Method of Ensuring the Functional Stability of the Information System based on Detection of Intrusions and Reconfiguration of Virtual Networks Iryna Zamrii1, Viktor Vyshnivskyi1, and Valentyn Sobchuk2 1 State University of Information and Communication Technologies, 7 Solomianska str., Kyiv, 03110, Ukraine 2 Taras Shevchenko National University of Kyiv, 64 Volodymyrska str., Kyiv, 01033, Ukraine Abstract The functioning of the information system takes place in conditions of constant interaction with the external environment under the influence of various destabilizing factors. Informational conflicts that provide information about bilateral interaction and have a destructive effect on the elements of the opposite party deserve special attention, which allows for obtaining, storing, and processing information necessary to achieve the goals of the entire system and even counteract the processes that have arisen under the influence of an informational conflict. Destabilizing factors and conflicts in the system lead to failures in the functional processes of the information system. Prevention of these effects occurs by ensuring the functional stability of the information system, that is, the ability of the system to preserve or restore certain system functions during the action of destabilizing factors. The article develops a method for ensuring the functional stability of the information system using software-defined wide area networks, which is aimed at solving the problem of increasing the stability and security of the information system against violations based on the detection of intrusions and the reconfiguration of virtual networks in virtual cloud environments. Keywords 1 Information system, software-defined wide area networks, reconfiguration, functional stability, security. 1. Introduction As technology evolves, it makes sense to consider enabling users to securely access applications In today’s environment, companies are forced to from anywhere, whether they are hosted in the transform all areas of their activities, using digital cloud or on a private host, locally or remotely, technologies to increase efficiency, speed of ensuring consistent security and transparency execution, and cost optimization [1, 2]. As a result for users regardless of access method, as well as of these changes, the traditional approach of protecting the company’s digital assets [7]. For centralizing applications, network centers, and this purpose, the integration of technologies security services no longer guarantees the necessary to provide users with secure access to performance of these applications [3–6]. data and programs regardless of location is Another factor that has affected the provision increasingly used [8–11]. At the same time, an of network and security services is the location of important component remains the maintenance workers and users. Traditionally, users worked of the normal functioning of the information from a central office or branch office from where system in conditions of constant destabilizing security and network services could be factors. The essence of this is to adopt effectively delivered. But for now, users need to countermeasures against various destabilizing be able to access apps regardless of location. This factors [12], adapt functional algorithms to new means that enhanced security services must now conditions, organize functional restoration or be provided in all locations. ensure continued functioning in conditions of CPITS-2024: Cybersecurity Providing in Information and Telecommunication Systems, February 28, 2024, Kyiv, Ukraine EMAIL: irinafraktal@gmail.com (I. Zamrii); vish_vv@ukr.net (V. Vyshnivskyi); v.v.sobchuk@gmail.com (V. Sobchuk) ORCID: 0000-0001-5681-1871 (I. Zamrii); 0000-0003-1923-4344 (V. Vyshnivskyi); 0000-0002-4002-8206 (V. Sobchuk) ©️ 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) CEUR ceur-ws.org Workshop ISSN 1613-0073 Proceedings 252 system failures, perform analysis and reliability survives external failures and attacks through assessment, and, based on these data, assess the autonomous reconfiguration. As a result, stability of the information system [13–15]. research [25] proposed an intelligent decision- Analysis and assessment of stability allow making model supported by edge computing to timely support and restoration of the main address the problem of real-time failures and functions of the system in the required amount attacks. and even allow for the influence of the external However, there is a need to develop a environment as a result of