Evaluating the relevance of the elements of distributed computing system infrastructure when solving tasks in managing an economic unit Dmitry Gorbachev Department of software for computers and automated systems Orenburg State University Orenburg, Russia gordiddd@gmail.com Abstract—From the point of view of its architecture, any  Manufacturing departments; information system (IS) represents a distributed information processing system. IS infrastructure ensures the execution of  ACS department. the enterprise business processes. However, the role played by This model represents an infrastructure component of an IS infrastructure elements in the execution of a certain enterprise automated information system (AIS), where the business process is different and can be evaluated with the help of a coefficient of element’s relevance. Taking the coefficient of system is formed by the information flows circulating relevance into consideration will make it possible to manage between the elements (while operating). the information flows rationally and to provide the necessary II. PROBLEM STATEMENT standby equipment. According to their structure and content, AIS information Keywords—distributed computing systems, relevance, the flows can be divided into three major categories: Perron-Frobenius theorem, relations matrix, diagram of major automation flows 1) the flows which ensure structural integrity of the system; I. INTRODUCTION 2) the flows which determine basic system properties; The infrastructure of modern enterprise distributed 3) the flows of process automation. computing systems (DCS) consists of components different While operating the flow can overlap or branch, but in both in their function and in design principles. However, any case the routes of the flows allow to evaluate the there are common points in the structure of all distributed participation of each element in the whole process of computing systems. So, any DCS includes the following functioning. The participation of an element can be evaluated elements: with the help of a relevance coefficient CR, which defines  data processing server; the significance of the element in the execution of IT- processes in the enterprise business system. The CR makes it  management server; possible to rationally manage the workload of system  data storage server; components, their maintenance and repair, as well as to determine the necessary cold and hot standby equipment.  auxiliary/additional (proxy, print, e-mail) servers; Thus, evaluating the relevance of the DCS infrastructure elements is an urgent problem which consists in making an  employees’ computer workstations; analytical model of evaluating the relevance of the DCS  plug-in mobile devices; infrastructure elements according to their participation in enterprise (organization) business processes.  switches; 3. PROBLEM SOLUTION  routers; As the structure represents a totality of stable relations  hubs; within the system ensuring its integrity and self-identity, the information flows of the enterprise business system can be  medium. divided into three major categories: A commonly used model of an enterprise distributed 1) the flows of DCS elements communication; computing system is shown in Figure 1. Enterprise departments: 2) the flows defining the specific application of DCS in the information system;  Management department; 3) the flows arising when solving tasks on automation  Accounting department; of business processes and processes management decision- making.  Personnel department; The flows of the first category arise from the following  Planning department; constituents:  General services department;  official traffic: the flows sent by the information interchange participants, comprising of requests about  Warehouse department; computer network status, number and activity of users,  Transport department; shared resources and responses to these requests. In different Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) Data Science AIS architectures different elements can serve as request Information systems based on a workgroup model are sources and receivers. For example, if computer network is usually rather small (10…15 network devices), they are based on a workgroup model, each computer sends nearly generally used for limited number of purposes, that is why the same official traffic which requests network resources this model will not be taken into consideration in this and informs about its own resources available. A domain research. From the viewpoint of evaluating AIS elements model has a more rigorous network, where a domain interdependency, various domain models appear to be of controller acts as the initiator of information interchange. most interest to us; manufactory 2 director secretary cashier economist Зам. директора marketing manager manufactory 1 Hub Hub accountant administrative part Hub garage manager manufactory 2 personnel director server manufactory 1 Control administrator server server personnel manager switch standby server Data processing server warehouse Hub router Internet Fig. 1. A model of an enterprise distributed system.  