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The problem of identifying deterministic cause-and-effect relationships, initially hidden in accumulated empirical data, is discussed. Statistical methods were used to identify such relationships. A simple mathematical model of cause-and-effect relationships is proposed, in the framework of which several models of causal dependencies in data are described - for the simplest relationship between cause and effect, for many effects of one cause, as well as for chains of cause-and-effect relationships (so-called transitive causes). Estimates are formulated that allow using the de Moivre-Laplace theorem to determine the parameters of causal dependencies linking events in a polynomial scheme trials. The statements about the unambiguous identification of causeand-effect dependencies that are reconstructed from accumulated data are proved. The possibilities of using such data analysis schemes in medical diagnostics and cybersecurity tasks are discussed.

The given article is a continuation of a number of works devoted to the development of models and methods for ranging the filtration rules to prevent a decrease in the firewall performance caused by the use of a sequential scheme for checking packet compliance with the rules, as well as by the heterogeneity and variability of network traffic. The article includes a description of a firewall mathematical model given in the form of a complex system and a queuing system with a phase-type discipline for request servicing, which formalizes the network traffic filtering process with the functionality of ranging the rules. The purpose of modeling is to obtain estimates for major firewall performance metrics for various network traffic behavior scenarios, as well as to evaluate an increase in the firewall performance due to ranging a filtration rule set. Calculation of estimates for the firewall (FW) performance metrics was made using the analytical method for a Poisson request flow. Based on the analysis of the modeling results, conclusions were drawn on the effectiveness of ranging the filtration rules in order to improve the firewall performance for traffic scenarios that are close to real ones.

Efficient allocation of radio access network (RAN) resources remains an important challenge with the introduction of 5G networks. RAN virtualization and division into logical subnetworks - slices - puts this task into a new perspective. In the paper we present a software tool based on the OMNeT++ platform and developed for performance analysis of a network slicing policy with SLA-based slice performance isolation. The tool is designed using the object-oriented approach, which provides flexibility and extensibility of the simulation model. The paper briefly presents the slicing policy under study and focuses on the simulators architecture and design. Numerical results are provided for illustration.

This article is a continuation of a number of works devoted to evaluation of probabilistic-temporal characteristics of firewalls when ranging a filtration rule set. This work considers a problem of the decrease in the information flow filtering efficiency. The problem emerged due to the use of a sequential scheme for checking the compliance of packets with the rules, as well as due to heterogeneity and variability of network traffic. The order of rules is non-optimal, and this, in the high-dimensional list, significantly influences the firewall performance and also may cause a considerable time delay and variation in values of packet service time, which is essentially important for the stable functioning of multimedia protocols. One of the ways to prevent decrease in the performance is to range a rule set according to the characteristics of the incoming information flows. In this work, the problems to be solved are: determination and analysis of an average filtering time for the traffic of main transmitting networks; and assessing the effectiveness of ranging the rules. A method for ranging a filtration rule set is proposed, and a queuing system with a complex request service discipline is built. A certain order is used to describe how requests are processed in the system. This order includes the execution of operations with incoming packets and the logical structure of filtration rule set. These are the elements of information flow processing in the firewall. Such level of detailing is not complete, but it is sufficient for creating a model. The QS characteristics are obtained with the help of simulation modelling methods in the Simulink environment of the matrix computing system MATLAB. Based on the analysis of the results obtained, we made conclusions about the possibility of increasing the firewall performance by ranging the filtration rules for those traffic scripts that are close to real ones.

Firewalls is one of the major components to provide network security. By using firewalls, you can solve such problems as preventing unauthorized access, and deleting, modifying and/or distributing information under protection. The process of information flows filtration by a firewall introduces additional time delays, thus possibly leading to disruption of stable operation of the protected automated system or to inaccessibility of the services provided by the system. Multimedia services are particularly sensitive to service time delays. The main purpose of the work presented in this paper is to evaluate the influence of the firewall on the time delays in data transmission process in the automated system with multimedia data transmission protocols. The evaluation is provided by the queuing theory methods while a session is initiated between two users by the Session Initiation Protocol (SIP) with firewall message filtration. A firewall is a local or functional distributing tool that provides control over the incoming and/or outgoing information in the automated system (AS), and ensures the protection of the AS by filtering the information, i.e., providing analysis of the information by the criteria set and making a decision on its distribution.

A mathematical model of the functioning of the switch of a software defined networks is constructed in the form of a queuing network consisting of two queuing systems: the first simulates an input data buffer and a device for reading information from the header of the packet; the second is a table for addressing the switch of a software defined networks. The receipt of data in software defined networks has a probabilistic character in their deterministic processing in communication channels and switching nodes. Therefore, this mathematical model of the functioning of the switch of a software defined networks was built on the basis of queuing systems and networks. The stream of requests flowing into the network was divided into two Poisson streams of various types of applications, the first of which corresponded to the packets that came to the control port of the switch (from the controller), and the second flow to the remaining packets arriving on the switch. The flow corresponding to the packets arriving at the switch from the controller has a relative priority over the flow from the remaining arriving packets As a result, formulas were obtained for calculating the performance indicators of this telecommunications equipment such as average waiting queues for priority and non-priority applications, the probability of loss of applications for each phase of the switch. Based on the received quality of service indicators for this telecommunications equipment, it is possible to assess the stability of switches in software defined networks for various information impacts.

Queueing systems with random resource requirements, in which an arriving customer, in addition to a server, demands a random amount of resources from a shared resource pool, have proved useful to analyze wireless communication networks. The stationary distributions of such queuing systems are expressed in terms of truncated convolution powers of the cumulative distribution function of the resource requirements. Discretization of the cumulative distribution function and the application of the fast Fourier transform are a traditional way of calculating convolutions. We suggest finding truncated convolution powers of the cumulative distribution functions by calculating the convolution powers of the truncated cumulative distribution functions via fast Fourier transform. This radically decreases computational complexity. We introduce the concept of resource load and investigate the accuracy of the proposed method at low and high resource loads. It is shown that the proposed method makes it possible to quickly and accurately calculate truncated convolution powers required for the analysis of queuing systems with random resource requirements.

In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution to be of product form and consider some particular cases of the subsystem interaction for which these conditions can be easily verified.

In this paper, we study queueing systems with an infinite and finite number of waiting places that can be modeled by a Quasi-Birth-and-Death process. We derive the conditions under which the stationary distribution for a loss system is a truncation of the stationary distribution of the Quasi-Birth-and-Death process and obtain the stationary distributions of both processes. We apply the obtained results to the analysis of a semi-open network in which a customer from an external queue replaces a customer leaving the system at the node from which the latter departed.