Stages of model formation - System theory and system analysis

Stages of model formation

The formation of a model that displays possible options for passing information to the AIS can be accomplished by performing the following steps (Figure 4.6).

1. Delimiting the system from the environment ( enumeration of system elements). The task enumerations can be represented in the language of set-theoretic methods as a transition from the name of the characteristic property reflected in the name of the system being formed (in this case, OASU for a specific industry), to enumeration of elements that correspond to this property and can be included in the set.

In Fig. 4.6. For example, a small number of initial elements are listed: MCC, ITC1, ITC2, ..., A1, A2, ... - points of information collection and processing; D1, D2, ... - forms of collection and presentation of information (documents, arrays); Computer, TT (teletype), T (telephone), etc. It is clear that in real conditions specific types of similar elements are much larger, and they will be called more specifically - not a computer, but the type of evaluation

Fig. 4.6

The computer; similarly - type TT, production recorders (RP), name or code of documents and arrays, etc.

Enumeration can be performed using the "brainstorming" method, and in real terms - methods such as commissions, seminars and other forms of collective decision making (see paragraph 4.1), which results in a certain list of elements of the future system.

2. Combining elements into groups. A complex real developing system can not be list completely. Should, after tying some set of elements, try to combine them into groups, find similarity measures, "proximity" and suggest a way to combine them.

If set-theoretic representations are chosen as the method of formalized mapping of a set of elements, then this sub-step can be interpreted as the formation of elements of the original set of certain subsets by passing from enumeration of elements that are similar in some way to the name of the characteristic property of this subset.

As a result, in this example, subsets of elements can be formed, which were first named: "Information Implementation Form (FRI)", "Technical Facilities (TC)", "Information Service Type (VIS)"; , executors, operators (O) etc. (see Figure 4.6, c), and in the subsequent - the relevant types of collateral: information, technical, organizational support - IO, TO, ORGO, respectively.

3. Formation of elements of subsets of new sets consisting of "pairs", "triples", "p-app", " elements of the original subsets. In this example, combining elements of subsets of FIS, FRI, TS, etc. in pairs and triples & quot ;, we get new components.

Example

We get: Д1_ЭВМ, Д1_ТТ, Д2_ЭВМ, etc .; Computer_GIIC, computer_IVC1, computer_A1, TT_GIVC, TT_IVTS1, TTA1, etc .; D1_EVM_HIVC, D1_TT_A1, etc.

Interpretation of the received components is difficult, and it is not possible to introduce any formal rule of comparison of elements of new sets that would help to make a decision about choosing the best options.

In such cases, according to the approach under consideration, it is necessary to return to system-structural representations and try to look for a further way for the development of the model.

4. A thorough analysis of the results and a search for new ways to develop the model. To conduct a meaningful analysis, you should return to the system views and use one of the methods of the MAIS group - structuring (in this case in the form of a hierarchical structure - Figure 4.6, 0 ).

Such a view is more convenient for decision-makers (managers of the work on the creation of the OASU) than set-theoretic representations, and helps them to first distribute the work among the relevant specialists, and then find a further way of developing the model on the basis of a meaningful analysis of the essence of the received " ; and triples from the point of view of the wording of the problem being solved. Since any task is a sequence of actions (functions) for collecting, storing, and initial processing of information, it becomes obvious that a new subset of the "Function-Operation ()" is added to the model, adding its elements to the previous "pairs" and triples allows us to get a new understanding of them. For simplicity, Fig. 4.6 shows only the fundamentally different functions of the relationship C, the storage of M (from the " memory" - memory) and processing K (from words computer ), i.e. gene information system, considered in paragraph 4.1.

After their addition, combinations are obtained that the DM can not only compare, but also evaluate. For example, combinations of type С_Д1_ТТ, С_Д1_Т differ from each other by the speed of information transfer, which under specific conditions can be measured or calculated.

5. Development of the modeling language. After the missing subset is found, in principle it would be possible to continue the further formation of the model, using set-theoretic representations. However, when the need for the formation of sequences of function-operations, specified by adding them as collateral-specific functions (CF), is realized, then it is more expedient to choose linguistic or a given model semiotic representations which are more convenient for development of a language for modeling CF sequences.

To explain the principles of developing a modeling language, we give a more detailed presentation of the stages (Figure 4.7).

The principles of developing a modeling language can be represented as follows:

■ development of the thesaurus of the modeling language;

■ Develop a grammar (or several grammars, depending on the number of levels of the model and the difference in the rules).

In this example, a combination of linguistic, semiotic and graphical representations is used, and the language of grapho-semiotic modeling , which in the initial variants of using the approach under consideration was sometimes also called - structurally-linguistic, (signed) modeling.

The thesaurus structure of the modeling language, shown in Fig. 4.7, r, includes three levels:

- the level of primary terms (or words), which are represented in the form of lists consisting of elements {e,} subsets of F, ВИС, FРИ, ТС;

is the level of phrases {/ j}, which in this particular language can be called the level of the specified functions (CF), since the abstract functions C, , combining with the elements of the WIS, TS, are specified in relation to the simulated process;

- the sentence level {p to }, displaying the options for passing information in the system under investigation.

