Development of a fuzzy GERT-model for investigating common software vulnerabilities

This paper has determined the relevance of the issue related to improving the accuracy of the results of mathematical modeling of the software security testing process. The fuzzy GERT-modeling methods have been analyzed. The necessity and possibility of improving the accuracy of the results of mathematical formalization of the process of studying software vulnerabilities under the conditions of fuzziness of input and intermediate data have been determined. To this end, based on the mathematical apparatus of fuzzy network modeling, a fuzzy GERT model has been built for investigating software vulnerabilities. A distinctive feature of this model is to take into consideration the probabilistic characteristics of transitions from state to state along with time characteristics. As part of the simulation, the following stages of the study were performed. To schematically describe the procedures for studying software vulnerabilities, a structural model of this process has been constructed. A "reference GERT model" has been developed for investigating software vulnerabilities. The process was described in the form of a standard GERT network. The algorithm of equivalent transformations of the GERT network has been improved, which differs from known ones by considering the capabilities of the extended range of typical structures of parallel branches between neighboring nodes. Analytical expressions are presented to calculate the average time spent in the branches and the probability of successful completion of studies in each node. The calculation of these probabilistic-temporal characteristics has been carried out in accordance with data on the simplified equivalent fuzzy GERT network for the process of investigating software vulnerabilities. Comparative studies were conducted to confirm the accuracy and reliability of the results obtained. The results of the experiment showed that in comparison with the reference model, the fuzziness of the input characteristic of the time of conducting studies of software vulnerabilities was reduced, which made it possible to improve the accuracy of the simulation results.

Development a mathematical model for the software security testing first stage

This paper reports an analysis of the software (SW) safety testing techniques, as well as the models and methods for identifying vulnerabilities. An issue has been revealed related to the reasoned selection of modeling approaches at different stages of the software safety testing process and the identification of its vulnerabilities, which reduces the accuracy of the modeling results obtained. Two steps in the process of identifying software vulnerabilities have been identified. A mathematical model has been built for the process of preparing security testing, which differs from the known ones by a theoretically sound choice of the moment-generating functions when describing transitions from state to state. In addition, the mathematical model takes into consideration the capabilities and risks of the source code verification phase for cryptographic and other ways to protect data. These features generally improve the accuracy of modeling results and reduce input uncertainty in the second phase of software safety testing. An advanced security compliance algorithm has been developed, with a distinctive feature of the selection of laws and distribution parameters that describe individual state-to-state transitions for individual branches of Graphical Evaluation and Review Technique networks (GERT-networks). A GERT-network has been developed to prepare for security testing. A GERT-network for the process of checking the source code for cryptographic and other data protection methods has been developed. A graphic-analytical GERT model for the first phase of software safety testing has been developed. The expressions reported in this paper could be used to devise preliminary recommendations and possible ways to improve the effectiveness of software safety testing algorithms

G-GERT network model of online public opinion reversal based on kernel and grey degree

PurposeIn recent years, online public opinion reversal incidents have been occurring frequently, which has increased the complexity of the evolution of online public opinion, and they have become a difficult issue for public opinion management and control. It is of great significance to explore the regularity of online public opinion reversal.Design/methodology/approachCombined with the grey characteristics of online public opinion information, a grey graphical evaluation review technique (G-GERT) network model is constructed based on kernel and grey degree, and the frequency, probability and time of online public opinion reversal nodes are calculated using C-marking method and Z-marking method.FindingsThroughout the online public opinion reversal events, there are all repeated outbreak nodes occurring, so the authors regard the repeated occurrence of outbreak nodes as reversal. According to the average frequency, probability and time of repeated outbreak nodes in the G-GERT network model, the authors predict the corresponding key information of reversal. It can simulate the evolution process of public opinion events accurately.Originality/valueThe G-GERT network model based on kernel and grey degree reveals the regulation of public opinion reversal, predicts the frequency, probability and time of reversal nodes, which are the most concerned and difficult issues for decision-makers. The model provides the decision basis and reference for government decision-making departments.