the effects of performance, configuration, and security destabilizing factors and changes in algorithms, management apparatus to effectively use the operating conditions, and system structure [16, information and hardware resources of the 17]. information system. For this purpose, a The development of approaches to solving methodology should be developed to ensure the the problem of synthesizing functionally stable effectiveness of the functioning of the systems is a complex process. One of the information system from the point of view of methods is the formation of a system of rules for functional stability. effective management of the functional stability of the system [18–20], and its specific 2. The Method of Increasing the implementation, in particular, for solving optimization problems. That is, in the problem of Functional Stability of the system stability synthesis, the development of Information System principles and methods of ensuring the functional stability of the system is carried out to Consider the objective function of the top of the solve the problem of its improvement. information system (IS) hierarchy graph: The analysis of recent studies shows that one 𝒴𝓆𝑖 → 𝑚𝑎𝑥, (1) of the methods of increasing security and where for each vertex that continues to stability is the reconfiguration of the information function without failure, the IS continues to system network. The article [21] discusses the function at full capacity: problem of dependent reconfiguration of NFV. A 𝑁𝑓 𝑎𝑓 𝑁𝓆𝑓 distributed approach is proposed to guarantee 𝒴𝓆∗𝑖 = ∑ ∑ ∑ 𝒩 |ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )|𝒴(𝑎𝑓𝑗 )𝓀, (2) consistency during dependent reconfiguration. 𝑓=1 𝑗=1 𝑖=1 This approach consists of a distributed multi- 1, if 𝓆𝑓𝑖 executes on 𝓆𝑖 , domain model that establishes the interaction 𝓀={ (3) 0, otherwise, between federation objects and a causal- coherent distributed orchestration algorithm 𝒴(𝑎𝑓𝑗 ) = ∑ 𝓆𝑖 𝒴𝓆𝑖 , (4) based on this model. 𝑖 where 𝒴(𝑎𝑓𝑗 ) is the general solution of the The paper [22] aims to enhance the reliability and quality of service of power smart grids by optimal scenario under the influence of searching for and applying reconfiguration- destabilizing factors, which is the sum of the oriented solutions. A novel definition of recovery products of vertices 𝓆𝑖 associated with an performance is provided in terms of automatic abnormal situation for solving the problem 𝑎𝑓𝑗 recoverability and unavailability rates. and the scenario of making the best decision for The paper [23] presents a performance solving the given problem 𝒴𝓆𝑖 , ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 ) is optimization algorithm for controller the matrix of functioning of vertices and reconfiguration in fault-tolerant distributed problems of the IS hierarchy graph. model predictive control for large-scale systems. If the set of executable functions is a Thе аrticle [24] exploits the potential benefits constant for the objective function, then of a blockchain system integrated with a 𝒴𝓆𝑖 = 𝒴𝓆∗𝑖 . (5) software-defined network. A new cluster- If some vertex is unable to withstand an structured routing protocol for IoT networks abnormal situation and continue to function in using blockchain-based architecture for SDN the same mode, the system imposes a controllers is proposed. This helped solve constraint 𝑄0 (𝑎𝑓𝑗 ) for failure to perform performance and security issues. assigned tasks on the vertex in the form of a An intelligent decision-making framework is function that acquires negative values. The necessary to ensure that the system as a whole 253 controller of the system, depending on how 𝒯𝑘 is the execution period of the user critical the failure of the vertex to complete or algorithm. partially perform the assigned tasks, adjusts The periods and execution times of the the restrictions on it. specified algorithms are shown in Error! The method of forming restrictions is Reference source not found.. proposed as follows: 𝑄0∗ (𝑎𝑓𝑗 ) is a restriction in the case of a partial loss of productivity, that is, of the assigned functions, and 𝛼 × 𝑄1∗ (𝑎𝑓𝑗 ) is a restriction in the case of a proportional loss of productivity α. Then 𝑄0 (𝑎𝑓𝑗 ) = 𝑄0∗ (𝑎𝑓𝑗 ) + 𝛼 × 𝑄1∗ (𝑎𝑓𝑗 ). (6) Figure 1: Periods and execution time of If the functions perform tasks with different algorithms quality, then, accordingly, they are predicted to win in this strategy 𝒮0 (𝑎𝑓𝑗 ), that is, in the The values of 𝒯с , 𝒯𝑘 , 𝓉𝑐 , 𝑘 determine the order of scenario of making the best decision for 𝑎𝑓𝑗 . application of algorithms in the methodology. The