Fundamentals of a Methodology for Selecting a Rational Structure of a Complex of Technical Means

Fundamentals of a Methodology for Selecting a Rational Structure of a Complex of Technical Means

A. A. Tereshchenko, R. E. Kalichkin

(Presented by the scientific-technical seminar of the Department of PM)

Questions of selecting a complex of technical means (CTM) have been insufficiently covered in the literature and, as a rule, amount to a set of recommendations for selecting one or another type of computing equipment depending on the tasks being solved. In this case, the selection of an individual device for a definite stage of information processing is carried out nonoptimally, i.e., it is not connected with the structure of the technical means as a whole.

The selection of a complex of technical means for automated control systems (ACS) must be reduced to determining the nomenclature of means and calculating their required number, which would ensure the functioning of the ACS according to a specified criterion and satisfy certain constraints, as well as provide for the possibility of further development of the system.

In the general case this problem is formulated as follows.

Given:

the set of information-processing algorithms in the ACS (functions of the CTM) \(F=\{f_i\}\), where \(i=1,2,\ldots,I\) is the index—the number of the task being solved;

the set of types of technical means \(H=\{h_j\}\), where \(j=1,2,\ldots,l\) is the index of the type of technical means;

the set of requirements (constraints) \(R=\{r_\gamma\}\), where \(\gamma=1,2,\ldots,\Gamma\) is the index—the number of the requirement (constraint) imposed on the sets \(F\) and \(H\).

It is necessary to determine:

a) the set of information-conversion points \(B=\{b_k\}\), where \(k=1,2,\ldots,K\) is the index of the designed data-conversion point;

b) the subset of technical means \(A=\{a_{qk}\}\) assigned to each \(k\)-th point, where \(q\) is the index of the technical means;

c) the methods of communication between levels and means within levels.

The principal characteristics of the tasks taken into account when selecting a CTM include [3]:

characteristics of information flows (indicating changes in intensity during the period under consideration);

requirements for the urgency of solving tasks and the moments when solution begins;

block diagrams of tasks, indicating the volumes of the arrays of source data used;

the approximate number of operations required for solving each task;

methods of representing input and output information; requirements for the reliability and accuracy of output results.

The problem of choosing a variant of a CTS can be represented as finding, in an \(n\)-dimensional space, each of whose coordinates represents some characteristic of a variant of such an \(n\)-dimensional volume, the bounding surfaces of which are determined by specified inequalities (all requirements imposed on the CTS are usually given in the form of inequalities; for example, the time for processing information in a computing complex must be no greater than \(T_{\text{allow}}\), etc.). Points lying inside this volume determine variants of complexes that satisfy all requirements simultaneously, while points lying outside the bounded volume fail to satisfy some or all of the specified conditions. In general, the set of points characterizing CTS variants will satisfy the specified set of inequalities and constraints, but only one or several points will correspond to the variant that is optimal with respect to some minimized selection criterion.

By the criterion of system effectiveness is meant a quantitative indicator that characterizes the degree of functioning of the system. This integral indicator is the most general for expressing quality and depends on a number of particular factors; such particular factors are called generalized parameters. Each of the generalized parameters must characterize the quality of fulfillment of the overall goal of the system and, where possible, be functionally connected with the general criterion of effectiveness. Each of the generalized parameters must [1, 2]: have a clear and unambiguous physical meaning; be related by observable dependencies, preferably functional ones, to the technical parameters of the system elements; be quantitative in character; and be effective in the statistical sense, i.e., it must have small variance and, consequently, be determined with sufficient accuracy.

The total number of generalized parameters should not be large, so as not to complicate the already difficult problem of system optimization.

The first and most important generalized parameter for a CTS is the time for solving computational problems, or the time of reaction to a disturbing action (the complete cycle of information transformation).

