fig. 3.3, where the main, specific and special symbols of the process are depicted. These include: Main Symbol: A - Process - The symbol displays the data processing function of any kind (executing a specific operation or group of operations, leading to a change in value, form or placement of information or to the definition by which from several flow directions should be moved); Specific Process Symbols: B - Solution - The symbol displays a solution or a switch function that has one input and a number of alternative outputs, one and only one of which can be activated after calculating the conditions defined within this symbol (the corresponding calculation results can be recorded next door with lines displaying these paths); B - Preparation - The symbol displays the command modification or group of commands to influence some subsequent function (setting the switch, modify the index register or program initialization); r - predefined process - the symbol displays a predefined process consisting of one or more operations or steps of a program that are defined elsewhere (in the subroutine, module); D - manual operation - the symbol displays any process performed by a person; Special Symbols: E - Connector - The symbol displays the output into part of the circuit and input from another part of this circuit and is used to break the line and continueing it elsewalk (the corresponding symbols connectors must contain the same unique designation); F Terminator - The symbol displays output to an external environment and input from the external environment (beginning or end of the algorithm schema, external use or data assignment).

Fig. 3.3. Symbols and schemes of modeling algorithms

An example of the image of the modeling algorithm scheme is shown in Fig. 3.3, s.

Usually the scheme is the most convenient form of representing the structure of modeling algorithms. In some cases, other forms of representing modeling algorithms are used, for example, the shape of the graph schemes (Fig. 3.3, and). Here - the beginning, - the end, - the calculation, - the formation, - the verification of the condition - the meter, - the issuance of the result, where is the total number of operators modeling algorithm. As an explanation to the graph scheme of the algorithm, the text is disclosed in the text of the operator's content, which makes it possible to simplify the representation of the algorithm, but complicates its work with it.

Modeling algorithms can also be presented as operator schemes. Operator designations on such a scheme correspond to the designations for graph schemes. For the considered example, the algorithm operator scheme has a view

In more detail with the form of representing the logical structure of modeling algorithms and machine programs, we will get acquainted when considering imitation models of the functioning of various systems and methods for their implementation on a computer.

Subjects of the second stage of modeling.

Consider the submets performed during the algorithmization of the system model and its machine implementation, the focus on the tasks of each sub-step and the methods of their solution.

2.1. Building a logical model pattern. It is recommended to build a model on a block principle, i.e. in the form of a certain set of standard blocks. Building model S systems from such

the blocks ensures the necessary flexibility in the process of its operation, especially at the stage of machine debugging. When building a block model, the process of functioning the system into separate autonomous subprocesses is carried out. Thus, the model is functionally divided into subdiments, each of which, in turn, can be divided into even smaller elements. Blocks of such a model are two types: basic and auxiliary. Each main unit corresponds to a certain real subprocess, which has a place in the simulated system S, and the auxiliary blocks are only an integral part of the machine model, they do not reflect the functions of the simulated system and are necessary only for machine implementation, fixation and processing of modeling results.

2.2. Obtaining mathematical ratios. Simultaneously with the implementation of the sub-stage of constructing a logic model of the model, it is necessary to obtain, if possible, mathematical ratios in the form of explicit functions, i.e. to build analytical models. This sub-step corresponds to an implicit task of possible mathematical relations at the stage of constructing a conceptual model. When performing the first stage, there can still be information on the specific form of such mathematical relations, and in the second stage it is already necessary to obtain these relations. The scheme of the machine model must be a complete reflection of the concept laid in the model and have: a) a description of all blocks of the model with their names; b) a unified system of symbols and numbering of blocks; c) reflection of the logic of the model of the system functioning; d) The task of mathematical relations explicitly.

Thus, in the general case, a constructed machine model of the system will have a combined character, i.e., reflect an analytical imitation approach, when part of the process in the system is described analytically, and the other part is mimicted by the corresponding algorithms.

2.3. Check the authenticity of the system model. This check is the first of the checks performed at the model implementation phase. Since the model is an approximate description of the process of functioning of the real system S, then until the model reliability is not proved, it cannot be argued that it will be obtained that they will be obtained that coincide with those that could be obtained when conducting a real-life experiment with a real system S. Therefore, the determination of the model of the model can be considered the most important problem when modeling systems. The degree of confidence in the results obtained by modeling method depends on the solution. Verification of the model on the under consideration should provide an answer to the question of how the logical scheme of the system model and the mathematical relations used reflect the idea of \u200b\u200bthe model formed at the first stage. At the same time checked: a) the possibility

solutions to the task; b) the accuracy of reflection of the plan in a logical scheme; c) fullness of the logic model scheme; d) the correctness of the mathematical ratios used.