developed technique consists of the It is obvious that if the function consumes following steps: resources, then it ensures the fulfillment of 1. Definition of source data. tasks, such as data transfer, management of 2. Using the Prisma Access infrastructure processing in distributed databases, etc. That to bypass failed connections, including is, the more the function consumes resources, dynamic routing using BGP and the better the result. And the size of the information about new IP address restriction will depend on the quality of the subnets on the user connection side of performance of each of the tasks 𝑎𝑓𝑗 . the Prisma Access infrastructure to Thus, the objective function for the top-level bypass failed connections when vertex of the IS network hierarchy will be to multiple routes exist between the maximize the wins in each of the strategies and client network and Prisma Access. minimize the constraints: 3. Checking whether all tasks 𝑎𝑓𝑗 have ℱ(𝑎𝑓𝑗 ) = ∑ 𝑎𝑓𝑗 ((𝒮0 (𝑎𝑓𝑗 ) − 𝒮𝑚 (𝑎𝑓𝑗 )) × 𝛿(𝑎𝑓𝑗 ) (7) been completed. If not all 𝑎𝑓𝑗 are + 𝑄0 (𝑎𝑓𝑗 )) → 𝑚𝑖𝑛, completed, then we proceed to the next where 𝛿(𝑎𝑓𝑗 ) is a weighting factor that allows step of the method. the controller to determine the priority of the 4. Determination of 𝒯с , 𝒯𝑘 , 𝓉𝑐 , 𝑘 using the performed functions in the system. IS controller reading the values of these Consider the case in which the IS is unable to parameters. perform the amount of tasks and functions that 5. For each function 𝑓, the following are arose as a result of extraordinary situations. In determined: 𝒮0 (𝑎𝑓𝑗 ), 𝛿(𝑎𝑓𝑗 ), 𝑄0 (𝑎𝑓𝑗 ) this case, there is a possibility that there are both and methods are set. server problems and problems arising as a result 6. 𝒯с , 𝒯𝑘 , 𝓉𝑐 , 𝑘 are defined. The order of of user actions, so restrictions can be imposed on application and execution time of the both components. methods is set. In this regard, within the framework of the 7. Selection of the 𝛼 value of the partial proposed methodology, algorithms have been productivity of the IS. developed both for users and for problems 8. Implementation of method ℬ1 . related to equipment, and their execution does 9. Implementation of method ℬ2 . not necessarily have to be simultaneous. 10. Evaluation of the level of functional For the server algorithm, we denote the stability of the IS at the current period of its execution by 𝒯с and impose the moment using the SD-WAN cloud following conditions: controller. 𝒯с = 𝓉𝑐 + 𝑘𝒯𝑘 , (8) 11. Determination of the need for where 𝓉𝑐 is the execution time of the task correction of 𝒯с , 𝒯𝑘 , 𝓉𝑐 , 𝑘 and decision, 𝑘 is the number of times the user assessment of the level of functional algorithm is executed during the period 𝒯с . stability of IS. 254 Figure 2: Block diagram of the method of increasing the functional stability of the information system In this methodology, ℬ1 is an algorithm for the functional reconfiguration of the hierarchical IS functional reconfiguration of the top of the network in real-time. graph of the top level of the IS network Visualization and order of interaction of the hierarchy, and ℬ2 is an algorithm for the steps are presented in Fig. 2. 255 3. Algorithm of Functional Let’s define tasks and connections between them in the hierarchical configuration of the Reconfiguration of the Top of information system network for algorithm ℬ1 . the Graph of the Upper Level of The algorithm is designed to provide three the Hierarchy of the types of functional restructuring of the Information System Network information system network, namely: • 𝛾1 is a functional rearrangement that will The selection of methods and mathematical allow saving the set of all performed apparatus for ensuring the functioning of the functions in the IC. vertices of the graph of the hierarchical • 𝛾2 is a functional restructuring, which configuration of the network of the information does not take into account the possible system involves: decrease in the quality of performance of • Each of the functional levels must be able specified functions under the influence of to make changes to the configuration and such restructuring. structural connections and take into • 𝛾∗ is a functional rearrangement that is a account the possibility of breaking the union of 𝛾1 and 𝛾2 . connection with the top of the higher Since for the functioning of the IS in level of the hierarchy. different periods, sets of different tasks and • The ability to quickly make changes in functions that have different levels of real time. productivity can be performed, but despite everything, none of the