The time of the complete cycle of information passage in an ACS, taking into account the implementation of a control action by the production personnel of the controlled object, can be represented by the following formula [1]:

\[ T_{\text{c.i}} = T_{\text{k.t.s}} + T_{\text{r.p.v}} = T_{\text{s.p}} + T_{\text{v.n.o}} + T_{\text{v.p}} + \sum_{i=1}^{3} t_{i\text{z}} + T_{\text{r.p.v}}, \tag{1} \]

where \(T_{\text{c.i}}\) is the time of the complete cycle of information passage;

\(T_{\text{s.p}}\) is the time spent on collecting, transmitting, and preparing information;

\(T_{\text{v.n.o}}\) is the time spent on input, accumulation, and processing of information;

\(T_{\text{v.p}}\) is the time spent on output and transmission of information to the user;

\(T_{\text{r.p.v}}\) is the reaction time of production personnel to the control action;

\[ \sum_{i=1}^{3} t_{i\text{z}} \]

is the total time of delays in the arrival of information during the information-processing period;

\(T_{\text{k.t.s}}\) is the time of information passage through the CTS, including the total delay time.

\[ T_{\text{r.p.v}} = t_{\text{percept}} + t_{\text{eval.inf}} + t_{\text{dec.mak}} + t_{\text{iss.act}} + t_{\text{iz.org}}, \tag{2} \]

where \(t_{\text{per}}\) is the time for personnel to obtain and perceive information;
\(t_{\text{eval.inf}}\) is the time for evaluating the information received;
\(t_{\text{dec}}\) is the time for personnel to make a decision;
\(t_{\text{iss.act}}\) is the time for personnel to issue a control action;
\(t_{i\text{z,org}}\) is organizational delays.

Despite the fact that the time values of individual stages and operations, and the relationships among them in the formulas given above, vary within wide limits, the admissible values of these quantities when using a CTS and the complete cycle of information processing in an ACS play an essential role in selecting a CTS for the system, since in an ACS the following condition must be satisfied

\[ T_{i\text{ dec.task}} \leqslant T_{i\text{adm}}, \tag{3} \]

where \(T_{i\text{ dec task}}\) is the time for solving the \(i\)-th task with the aid of the given CTS;
\(T_{i\text{adm}}\) is the admissible time for solving the \(i\)-th task.

The second most important generalized parameter is the accuracy (reliability) of the output information [1, 2].

The accuracy of solving a task is quantitatively expressed through the probability of correctly solving each task within a specified time. The probability of a correct solution depends, on the one hand, on the characteristics and parameters and, in particular, on the reliability parameters of all technical means and servicing personnel participating in solving the task at all its stages, and on the methods of checking information conversion; and, on the other hand, on the magnitude of the reserve of time during which an error can be detected and corrected.

If the CTS is formed by \(n\) information-collection devices, \(m\) information-transmission devices, \(k\) information-output devices, and \(r\) information-processing devices, then in the general case the probability of a correct solution of the task will be:

\[ Q_{\text{corr}} = 1 \mp P_{\text{err}} = \prod_{i=1}^{n} (1 - P_{i\text{coll}})\cdot \prod_{j=1}^{m} (1 - P_{j\text{trans}})\times \]

\[ \times \prod_{\xi=1}^{k} (1 - P_{\xi\text{out}})\cdot \prod_{\Theta=1}^{r} (1 - P_{\Theta\text{proc}}), \tag{4} \]

where \(P_{\text{err}}\) is the probability of an error occurring during information conversion at all stages;
\(P_{i\text{coll}}\) is the probability of an error occurring in the \(i\)-th device of the collection system;
\(P_{j\text{trans}}\) is the probability of an error occurring in the \(j\)-th device during information transmission;
\(P_{\xi\text{out}}\) is the probability of an error occurring in the \(\xi\)-th device of the information-output system;
\(P_{\Theta\text{proc}}\) is the probability of an error occurring in the \(\Theta\)-th information-processing device.

The third most important generalized parameter is the reduced cost of the CTS

\[ C = A + K\cdot B, \tag{5} \]

where \(C\) is the reduced cost;
\(A\) is the operating cost of the CTS;
\(B\) is the cost of acquiring or manufacturing the CTS;
\(K\) is the coefficient for reducing the costs of acquiring or manufacturing the CTS to operating costs.