The grammar of the language includes rules of two kinds:

- transformations of elements {e,} of the first level of the thesaurus into components {fj} of the second level, which have the character of rules of type "rooms next to" (concatenation, cohesion) R,;

- the transformation of the components {fj } into sentences { p k} - a conditional-type rule for R n ; rules of this kind exclude inadmissible variants of information following from consideration: for example, after the function С1_Д2_А1-ИВЦ1_ТТ (transfer of document Д2 from А1 to ИВЦ1 by means of ТТ) can not follow function M1_D2_HIV_MN, because as a result of the previous function, the document D2 was not received at the GIVC (here MN is the machine medium).

Fig. 4.7

As a result of the performed transformations, the structure of Fig. 4.7, in, the composition of the providing part of the OACS, is transformed into a structure (Figure 4.7, e), displaying the information paths.

The dictionary of primary terms of the language of grapho-semiotic modeling, the number of levels in it and the rules of grammar are determined by the results of the previous development of the model.

Thus, using a modeling language, a multi-level model is developed.

In our example - two-level if we consider the level of initial sets as zero ({e,} in Fig. 4.6, x and 4.7, d). The comprehension of this model (at the MAIS level) leads to the transformation of the structure originally formed as a structure-composition, in which the types of OASS provision and their detailing were presented (Figure 4.7, c) in structures, (Figure 4.7, q).

6. Evaluation and analysis of information flow options. After forming the variants of following the information, it is necessary to evaluate them. For this, different variants can also be taken: from a meaningful evaluation by collecting and initial processing of information (lower level, Figures 4.6, x and 4.7, d) to the search for algorithms for sequential transformation of estimates of components of previous model levels in evaluation of components of subsequent levels, which is carried out by analyzing the generated grapho-semiotic model.

The options for estimating the model are illustrated in Fig. 4.8.

In this example, you can evaluate in three ways:

a) at the level of the information flow options { p k}, which can sometimes be done by competent experts through a collective discussion of the options offered to them (if the number of these options is not very large - no more than 7 + 2);

b) at the level of the specified functions (CF) {/)} with the subsequent conversion of these estimates W ' {/ •} to the estimates of the variants W {p to } ',

c) at the level of the elements {e ^} with the subsequent transformation of the estimates W {e t } into the estimates W {/}, and their - in the estimates W "{p to }.

Fig. 4.8

With the second method, you can highlight the spheres of competence and assign the assessment of CF in the spheres to relevant specialists; CF estimates are also expert in most cases, but in some cases they can be measured; this method is similar to the estimation of the network model, and in the determination of the algorithm for converting the estimates of φP, one can use the experience of network modeling (for most evaluation criteria, the transformation algorithm is summation, and for the reliability of transfer or storage of information estimated with probabilities, the algorithm is more complex)

In the third method, the transformation algorithms φ1 can be found by analyzing the various QFs from the point of view of the effect on their evaluation by this or that criterion of the elements of the corresponding type. For example, the estimation of the information transfer by the time criterion t can be obtained on the basis of finding out what in the structure of the CF affects the estimate with respect to t. If technical means of communication are used, then, knowing the principles of information transfer, with their help one can determine vTC and the dependencies , where - the amount of information transmitted (for example, measured by the number of characters), i.e. estimation of the elements belonging to the subset of the FRI; - the speed of information transfer using an appropriate technical means, i.e. an estimate of an element belonging to a subset of TC. Thus, in this example, the KF estimates "C ... the elements of the subsets of the FRI and TS are influenced, and their evaluation should be provided in the source lists of the elements. Similarly, it is possible to determine which of the elements affect the CF estimates by cost, reliability, timing of implementation, and other recognized evaluation criteria.

The choice of the method for evaluating the model depends on the type of grapho-semiotic model, and the algorithms for converting the estimates φI and φII are determined on the basis of the analysis of this model. The choice of evaluation criteria depends on the chosen method of estimating the model.

For example, with the first two methods of estimation (at the level and at the level ), such assessments as efficiency (time), reliability (the probability of failure in the transfer of information, errors in processing it, etc.), labor intensity, implementation costs, operating costs, timing of implementation, etc., and in evaluating the model at the element level - estimates of the type , etc., on the basis of which estimates of the KF can be calculated , or an estimate of the complexity, the rate of filling the forms or entering information, etc.

The way of evaluating the model at the level of options - expert; at the level spheres of competence can be singled out for expert evaluation and relevant specialists are involved, who know the specifics of specific technical means, etc .; and in addition, along with expert evaluation, experiments can be conducted on a particular CF.

Estimations of the elements necessary to calculate the estimates of the corresponding QFs can in most cases be obtained from the reference literature or measured.

The multilevel model under consideration can be represented in the generalized form in the form of analytical dependencies.