MATHEMATICAL MODEL FOR CALCULATING THE PROBABILISTIC RESOURCE CHARACTERISTICS OF TELECOMMUNICATION NETWORKS BASED ON IMPORTANCE OF THE ALLOCATED RESOURCES

Рассматривается задача определения условных плотностей вероятностей ресурсов в телекоммуникационной сети с обновлением информации, содержащейся в заявках, передаваемых по сети. Разработана математическая модель вычисления вероятностно-ресурсных характеристик GERT-сети по экспоненциальным и нормальным распределениям. The problem of determining the conditional probability densities of resources in a telecommunication network with updating the information contained in requests transmitted over the network is considered. The work developed a mathematical model for calculating the probabilistic resource characteristics of the GERT-network by exponential and normal distributions.

Analysis of Aviation Incidents Using the GERT-Network Taking Into Account the Psychological Characteristics of the Operator

In this chapter, the authors considered the construction of network models of aviation incidents taking into account the psychological characteristics of the operator. In particular, the GERT-network of aviation disaster was built. Applying of software to calculate the elements of the GERT-network was presented. The use of network models in the analysis of aviation incidents allows one to visualize the cause-and-effect relationship in aviation incidents and gives the opportunity to obtain quantitative characteristics of the incident for subsequent analysis.

MATHEMATICAL AND COMPUTER MODELING OF HETEROGENEOUS RESOURCES PLANNING AND ALLOCATION IN INDUSTRIAL NETWORKS

The aim of the work is to develop mathematical and software tools for modeling planning and allocating processes of heterogeneous resources in industrial networks. Two approaches to the application of functional dependencies of random values of resources to the model of GERT-network are proposed: parallel and sequential, which corresponds to the processes of planning and allocating resources. The approaches proposed in the work allow expanding the capabilities of classical GERT-networks. To generalize the process of implementation and automation of calculations, a computer modeling system has been developed. The main stages of mathematical modeling of industrial networks based on GERT-models are also proposed. An algorithm for planning and allocating of heterogeneous resources in t industrial networks has been developed. A computer modeling system ResourceModeler has been developed, which allows calculating the distribution laws of output values in a GERT-network using linear functional dependencies based on the heterogeneity of resources.

THE PROBLEM OF PLANNING THE AMOUNT OF HETEROGENEOUS RESOURCES IN INDUSTRIAL GERT-NETWORKS WITH FUNCTIONALLY DEPENDENT RANDOM OPERATIONS

В работе рассмотрена задача планирования объема разнородных ресурсов в промышленных GERT-сетях с функционально зависимыми случайными операциями. Представлены основные шаги алгоритма для применения линейных функциональных зависимостей случайных величин в экспоненциальных GERT-сетях ресурсов. Рассмотрены примеры расчета объема ресурса одинакового или разного типов. Даны сравнительные результаты выходной величины GERT-сети, полученные численным и математическим методами. The paper considers the problem of planning the amount of heterogeneous resources in industrial GERT networks with functionally dependent random operations. The main steps of the algorithm for applying linear functional dependencies of random variables in exponential GERT-networks of resources are presented. Examples of calculating the volume of a resource of the same or different types are considered. The results of the output value of the GERT-network obtained by numerical and mathematical methods are compared.

An approach to building a predictive model of the life cycle of information resources based on stochastic gert-networks and process mining technology

The article proposes an approach to predicting the numerical parameters of the life cycle of information resources. The main task of this work is to develop a tool for numerical forecasting of the life cycle of information resources based on actual life cycle data in the form of resource history event logs. The forecast is carried out using the apparatus of stochastic GERT networks. The construction of the GERT model is performed using the Process Mining algorithmic apparatus and the ProM software framework. The object of the analysis was the data of the Scientific Electronic Library Online. The data is publicly available on the Kaggle.com website. To build a GERT network describing the life cycle model of an information resource, we used the methods of intellectual analysis of Process Mining processes implemented using the ProM Framework. In the course of the work, an analysis of the life cycle of information resources of the Scientific Electronic Online Library was carried out. The paper presents the process of extracting data used to model a GERT network using the ProM framework. The data obtained made it possible to restore the topology of the stochastic network and identify the laws of probability density distribution of the duration of the life cycle stages. On the basis of the constructed GERT-network, the law of distribution of the probability density of the duration of the life cycle of an information resource was described. The obtained result confirms the applicability of Process Mining technology to probabilistic analysis and forecasting of the life cycle of information resources.