functions can be • Possibility of scaling. neglected, the ℬ1 algorithm is based on the • Possibility of use in dynamic models. priority execution of the functional The need to ensure the specified rearrangement 𝛾1 and only under the condition requirements determines the possibility of the impossibility of ensuring the functioning of applying the model of self-organizing systems the system without losing the quality of part of in crises and the method of operational the functions, the transition to functional management of the theory of active systems. restructuring 𝛾∗ . According to the theory of active systems [26], The steps of performing the algorithm ℬ1 a parameter called the incentive fund is include: introduced, the task of which is to be distributed 1. Entering input data, which includes the among the vertices of the network. The optimal collection and processing of information about solution is to distribute the parameter between the vertices and the configuration of the performers who have not yet performed their network of the IS, namely: updating the data function. This distribution mechanism is 𝒟(𝑎𝑓𝑗 , 𝒦) and 𝒟с (𝑎𝑓𝑗 , 𝒦) by each of the centralized, which creates certain difficulties for the survivability of the system, in addition, even vertices for tasks 𝑎𝑓𝑗 ; update of current data in distributed systems there are problems with from the network controller of the IS about the the operation and distribution of this parameter. values of 𝒯с , 𝓉c . The possibility of applying the distribution 2. Determination of the number of tasks of this parameter due to the anticipatory self- performed by the vertex according to the monitoring approach solves the problem of formula: 𝑁𝑓 𝑎𝑓 𝑁𝓆𝑓 timely response to failures in the vertices of the network graph and edges, that is, the ℛ = ∑ ∑ ∑ 𝒩 |ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )|𝒴(𝑎𝑓𝑗 )𝓀 (9) connections associated with these vertices. 𝑓=1 𝑗=1 𝑖=1 That is, during the performance of the to calculate the complexity of decision- functions assigned to the top, its behavior making in the performance of tasks to ensure should be structured in such a way as to the functioning of the IS network and the minimize restrictions (penalties in game algorithm for further actions. theory [26]) and maximize decision-making 3. Determination of the tasks performed strategies (incentives), due to which the by the vertex at the current time. If the vertex system’s efficiency increases. In addition, this does not perform tasks, then the method is not approach is applicable during the functioning applied to this vertex. of the system in real-time. 4. Analysis of configurations ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )(𝑡) at the current time and 256 comparison with the previous configuration network, based on 𝒮0 is the maximum possible ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )(𝑡 − 1). Analysis and comparison assessment of the quality of execution of 𝑎𝑓𝑗 in take place sequentially for each task at a given the configuration 𝒦𝑎𝑓𝑗 , and at this stage of top of the hierarchy. If ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )(𝑡) and execution, the most important thing is to ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )(𝑡 − 1) are identical, i.e. have no maximize the total value of these estimates: differences, then a check of changes in the 𝑁𝑓 𝑎𝑓 𝒮𝑐 (𝓆𝑓𝑖 ) = ∑ ∑ (𝒮0 (𝑎𝑓𝑗 , 𝒦𝑎0𝑓𝑗 )) 𝒩(|ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )| (11) system state is started. 𝑓=1 𝑗=1 5. Analysis of changes in the state of the IS where 𝒮0 is a non-decreasing function of the network. If there have been changes in the best possible value of the assessment of the network of the information system, that is, an quality of the task 𝑎𝑓𝑗 with the configuration increase or decrease in the total maximum 𝒦𝑎0𝑓𝑗 , 𝒦𝑎0𝑓𝑗 = 1, 𝑎𝑓𝑗 . speed of information transmission through specific vertices, then it is necessary to All configurations have a number that implement the main part of the algorithm. depends on the growth of the maximum 6. Application of the approach of a possible assessment of the quality of the task 𝒮0 complete search in one step. To apply the best and the following conditions are imposed on configuration for the top-level vertex of the them: hierarchy, it is necessary to perform a 𝒦𝑎𝑛𝑓𝑗 ≥ 𝒦𝑎𝑛−1 𝑓𝑗 , restructuring depending on each of the tasks. { (12) Then, the top of the network executes a set of 𝒮0 (𝑎𝑓𝑗 , 𝒦𝑎𝑛𝑓𝑗 ) ≥ 𝒮0 (𝑎𝑓𝑗 , 𝒦𝑎𝑛−1 𝑓𝑗 ), tasks to implement the best configuration in where 𝒦𝑎𝑛−1 = 1, 𝑎𝑓𝑗 , 𝒦𝑎𝑛𝑓𝑗 = 1, 𝑎𝑓𝑗 . terms of