Only after the developer is convinced by appropriate verification in the correctness of all these provisions, we can assume that there is a logical scheme of the system of system 5, suitable for further work on the implementation of the model on a computer.

2.4. Selection of tools for modeling. On this sub-step, it is necessary to finally resolve the question of which computing machine (computer, AVM, GVK) and which software is advisable to use to implement the System S. System model in general, the choice of computing tools can be carried out on previous sub-payments, but the sub-step in question is the last When this choice should be made finally, since otherwise it will be difficult to carry out further work on the implementation of the model. The issue of choosing a computer is reduced to ensuring the following requirements:

a) the presence of the necessary software and technical means; b) availability of the selected computer for the model developer; c) providing all stages of model implementation; d) the possibility of timely receipt of results.

2.5. Drawing up a programming work plan. Such a plan should help in programming the model, given the assessment of the scope of the program and labor costs to its preparation. The plan when using a universal computer should include: a) Selecting a language (Systems) of model programming; b) specifying the type of computer and necessary for modeling devices; c) an estimate of the approximate volume of the necessary operational and external memory; d) the approximate costs of machine time on modeling; e) the estimated time spent on programming and debugging a computer program.

2.6. Specification and construction of the program scheme. Program Specification - Formalized presentation of the requirements for the program to be satisfied when developing it, as well as a description of the problem, conditions and effects of action without specifying the method of its achievement. The presence of a logical block diagram of the model allows you to build a program scheme, which should reflect: a) splitting the model to blocks, subblocks, etc.;

b) features of model programming; c) carrying out the necessary changes; d) program testing capabilities; e) assessment of machine time costs; e) form of submission of input and output.

Construction of the program scheme is one of the main tasks at the machine implementing the model. At the same time, special attention should be paid to the peculiarities of the language selected for the implementation of the model: the algorithmic language of the general

assignment or modeling language (for example, Simula, Simscript, GPSS).

2.7. Verification and verification of the reliability of the program scheme. Verification of the program is proof that the behavior of the program complies with the specification for the program. This check is the second at the machine implementation of the system model. Obviously, it makes no sense to continue the work on the implementation of the model, if there is no confidence that in the program scheme, on which further programming will be carried out, errors that make its inadequate logic diagram of the model, and therefore the inadequate model of modeling itself are allowed. At the same time, the conformity of each operation presented in the program scheme similar to the operation in the logical diagram of the model is carried out.

2.8. Conduct programming model. With a sufficiently detailed scheme of the program, which reflects all operations of the logic model of the model, you can proceed to programming the model. If there is an adequate program diagram, the programming is only for a programmer without participation and help from the model developer. When using packages of modeling application programs, direct generation of working programs are carried out for modeling a specific object, i.e. the model programming is implemented in an automated mode.

2.9. Check the reliability of the program. This last check at the machine implementation phase of the model, which must be carried out by: a) reverse transfer of the program to the original scheme; b) checking individual parts of the program when solving various test tasks; c) combining all parts of the program and checking it in general on the control example of simulation of the version of S.

On this sub-step, it is also necessary to check the assessments of the cost of machine time for modeling. It is also useful to obtain a fairly simple analytical approximation of the dependence of the cost of machine-time from the number of implementations, which will allow the developer of the model (Customer) to correctly formulate the requirements for the accuracy and reliability of modeling results.

2.10. Drawing up technical documentation for the second stage. To complete the stage of the machine implementing the model, it is necessary to compile a technical documentation containing: a) the logical scheme of the model and its description; b) adequate program scheme and adopted designations; c) full program text; d) a list of input and output values \u200b\u200bwith explanations; e) instructions for working with the program; (e) Evaluation of machine time costs for modeling with the required computer resources.

Thus, at this stage, the scheme of the model S system is being developed, its algorithm and programming is carried out.

using specific software and hardware, i.e., a machine model is built with which it is necessary to work to obtain the necessary results of modeling according to the evaluation of the characteristics of the functioning of the system S (problem of analysis) or to search for optimal structures, algorithms and system parameters S (synthesis problem ).