For example, for the variant estimates shown in Fig. 4.8, a:

(4.2)

For the variant shown in Fig. 4.8, in:

(4.3)

The symbol denotes any interaction of the components "conditional following for", complex interaction or simply "placing nearby"; a functional linking the evaluation criteria of the chosen solution to the components that depend on the components of the previous level ; in the general case, depend on the components - sets of meaningful elements (thesaurus) tasks; - criterial displays of elements (components) of the structural levels of the thesaurus of the modeling language; - algorithms for converting criterial mappings of one structural level to another; - a collection of components of all levels.

The result is a system of algorithms that provides the possibility of automation and, accordingly, the repeatability of the process of forming and analyzing the model when changing sets of primary elements and their estimates.

This system of algorithms provides a relationship between components and system goals (when modeling information flows for individual tasks - between components and the requirements of this task). The result is a formal, analytical model, only presented not in the form of formulas or equations customary for this kind of model, but in the form of algorithms in computer memory.

However, it is almost impossible to obtain such a complex system of algorithms that allows us to formalize the mapping of a specific situation and choose the best solution without the organization of a directed gradualization of the decision-making process.

Thus, on the basis of this approach, it is possible to set the task of sequentially forming, using the grapho-semiotic language, the modeling of the options for passing information and choosing the best from them by gradually limiting the range of permissible solutions. This procedure is as follows: first, delete all the p k that do not satisfy the boundary values ​​of the criteria considered, then offer to consider the remaining options of the decision maker who can either choose the most preferable from them, or enter the weight coefficients of the criteria, or to investigate the area of ​​admissible solutions by the Pareto method.

You can also add new criteria of a qualitative nature, not included initially because of the inability to quantify them.

The adequacy of the models is proved sequentially (as the generalized model is formed) by evaluating the correctness of the reflection in each subsequent model of the components and relationships necessary to achieve the goal and solve the problems that realize it.

After all stages of gradual formalization have been passed for some class of tasks and the foundations of the modeling language have been found, it is possible to apply not the entire methodology, but immediately begin with the sub-step shown in Fig. 4.6, x. However, in the case when it is necessary to set a task for a fundamentally new object or process, it is useful in justifying the model to perform all the sub-stages of the gradual formalization of the task, which will justify the adequacy of the model and the principles of developing the modeling automation language and algorithm model estimates.

At the same time, passing the stages of gradual formalization, it is useful to take into account recommendations of the type use what you know "," do not get carried away with the listing "," do not forget to return to the system views "," remember the purpose " , do not be afraid to change methods , etc. (as illustrated in Figure 4.6).

To explain the usefulness of the method of gradual formalization, we give the result obtained in solving the problem considered.

After modeling the options for passing information and evaluating options using the algorithm shown in Fig. 4.8, в, , an unexpected result was obtained: a variant of the information network structure for collecting and preliminary processing of information with location in the territorial centers of computers and a similar option with teletypes in time for the collection of information differ only by 0.5 hour (8.5 and 9 hours!). In this case, the second option is significantly (by an order of magnitude) cheaper. It's about the 1970s, when there were no personal computers yet, and large computers (at that time Minsk-32, Minsk-22) were very expensive.

By the time VNIPIOASU, which was the customer of the task, had already begun to develop a technical project with the first option (much more expensive than the second one), because based on the "common sense" it was assumed that this project will almost all of an order of magnitude faster collect information during the quarterly or annual reporting.

An unexpected result that destroys the ideas of "Common sense", was obtained through the development of a technique for automating the modeling and distribution of work between performers as follows: the development of models was carried out by the student R. Cooper, and the student L.Zharova processed the results of the model evaluation. Cooper was half American, he thought unconventional and did not exclude teletype from the pre-processing facilities! Clearly conducted a conscientious, impartial analysis, without delving into the meaningful meaning of the options, so that this does not affect the results.

After further analysis of information flows on the most voluminous tasks, "manually" it was found out that the resulted unexpected result has been received because the information from the enterprises located in one city which it would seem it was possible to enlarge, having processed on territorial VC, is necessary for decision-making to various main managements (so-called Glavkas) of branch ministry, and therefore to generalize this information is not only at the city level, but even at the enterprise level it is impossible, and to speed up the transfer of this information it is enough to have its pre-accumulation in a teletype that is read in the mode I was faster than in the packing mode.

In VNIPIOASU, of course, the project did not begin to be reworked, but later they began to develop registers of information about the state of production instead of teletypes with preliminary accumulation of information. The main result was the fact that the developed and applied method of system inspection of information flows and the adoption of a pre-project solution for choosing the structure of a system for collecting and initial processing of information helped to obtain a nontrivial solution.

For convenience of application of the considered approach in practice the resulted sequence of actions (a technique) is accepted to represent in the form of the block diagram (an example of a technique is shown in a picture 4.9).

Developing a technique for practical use, the names of stages can be changed taking into account the specific conditions of its application. In Fig. 4.9 the names of the approaches and methods used to solve the problem for VNIPIOASU are given.

Similarly to the task considered, it is possible to set the tasks of forming a structure that provides parts of an automated system, modeling organizational and technological procedures for preparing and implementing managerial decisions in an operating enterprise (see Chapter 9).

Fig. 4.9

thematic pictures

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