performance and survivability, while 𝑓𝑗 In addition, depending on the task, network its selection for each of the tasks is made taking and computing resources may vary. into account the maximum speed in the A necessary condition for the performance of network and the amount of system resources the assigned functions is their performance in the required for the calculation. full scope of the task 𝑎𝑓𝑗 by the vertex 𝓆𝑓𝑖 , i.e.: 6.1. Searching for all possible 𝑁𝑓 𝑎 𝑓 configurations with lower requirements for 2 𝑅𝑖 ≥ ∑ ∑(𝒩(|ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )| ) × 𝒟 (𝑎𝑓𝑗 , 𝑡𝑟𝑒𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛,𝓆𝑓𝑖 , 1) , computing and channel resources. If there is no 𝑓=1 𝑗=1 𝑁𝑓 𝑎 𝑓 simplification of the configuration, then the 2 𝓊𝑖 (𝓆𝑓𝑖 ) ≥ ∑ ∑(ℳф (|𝒦(𝑎𝑓𝑗 , 𝓆𝑓𝑖 )| ) × 𝒟(𝑎𝑓𝑗 , 𝑡𝑟𝑒𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛,𝓆𝑓𝑖 , 1) + (13) network is forced to stop performing part of 𝑓=1 𝑗=1 + ∑ 𝒟𝑐 (𝑎𝑓𝑗 , 𝑡𝑟𝑒𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛,𝓆𝑓𝑖 , 1) . the tasks. { ℳф (𝑎𝑓𝑗 ,𝓆𝑓𝑖 )=𝓆𝑓𝑖 6.2. Determination of the time 𝑡𝑠𝑡𝑒𝑝 for the The necessary values are calculated at step execution of one step of the approach with a 6 of the algorithm. review of all configuration options and The algorithm can be continued only if the determination of the time 𝓉𝑐 of the execution of necessary conditions are met. At this step, a the solution of the task by the server algorithm complete review of configuration options and using two-dimensional packaging with a full checking them for the possibility of review of all options using the formula: implementation takes place in one step. 𝓉с 𝑐𝑜𝑚𝑝𝑢𝑡𝑒 = 𝑡𝑠𝑡𝑒𝑝 𝒥𝑎𝑓𝑗 𝒦𝑎𝑓𝑗 + 𝑡𝑟𝑒𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 , (10) 9. Determination of the method of where 𝑡𝑟𝑒𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 is the time to apply the choosing a configuration by comparing current configuration into action; 𝒦𝑎𝑓𝑗 is the calculated and input data. Namely, when the 𝑐𝑜𝑚𝑝𝑢𝑡𝑒 configuration for the task 𝑎𝑓𝑗 ; 𝒥𝑎𝑓𝑗 is a inequality 𝓉𝑐 − 𝑡𝑠𝑡𝑒𝑝 > 𝓉𝑐 is fulfilled, a complete enumeration of all configurations is condition of the correctness of the impossible, and therefore a genetic method is configuration, which ensures the execution of performed, which ensures that the at least one of the functions of the task 𝑎𝑓𝑗 . The 𝑐𝑜𝑚𝑝𝑢𝑡𝑒 enumeration of configurations is interrupted at time 𝓉с for different vertices in the an arbitrary step and provides a result no 𝑐𝑜𝑚𝑝𝑢𝑡𝑒 network may be different, but 𝓉с ≤ 𝓉с . worse than the current one. 𝑐𝑜𝑚𝑝𝑢𝑡𝑒 7. Calculation of 𝓉с according to 10. Solving during the time 𝑡𝑠𝑡𝑒𝑝 𝒥𝑎𝑓𝑗 𝒦𝑎𝑓𝑗 equality (10). the 𝒲𝑚𝑎𝑥 the problem of maximizing the total 8. Determining whether a functional benefit of choosing configurations without reconstruction of 𝛾1 is possible for the IS exceeding the maximum permissible loss of 257 functions. For this, a complete enumeration of 26. Set the hierarchy level counter to all possible configuration options is used, and decrease by one. the result of the decision is a vector of 27. The verification of the possibility of configurations. performing functions by vertices is carried out. 11. Setting the initial time 𝑡𝑔𝑚 = 𝑡 for the 28. A vertex that cannot perform a function genetic method of sorting configurations 𝒦 ⃗⃗ . is assigned a configuration of zero, and the value 12. We set the required number of steps of consumption of computing resources is 0. 𝓇𝑔𝑚 for the counter in the execution of the 29. The resulting condition for the system genetic method, after which the cycle is reset. function selection algorithm is determined. 13. Execution of one step of the 𝒲𝑚𝑎𝑥 30. The resulting condition for the task problem by the genetic algorithm for finding selection algorithm is defined. ⃗⃗ for which inequalities (13) hold. 31. The resulting condition is determined the vector 𝒦 by the algorithm for sorting the tops of the 14. We set the value 𝓇𝑔𝑚 + 1 for the hierarchy for the current task and function. counter. 32. Configuration application block: in the 15. We check the restrictions: block, not updated data is sent to the nodes. (𝑡𝑔𝑚 + 1)(𝑡 − 𝑡𝑔𝑚 ) > 𝓉𝑐 . (14) The block diagram of the functional 𝑡𝑔𝑚 reconfiguration of the top of the graph of the 16. We perform the description of the top level of the information system network search results using the genetic algorithm and hierarchy is shown in Fig. 3 inequalities (13) by entering the parameter 𝜃 We will evaluate the correctness of this into the matrix 𝒪(𝑎𝑓𝑗 , 𝓆𝑓𝑖 , 𝜃) such that: 𝜃 = 1 algorithm according to the following criteria: for network restrictions; 𝜃 = 2 for resource the possibility of obtaining a solution for a constraints. If there is a lack of resources, then finite number of steps; stability according to the value in the matrix is 1, otherwise, it is 0. input data; and stability in calculations. 