the flows determined by the information transmitted support. These flows arise each time when a user runs a while AIS functioning. The flows of this category are not certain pre-programmed information processing model. regular and proceed from AIS users’ tasks. For example, to Such division of information flows into categories make a sales report, a manager can use several data bases enables us to regard the distributed computing system as an and his requests physically pass through various object possessing structure, substrate and concept. This communicators, servers, etc. As a rule, request processing approach allows to evaluate the relevance of the system results have the route of the request but in a backward elements depending on the structure, substrate and concept. direction. So, the structural coherence of elements within the system is determined by the routes of requests and responses. The systemic notion of «relevance» implies a substantial difference between a systemic examination of objects and The flows of the second category condition the system system parameters. Along with attributive system properties which attribute AIS to data processing systems parameters, which characterize each particular system, there (ADPS), automated control systems (ACS), or to automated are also relational system parameters, which define the information retrieval system (AIRS). Business intelligence relations between the objects. systems belong to ADPS, the class of ACS is represented by enterprise resource management systems, for example: ERP, One system (one object) can be more significant than MRP, MRP II. Library information systems fall into the another in concept, in structure, in substrate. That is why a category of AIRS. relational system parameter is more «relevant», and the respective attributive parameter is a vector [2]. Quantitative and qualitative properties of the flow of this category depend on the specific content of users’ requests Let   and responses to them and are predetermined by the processes running in the system. mS  R m P – be a system The flows belonging to the third category are determined where m – is a substrate (the foundation of phenomena and by AIS automation processes and are formed in accordance processes, which determine the system properties); R – is a with designed-in data processing algorithms. They ensure the structure (a totality of stable relations between the objects); P conceptual integrity of the system. The content of these of – a concept of the system (the content of the notion). flows is provided by functional, mathematical and software VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 310 Data Science A systemic examination of the object gives the  processes of accounting, inventory, documentation opportunity to classify various types of objects’ «relevance» and staff control; in accordance with the aspects concerned. In the case under study structure relevance, substrate relevance and concept  processes of manufacturing tasks planning and relevance can be distinguished depending on what is being designing, as well as project management; evaluated: m, R or P.  research and analytical processes. Further on we can evaluate not m, R or P themselves but In topological mapping the model of the enterprise certain relations of n-order between the AIS elements. distributed system (see Fig. 1) represents a tree structure Let us consider the system in Figure 1. This system can overlapped with the information flows of the processes be referred to the ADPS class as the main processes running mentioned above (Fig. 2). in it are on-line transaction processing (OLTP), online The technique of evaluating the system elements analytical processing (OLAP), generating various reports and relevance is as follows. documentation processes. The major automation processes are: Information flows of production planning and design Accounting Automation Information Streams Information flows of Warehouse accounting documents and personnel information flows records Research and Analysis Information Flows Fig. 2. A simplified diagram of major automation flows. There are two cases possible here: 1) if the extensional Firstly, relations register is arranged in accordance with lengths exceed the range of scale, the element obtains the number of workstations. The sign «=» is used to denote maximum relevance rank; and 2) if the extensional lengths of the identity of each object to itself. The relation a «source» the elements compared are equal, we create a new relations of information is represented with «» symbol. A passive register, which considers only these AIS elements. The relation, i.e. a «receiver» of information, is denoted by «» results obtained are put into the matrix А of relevance ranks. symbol. At the same time the preference is always given to the «source of information» as it is a more active element This matrix must be consistent, nonnegative, irreducible than the «receiver of information». and have a single rank. Then the notion of «extensional length» is introduced. Then The extensional length is determined by the total number of active relations of one system element towards the other   A   max , (1) ones. The system element of the highest relevance is the one where max – is the largest of matrix А eigenvalues. that has the biggest extensional length of relations vector, or in other words the one that acts as a «source of information» According to the Perron-Frobenius theorem, the equation (1) in regard to other system elements most of the times. In the has a unique (accurate to the constant factor) nonnegative opposite extreme case the «relevance» of an AIS element solution  [4] The value of  is taken for a relevance should be identified with a «passive» relation towards (i.e. coefficient CR of the AIS element. For the sake of to be a receiver of information ). convenience and clarity CR is usually normalized. Having defined extensional lengths of AIS elements As applied to the objects of automated information vectors, we assign a certain rank of relevance to the objects system, the technique of evaluating the relevance is as of different types in accordance with the rank scale (Table 1) follows. As applied to the objects of automated information and create a matrix of relevance ranks [3]. system, the technique of evaluating the relevance is as follows. VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 311 Data Science TABLE 1. RANK SCALE х7 = 8; х6 = 7; х3 = 5; х10 = 3; х13 = 2; х1 = 1; Relevance Definition Explanation х2 = 1; х4 = 1; х5 = 1. rank 0 The objects are incomparable. It is pointless to After that we create a matrix А of relevance ranks (Table The objects are equally relevant. compare the objects. 