The coefficients \(K\) are established by sectoral ministries. In calculations it is recommended to take \(K = 0.2 \div 0.25\) for computers and \(K = 0.25 \div 0.33\) for other equipment (data-transmission apparatus, information-collection means, etc.) [1].

The costs of operating the CTS are determined by the formula

\[ A = \sum_{i=1}^{m} \mathcal{E}_{i} n_i + \mathcal{E}_{\text{a.u.p}}, \tag{6} \]

where \(\mathcal{E}_i\) is the specific operating cost per unit of equipment of the \(i\)-th type for the adopted shift mode of operation;

\(n_i\) is the calculated quantity of equipment of the \(i\)-th type;

\(m\) is the number of types of equipment;

\(\mathcal{E}_{\text{a.u.p}}\) is the annual cost of maintaining the administrative and managerial personnel of the ICC and the services participating in the operation of the CTS.

For calculating the capital expenditures for the acquisition or manufacture of the CTS, the following formula may be applied:

\[ B = \sum_{i=1}^{n} B_i = B_{n i} + B_{t i} + B_{o i} + B_{c i} + B_{\text{v.o} i} + B_{m i} + B_{p i}, \tag{7} \]

where \(B_{\text{p}}\) denotes production costs, including the costs of design studies, the development of original technical means, and the introduction of the CTS;

\(B_{\text{t}}\) is the cost of purchased technical means;

\(B_{\text{o}}\) is the cost of original technical means and the costs of modernization;

\(B_{\text{c}}\) is the cost of constructing and reconstructing buildings (premises) necessary for accommodating computing facilities, collection facilities, APD, auxiliary equipment, etc.;

\(B_{\text{v.o}}\) is the cost of auxiliary equipment;

\(B_{\text{m}}\) is the cost of installing technical means;

\(B_{\text{p}}\) is the amount received from the sale of technical means released in connection with the introduction of the system;

\(i\) is the index of a technical means;

\(n\) is the total number of technical means in the complex.

In this case, the capital expenditures must include the cost of the computing equipment already operating at the enterprise that is intended to be used as part of the CTS.

In addition to the listed generalized parameters, it is possible to name certain others that cannot be reduced to the three selected generalized parameters, but that characterize the rationality of constructing the CTS from other points of view, for example:

flexibility of the CTS, i.e., the ability, when necessary, to restructure itself for the solution of new tasks, for other methods of solving old tasks, for the redistribution of tasks between the computer and the CTS, for expanding the volume of computational work, etc.;

feasibility of the CTS, i.e., the possibility of creating the entire volume of apparatus and equipment of the CTS by the country’s industrial enterprises.

Without diminishing the importance of these cited parameters, especially in the creation of multimachine complexes operating on a real-time scale, they are nevertheless considered secondary, since they do not characterize the CTS as a functional element of the control system [2].

However, when selecting a CTS, one should stipulate the conditions for the development (expansion) of the CTS, and also take into account the prospects for the use of particular technical means in an ACS, since, when selecting a CTS according to the main reduced parameters, these features are not always taken into account.

When selecting a CTS, the following constraints must be taken into account: permissible approximate amounts of expenditure for acquiring technical means; acquisition of the CTS within specified time limits; compatibility (technical and code compatibility); aggregability of technical means; reliability and dependability; operating conditions (temperature, humidity, vibration, industrial interference, noise level, etc.); territorial and architectural-construction conditions (a large number of subdivisions located at considerable distances, the possibility of constructing a special building for the CC, anticipated reconstruction, etc.).

Thus, the approach set forth for selecting a CTS made it possible, using the example of a specific enterprise, to select the necessary technical means.

REFERENCES

1. S. Mikhalev, R. Sedegov et al. Experience in developing automated enterprise management systems. Minsk, “Belarus,” 1972.

2. Yu. S. Golubev-Novozhilov. Multimachine complexes of computing facilities. Moscow, “Sovetskoe radio,” 1967.

3. A. G. Mamikonov. Methods for developing automated management systems. Moscow, “Energiya,” 1973.

4. E. M. Salpynov, E. V. Bazhinova. Issues in selecting technical means for the ASUP of a republic. Alma-Ata, 1971.