17. We calculate the lack of resources for To check the fulfillment of the criteria, we vertices located below in the hierarchy: will perform the following steps: 𝑎 −1 𝒟 (𝑎𝑓𝑗 , 𝒦𝑎𝑓𝑗𝑓𝑗 , 1) = 1, 1. We define the critical sections of the [ 𝑎 −1 algorithm. These include: 𝒟 (𝑎𝑓𝑗 , 𝒦𝑎𝑓𝑗𝑓𝑗 , 1) = 2. • Steps 13–14 for the 𝒲max problem. 18. We set the zero configuration in the • Step 15, since it is critical to determine presence of a lack of resources in step 17: whether the genetic algorithm for the 𝑎𝑓𝑗 −1 𝒮0 (𝒦𝑎𝑓𝑗 ) = 0. 𝒲max the problem has been resolved. 19. We determine whether a functional • Steps 24–31 for three loop algorithms. reorganization of 𝛾1 is possible for the IS 2. We determine what restrictions are network similarly to step 8. imposed on critical areas. 20. If the functional reconstruction of 𝛾1 for The execution of steps 13–15 implies the the information system network is not fulfillment of the necessary condition (13). possible, then the possibility of functional Execution of step 15 is not possible without reconstruction of 𝛾2 is determined. To do this, the condition 𝓇gm ≠ 0. For this, in step 12, the the configuration is sent to all vertices. number of counter steps is set to 𝓇gm = 0, and Implementation of 𝛾2 occurs in steps 21–31. in step 14, 𝓇gm = 1. In this case, the counter 21. Setting the initial values for the system will iterate over values from [1, + ∞) and function selection algorithm. ensure the condition 𝓇gm ≠ 0. 22. Setting the initial values for the current For steps 24-31, conditions 𝑖 = 0, 𝑗 = 𝑓𝑓 , tasks sorting algorithm. 𝑓 = ℓ must be met. 23. Setting the initial values for the 3. We determine the changes in the algorithm for sorting the tops of the hierarchy postconditions for the initial conditions of the for the current task and function. critical sections and add them to the system of 24. We set the system function counter to criteria for the correctness of the algorithm. increase by one. The correctness of ensuring steps 13–15 25. We set the system task counter to determines infinity in the cyclic genetic increase by one. algorithm. That is, if 𝑡 → ∞ then 𝓇gm → ∞ and 258 t−𝑡 lim 𝑡 𝑔𝑚 = const. Then, in the last equality, the Then the system of correctness conditions has t→∞ 𝑔𝑚 the form: limit goes to ∞, and the right-hand side of the 𝑎𝑓𝑗 ≥ 0, equality remains a constant number. Thus, in 𝒦𝑎𝑓𝑗 ≥ 2, the cyclic genetic algorithm, the number of 𝒥= (15) steps necessarily remains a constant number at 𝑡𝑔𝑚 ≥ 1, 𝑡с ≠ ∞. { ℓ > 0. For step 15, the correctness conditions are Conditions (15) determine the execution of at defined in steps 11 and 14. least one function from a set of tasks. In addition, For steps 24–31, і is a natural number, so the each of the tasks must have at least two levels of number of configurations 𝒦𝑎𝑓𝑗 ≥ 2. hierarchy to ensure a hierarchical configuration. For step 30, the correct initial condition is 𝑎𝑓 The check is carried out in step 6.2. is a natural number for the postcondition, and for step 31 𝑎𝑓 is a natural number and ℓ > 0. Figure 3: Block diagram of the functional reconfiguration of the top of the graph of the upper level of the hierarchy of the IS network Thus, the method of functional reconfiguration network functions by the set of vertices and the of the top of the graph of the upper level of the set of assumed configurations. If k acquires IS network hierarchy is correct. sufficiently large values, then the part of the The problem of determining the best method based on the genetic algorithm is configuration for 𝑎𝑓𝑗 is NP-complete. A less executed. The complexity of the calculation optimistic option, which will ensure the depends on the number of transformations performance of the system functions properly, and the dimensions of the source data. The is the tenth step of the method, in which a computational complexity of the algorithm due complete enumeration of configurations is to the time limitation is inversely proportional carried out, the number of which can be to the computing power of the top of the defined as 𝜑(2𝑘), the use of which for small information system network hierarchy graph. values of 𝑘 leads to a reduction in the execution time of the part of the algorithm, where 𝑘 is defined as the product of the set of tasks of 259 4. Algorithm of Functional