A Revised Gomory-Hu Algorithm Taking Account of Physical Unavailability of Network Channels

Auzinger, Winfried; Obelovska, Kvitoslava; Stolyarchuk, Roksolyana

doi:10.1007/978-3-030-50719-0_1

Cited by 7 publications

(5 citation statements)

References 5 publications

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“…To determine the Lagrange multipliers, we express the balance Eq. ( 14) in terms of expressions ( 25), (26) for i ∈ [0, N e ]: where Let's open the second term from expression (27). We will get: ( We obtain the roots of Eqs.…”

Section: Forecasting the Development Of The Cyber Epidemic In Terms O...mentioning

confidence: 99%

“…If we take into account that u depends on the number of infected members of the population, then we get the Reed Frost model [24][25][26] . If it is assumed that the probability of infection does not depend on the number of infected, then we get the Greenwood model [27][28][29][30] . These are more flexible, non-continuous models.…”

mentioning

confidence: 99%

“…These are more flexible, non-continuous models. They are also called branching models [24][25][26][27][28][29][30] . Stochastic models became widespread in the 1970s, are constantly evolving and now generally agree with the results of observations of the course of various biological infections.However, in the case of describing computer virus epidemics or cyber epidemics, the acquired "biological" experience is not inherited.…”

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confidence: 99%

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Stochastic forecasting of variable small data as a basis for analyzing an early stage of a cyber epidemic

Kovtun,

Grochla,

Kharchenko

et al. 2023

Sci Rep

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Security Information and Event Management (SIEM) technologies play an important role in the architecture of modern cyber protection tools. One of the main scenarios for the use of SIEM is the detection of attacks on protected information infrastructure. Consorting that ISO 27001, NIST SP 800-61, and NIST SP 800-83 standards objectively do not keep up with the evolution of cyber threats, research aimed at forecasting the development of cyber epidemics is relevant. The article proposes a stochastic concept of describing variable small data on the Shannon entropy basis. The core of the concept is the description of small data by linear differential equations with stochastic characteristic parameters. The practical value of the proposed concept is embodied in the method of forecasting the development of a cyber epidemic at an early stage (in conditions of a lack of empirical information). In the context of the research object, the stochastic characteristic parameters of the model are the generation rate, the death rate, and the independent coefficient of variability of the measurement of the initial parameter of the research object. Analytical expressions for estimating the probability distribution densities of these characteristic parameters are proposed. It is assumed that these stochastic parameters of the model are imposed on the intervals, which allows for manipulation of the nature and type of the corresponding functions of the probability distribution densities. The task of finding optimal functions of the probability distribution densities of the characteristic parameters of the model with maximum entropy is formulated. The proposed method allows for generating sets of trajectories of values of characteristic parameters with optimal functions of the probability distribution densities. The example demonstrates both the flexibility and reliability of the proposed concept and method in comparison with the concepts of forecasting numerical series implemented in the base of Matlab functions.

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Section: Forecasting the Development Of The Cyber Epidemic In Terms O...mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Stochastic forecasting of variable small data as a basis for analyzing an early stage of a cyber epidemic

Kovtun,

Grochla,

Kharchenko

et al. 2023

Sci Rep

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“…As an example, we consider a technical equipment of a computer network [42][43][44][45] of the Ethernet 10 Base-T standard, which includes a server, two hubs, and workstations (Figure 1). We can update the network configuration with Ethernet 100 Base-T or Ethernet 1000 Base-T.…”

Section: Representation Of a Technical Equipment Of A Local Area Comp...mentioning

confidence: 99%

Modelling Reliability Characteristics of Technical Equipment of Local Area Computer Networks

et al. 2021

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Technical systems in the modern global world are rapidly evolving and improving. In most cases, these are large-scale multi-level systems and one of the problems that arises in the design process of such systems is to determine their reliability. Accordingly, in the paper, a mathematical model based on the Weibull distribution has been developed for determining a computer network reliability. In order to simplify calculating the reliability characteristics, the system is considered to be a hierarchical one, ramified to level 2, with bypass through the level. The developed model allows us to define the following parameters: the probability distribution of the count of working output elements, the availability function of the system, the duration of the system’s stay in each of its working states, and the duration of the system’s stay in the prescribed availability condition. The accuracy of the developed model is high. It can be used to determine the reliability parameters of the large, hierarchical, ramified systems. The research results of modelling a local area computer network are presented. In particular, we obtained the following best option for connecting workstations: 4 of them are connected to the main hub, and the rest (16) are connected to the second level hub, with a time to failure of 4818 h.

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“…Graphical interpretation of structural-logical models is the corresponding schemes of functional integrity 22 – 25 , depicted in the form of block diagrams, trees of faults or (and) events, the "bow-tie" techniques, and so on. An algebra of groups of incompatible events in the paradigm of the general logical-probabilistic method 20 , 23 , 24 , 26 has been developed to remove the binary constraint (the stay of the model element in only one of two defined states), characteristic of structural-logical models. Note also that the fault tree analysis method is the basis for forming dynamic fault trees (have a wide range of logical operators) or generalized fault trees (possible further conversion to Bayesian networks, Petri nets, etc.)…”

Section: Introductionmentioning

confidence: 99%

Reliability model of the security subsystem countering to the impact of typed cyber-physical attacks

Kovtun

Izonin

Greguš

2022

Sci Rep

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The article's main contribution is the description of the process of the security subsystem countering the impact of typed cyber-physical attacks as a model of end states in continuous time. The input parameters of the model are the flow intensities of typed cyber-physical attacks, the flow intensities of possible cyber-immune reactions, and the set of probabilities of neutralization of cyber-physical attacks. The set of admissible states of the info-communication system is described taking into account possible variants of the development of the modeled process. The initial parameters of the model are the probabilities of the studied system in the appropriate states at a particular moment. The dynamics of the info-communication system's life cycle are embodied in the form of a matrix of transient probabilities. The mentioned matrix connects the initial parameters in the form of a system of Chapman's equations. The article presents a computationally efficient concept based on Gershgorin's theorems to solve such a system of equations with given initiating values. Based on the presented scientific results, the article proposes the concept of calculating the time to failure as an indicator of the reliability of the info-communication system operating under the probable impact of typical cyber-physical attacks. The adequacy of the model and concepts presented in the article is proved by comparing a statically representative amount of empirical and simulated data. We emphasize that the main contribution of the research is the description of the process of the security subsystem countering the impact of typed cyber-physical attacks as a model of end states in continuous time. Based on the created model, the concept of computationally efficient solution of Chapman's equation system based on Gershgorin's theorems and calculating time to failure as an indicator of the reliability of the info-communication system operating under the probable impact of typed cyber-physical attacks are formalized. These models and concepts are the highlights of the research.

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A Revised Gomory-Hu Algorithm Taking Account of Physical Unavailability of Network Channels

Cited by 7 publications

References 5 publications

Stochastic forecasting of variable small data as a basis for analyzing an early stage of a cyber epidemic

Stochastic forecasting of variable small data as a basis for analyzing an early stage of a cyber epidemic

Modelling Reliability Characteristics of Technical Equipment of Local Area Computer Networks

Reliability model of the security subsystem countering to the impact of typed cyber-physical attacks

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