Development of the Software Application with Graphical User Interface for One Model Cyber Security

The article is dedicated to the development of software application with graphical user interface for analyzing of the operation of Integrated System of Data Defense from cyber-threats (ISDD) which includes subsystems of detection and elimination of vulnerabilities existing in the system, as well as Requests of Unauthorized Access (RUA). In the subsystems of eliminations of vulnerabilities and queues of unauthorized access considered as multichannel queueing systems with corresponding servers and queues, at random times there come requests to fix threats detected by the system. It is supposed that flows of requests demanding to eliminate threats coming to the mentioned subsystems of queueing systems are described with the Poisson distribution of probabilities, but processes of their elimination obey exponential law. For the system described above, there has been developed software realization of graphical interface which allows easily to change input parameters and ob-serve graphical reflection of changes of the output indicators of the system.


Introduction
On the current level of development of information and communication tech-

Statement of the Problem
This article offers a user model adapted to the scopes of providing cyber security and completed with graphical interface abilities of user options, the model which is a version of complex technical system discussed in the article [4]. The target of research in this article is a complex intelligent computer system of information security (CSIS) that defends from factors destabilizing operation of information system (IS), (the factors like occurrence of vulnerabilities and requests for unauthorized access (UA)), the system comprises subsystems of detection and elimination of vulnerabilities, as well as requests of UA in order to prevent results of cyber threats.
The subsystem of detection of vulnerabilities at random time, distributed according to Exponential law, carry out the scanning of information system in order to discover abovementioned destabilizing factors, in case they are discovered, they are passed to corresponding subsystem of elimination, that happens at random time too, distributed according to exponential law. For modelling the system that has been described, approaches of queuing theory is used, the theory of Markov processes, in particular [5]- [11].
It is supposed that complex security system (CSS) shown in Figure 1, as QS consists of two types of homogenous means of defense, total number of which is m = m1 + m2, where m1 is the number of homogenous means of defense supposed for detecting and elimination of vulnerabilities of functional type (FP -functional protection), and m2 is for detecting and elimination vulnerabilities of structural type (S3-structural protection) It is expected that the flow of arrivals coming from the subsystem of detecting vulnerabilities on the subsystem is Poisson and its total intensity equals to О = O1 + O2, where O1 is intensity of discovery of functional vulnerabilities, and О2is the intensity of detecting structural vulnerabilities. Elimination of vulnerabilities coming into corresponding subsystem happens according to the exponential law with total intensity V = V1 + V2, where V1-intensity of removal of functional vulnerabilities, but V2-intensity of removal of structural vulnerabilities. In the above-described system there comes Poisson probable flow of requests for unauthorized access with collective intensity M = M1 -M2, where M1 and M2 are intensities of flow of requests for unauthorized access with the use of vulnerabilities existing correspondingly in the functional and structural parts of computer system of information security (CSIS).
Security system fulfills neutralizing attempts of unauthorized access discovered while appropriate scanning. Neutralizing time is distributed according to exponential law with total intensity L = L1 + L2, where L1-neutralization intensity of UA attempts into the functional part of CSDD, and L2 is neutralization intensity of attempts UA into the structural part of ISDD.
It should be taken into consideration that in the system is provided/is able to react to the existence of queues for requests coming from appropriate subsystems ISDD at the moment when equipment eliminating threats is busy with eliminating previously received requests. The total number of requests, being simultaneously in the system, is limited., and it equals to K = K1 + K2 + K0, where K1 is the number of requests on the servers for removing vulnerabilities, K2 is the number of requests on the servers for preventing attempts of unauthorized access and K0 is a total number of both type of requests in the appropriate queues.
For description of the states of the system there are introduced probability functions ( ) i P t , which characterize the transition from one state into another, being under influence of the different flows happening in the system (flows of detection and elimination of threats), and are determined as product probability of the i-state from which the transition to the corresponding intensity takes place [12]- [19].
The use of Kolmogorov's mnemonic rule of setting up equations in the abovementioned system enables to write down the system of differential equations determining probabilities of transition between its states in the form of: where ( ) ( ) 1, 2; 1, 2, 0; 1, 2; 1, 2; 1, 2; 1, 2;  Matlab, the function ODE23 was used which is supposed for numerical integration of systems of homogenous differential equations (HDE). It is applicable for both: solving simple differential equations and modelling of complex dynamic systems.
As it is known any system of nonlinear homogenous differential equations (HDE) can be represented as the system of differential equations of the first order in the explicit form of Cauchy: , where x is state vector, t is time, f -nonlinear vector-function from the variables x, t.

Conclusions
The article presents with the software development of application with graphical interface for Integrated Security System from cyber-threats that consists of detection and elimination subsystems for existing in the system vulnerabilities as well as for unauthorized access requests (UA).
In the subsystems of vulnerability elimination and requests for unauthorized access, considered as multichannel queueing systems with corresponding queues, at random time, there come requests for elimination of threats detected by the system.
It is supposed that the request flow coming into the mentioned queueing system for elimination of threats is Poisson, but the flow of their elimination is exponential. The graphical interface developed in the research enables to watch the graphical reflection of changes of output indicators depending on the change of input parameters of the system.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.