Let the decision regarding the presence of a reserve vertex be made at the level of the Reconfiguration of the functional element 𝜇. Hierarchical Network of the For minor changes in the system not to lead Information System in Real to permanent reconfiguration, we will set the Time following requirements: • Before starting the IS, the value of the To ensure that external and internal influences minimum and maximum quality of on the IS will not lead to malfunctions, network performance of the functions is set, as reserves, computing reserves, and temporary well as the possibility of receiving a reserves are provided, which are also called “reward”, that is, a reserve of resources, compensatory measures, and the mechanisms in proportion to the quality of the for their implementation are compensatory performed function. mechanisms [27]. In this method, in • “Bonus rewards” in the form of excess connection with the operation of IS in real- resources are also received for the time, the temporary reserve is excluded. performance of 𝜇 certain sets of In IS, the number and configuration of functions. vertices and connections at the structural level • Restrictions are introduced for partial or can change, as can the number of functional complete loss of functionality. elements and the list of functions they perform. These requirements are created in the The IS must quickly react to changes, therefore, function reconfiguration step for the during reconfiguration, the 𝒬𝑚𝑎𝑥 of vertices corresponding 𝜇 and are determined by the and connections is recalculated. following sequence of actions. Let’s denote the number of functions At the beginning, a list of functions up to 𝜇 performed by the IS in the current state by 𝑁 = is received. Combinations of functions by ∑𝓂 individual elements are added to this list in 𝑖=1 𝑁𝑓𝑖 , where 𝑁𝑓𝑖 is the number of functions performed by the 𝑖-th functional element. case of additional evaluations. This is followed To be able to respond quickly, each vertex by assigning a score to each feature based on must have several solutions to choose the best, priority to encourage support for existing they provide a reserve of the necessary functionality. The value of the extra point is network and computing resources. In doing so, small enough to prevent the system from each vertex tries to perform the most “useful” making changes to the list based on available function to try to maximize performance. resources, performance, or other reasons. But according to the emerging various It is necessary to introduce mechanisms for destabilizing factors, the vertices cannot collecting information about the network and always predict which of the solutions, in this channel resources of 𝜇 vertices, synchronizing case, will be better, therefore it is important to the list of functions, as well as redistributing develop a method in which the adopted additional estimates between the vertices of decision will be better for at least one of the the hierarchy graph. vertices, and will not cause harm or damage to The method of complete selection of the rest. In addition, in real-time systems, it is configurations or genetic is used for the 𝒲max necessary to ensure fast decision-making, and problem of maximizing the total benefit of this can be ensured by pre-generated choosing configurations without exceeding the strategies. maximum allowable loss of functions in the It should be noted that with decentralized case when each of the vertices has both a management, the system operates under computing and a network resource. The choice conditions of uncertainty and therefore makes of the method is due to strict limitations on the changes based on the data available to each time of execution of the functions. node of the system. Therefore, it is necessary The choice of the most suitable strategy is to check how it affects the vertices with which made to preserve the functionality, so each there is a direct connection and the system as vertex checks the list of actions to ensure the a whole. performance of the set functions. 