2) and define a set (1, … n) of relevance values of each n The objects have 3 The object is slightly more identical (or element, then the comparative evaluation of the relevance relevant than the other one commensurable) values obtained takes place. The element аij of the 5 One object is more relevant than information relations. comparative matrix А evaluates the relation i/j. the other one There is some 7 (strong superiority). superiority of one For this matrix to be consistent the following correlations One object is obviously more object over the other must be fulfilled [5]. relevant than the other one. one on some level of 9 One object is absolutely more relations. аij а  а (2) jk ik relevant than the other one. There are compelling The values of intermediate reasons that one and in particular 2,4,6,8 results. object is more relevant than the aij = 1 и а ji  1 (3) other one. а ij There are irrefutable The fulfillment of the correlation (3) is necessary to reasons to prefer one object to the other define the difference between the objects’ relevance values one. and to calculate the second value’s fraction of the first one. The superiority of one of the object is TABLE 2. RELEVANCE RANKS OF THE ELEMENTS (EXAMPLE) obvious and lies beyond any doubt. i \ j х7 х6 х3 х10 х13 х1 х2 х4 х5 х7 = 4 5 7 8 9 9 9 9 Reciprocals of If object i when compared to object j obtains one of the х6 1/4 = 5/4 7/4 8/4 9/4 9/4 9/4 9/4 the numbers relevance ranks mentioned above, then j obtains a х3 1/5 4/5 = 7/5 8/5 9/5 9/5 9/5 9/5 mentioned reciprocal value when compared to i. х10 1/7 4/7 5/7 = 8/7 9/7 9/7 9/7 9/7 above. х13 1/8 4/8 5/8 7/8 = 9/8 9/8 9/8 9/8 Rational Rational numbers are the results of arithmetic operations х1 1/9 4/9 5/9 7/9 8/9 = 1 1 1 numbers. with the numbers of the given scale. х2 1/9 4/9 5/9 7/9 8/9 1 = 1 1 х4 1/9 4/9 5/9 7/9 8/9 1 1 = 1 Let the extensional length Li of the vector of AIS х5 1/9 4/9 5/9 7/9 8/9 1 1 1 = elements information relations be defined on the basis of relations register (Fig. 3). It is clear that being consistent the matrix А has a single rank because to know only one row is enough to determine the other elements. Moreover, a1i , for every i. And the null result of objects pairwise comparison means that they are incomparable, i.e. have no information relations. For consistent matrix А we have: n   a ij i  n, i  1,..., n (4) j 1 j where n – is maximum eigenvalue А, and all the rest eigenvalues are null because А has a single rank and the sum of all its eigenvalues is equal to the spur of matrix. n  Т r А   a ij  n i 1 (5) In the general case it can be considered that the set should satisfy the equation (1). Then for nonnegative n n x ' Ax    a ik i   0,  ,..., n  0 (where x   – i 1 k 1 k 1 Fig. 3. Relations matrix (example). is a row vector from А) and for irreducible matrix А, there As it is seen from Figure 3, Li is equal for {х6, х17, х23} exists a unique (accurate to the constant factor) solution of and {х7, х8, х9, х18, х19, х20, х24, х25, х26}. That is why a new equation (1). In other words if matrix А is consistent, we can relations register is being made, but now it is based on the take the row ai1, ai2, …, ain and multiply ai1 by 1, ai2, by 2, relations within the automation channel system (Fig. 4). …, ain, by n, and thus get i, i, …, i,. So, multiplying matrix А by vector  we get vector n Therefore,  is the solution of the equation А  n In the general case, when multiplying i-row as mentioned Fig. 4. Relations matrix in the automation channel. above, we do not always get exactly i, i, …, i because of errors of the values aij. In the theory of matrices it is Thus, common lengths of the vectors Li are equal for established that eigenvalues represent continuous functions elements of all types: VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 312 Data Science of the elements [4]. When the perturbation of the consistent based upon real information relations between the system matrix elements is small, its largest eigenvalue will be close elements. Knowing precise numerical values of relevance of to n, all the rest will be approximate to zero. Thus, judging system elements and their quantity, it is easier to make by the solution of the equation (1), we can say how close n reasoned decisions while managing a DCS. Besides, on the will appear to be to max. That is why to improve consistence early stages of designing when a new system is only being it is recommended to fulfill the correlation (3). built up, there appears an opportunity to evaluate the relevance of each element of each type in the system As a result we obtain the following set of vectors  effectiveness, which will assist in making the right emphasis from Table 2: while designing redundancy subsystems. 1 = 61; 2 = 15,25; 3 = 12,2; 4 = 8,7; 5 = 7,6; REFERENCES 6 = 6,7; 7 = 6,7; 8 = 6,7; 9 = 6,7. [1] L.Y. Lischinsky, “Structure and Parametric Synthesis of Flexible Manufacturing Systems,” Moscow: Mashinostroenie, pp. 195-222, Having normalized  according to the condition 1990. n A.I. Ujemov and E.A. Mamchur, “The Simplicity Principle and   i  1, we obtain numerical values of AIS elements [2] Complexity Measures,” Moscow: Nauka, pp. 109-158, 1991. i 1 relevance, expressed by the coefficient of relevance (Table 3) [3] T.L. Saaty, “Mathematical Models of Arms Control and Disarmament,” Moscow: Sovetskoe Radio, pp. 91-114, 1977. [6]. [4] R. Bellman, “Introduction to Matrix Theory,” Moscow: Nauka, pp. 265-267, 1969. TABLE 3. VALUES OF AIS ELEMENTS RELEVANCE COEFFICIENT (EXAMPLE) [5] D.V. Gorbachev, “Substantiation of repair techniques of electronic х7 х6 х3 х10 х13 х1 х2 х4 х5 radio equipment in front-line air defense missile systems at the CR 0.114 0.045 0.045 0.115 0.102 0.102 0.236 0.13 0.11 expense of maintenance and repair optimization,” Ph.D. thesis in Engineering Science. St.Petersburg Higher Command Air Defense CONCLUSION School for Anti-Aircraft Missile, St.Petersburg, pp. 32-39, 1997. One of the advantages of this technique is that experts’ subjective opinions are not used here, the whole system is VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 313