260 During the execution of a new cycle by the imposed on the choice of configuration system, the vertices analyze the results of the and the volume of tasks to be changes made to the configuration and performed. At the same time, the calculate new combinations of functions and genetic method is used, since these their possible additional evaluation. constraints require an increase in Therefore, the IS network is organized in computing resources and time to such a way that allows 𝜇 and vertices to make search for a solution, and the result is decisions independently, refusing centralized no worse than the initial one. management and ensuring efficient operation 9. Checking the maximum possible time in conditions of functional degradation. for the implementation of the solution: We will describe the steps of the algorithm 𝑡(𝓂 + 1) − (𝓂𝓉𝜃 + 𝓉𝜃∗ ) > 𝒯𝑘 . (18) of functional reconfiguration of the 𝓂 hierarchical network of the information 10. Calculation results are exchanged. system in real-time. 11. The top with the highest additional 1. We fix the start time 𝓉𝜃 . score is determined. If there is more 2. The vertex 𝓆𝑓𝑖 is determined for the than one such vertex, then the vertex implementation of the configuration, that initiated the reconfiguration is by selecting neighboring vertices and selected. some remote vertices of the same 12. The reconfiguration process is in functional level, which can perform the progress. same functions and between which 13. Updating information in the vertices of connections are formed. In addition, the zero level of the hierarchy for each the number of neighboring vertices is of the changed tasks. inversely proportional to the number The block diagram of the described of remote ones. algorithm is shown in Fig. 4. 3. The vertices selected in step 2 Let’s evaluate the correctness of the exchange the matrices of functioning algorithm. Critically important steps in the ℳф (𝑎𝑓𝑗 , 𝑞𝑓𝑖 ) and matrices of functional real-time hierarchical network functional reconfiguration algorithm are the sixth possibilities ℳм (𝑎𝑓𝑗 , 𝑞𝑓𝑖 ). through the eighth. In this case, the completion 4. It is determined which of the functions of the cycle is possible only when (19) is placed on the vertex q_fi, it is capable of executed. That is, correctness is determined by performing: the following conditions: ℳф (𝑎𝑓𝑗 , 𝑞𝑓𝑖 ) = ℳф (𝑎𝑓𝑗 , 𝑞𝑓𝑖 ) (19) (16) 𝒯𝑘 ≠ ∞, 𝓂 ≠ 0, × ℳм (𝑎𝑓𝑗 , 𝑞𝑓𝑖 ). where 𝒯𝑘 is the period of functional 5. The number of tasks for the vertex 𝑞𝑓𝑖 reconfiguration, 𝓂 is the number of counter that it can perform is determined by steps in the genetic method. the formula: Since the conditions are checked in step 9, but 𝑁𝑓 𝑎𝑓 𝑁𝓆𝑓 first for the genetic method, then (19) are ℛ = ∑ ∑ ∑ 𝒩 |ℳф (𝑎𝑓𝑗 , 𝓆𝑓𝑖 )|𝓀. (17) performed regardless of the obtained result. 𝑓=1 𝑗=1 𝑖=1 Algorithm complexity assessment. For a 6. When ℛ > 0, the search for a solution complete search of all possible configurations, for the functional reconstruction of the complexity of the solution is defined as vertices and their connections is 𝜑(2𝑘), but it is rational to implement it only for initiated. If a solution is found, the small values of 𝑘. For large values of 𝑘, a search result is implemented in steps genetic method is used, the complexity of 7–9, otherwise, the results of which is limited by the number of operations. calculations from the neighboring node Thus, the complexity of the calculation for one are expected. step can be defined as 𝜑(𝑘 2 ). In steps 2–3, the 7. The reference point for performing the complexity of the method is 𝜑(𝑘) for each of genetic method for the 𝒲max problem them, which in sum gives 𝜑(2𝑘). is determined. Then, with a complete search, the 8. The solutions of the 𝒲max the problem complexity is 𝜑(2𝑘 + 2𝑘 2 ) and with the is supplemented by restrictions genetic method, it is 𝜑(2𝑘 + 2𝑘 2 ). 261 The other steps do not significantly affect the The accuracy of the algorithm depends on computational complexity. the time of determination of the decision by the genetic method. Figure 4: Block diagram of the functional reconfiguration of the hierarchical network of the IS in real-time providing flexibility and manageability to 5. Conclusions network services. A method of ensuring the functional stability of the information system using The conducted analysis of the requirements for software-defined wide area networks has been functionally stable information systems developed, which differs from the existing ones revealed the expediency of implementing in that it is based on the detection of software-defined wide area networks, which destabilizing factors and the reconfiguration of help ensure security, productivity, reliability, the information system network into which the Prisma Access solution is integrated. 262 The use of this method helps ensure the Firms’ Research and Development— functional stability of the information system by Automation or Augmentation, Explo- ensuring availability, integrity, confidentiality, ration or Exploitation? Technol. 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