Vol 17, No 3 (2019)

This article presents the results of 22 / /1HE E queuing system studies with Hyper-Erlang and Erlang second-order input distributions. By Kendall’s defi nition, these systems belong to G/G/1 class with arbitrary distribution laws of input fl ow intervals and service time. In the queueing theory, the study of such systems is particularly relevant due to the fact that it is still not impossible to fi nd a solution for the average waiting time in a queue in the fi nal form. Higher-order Erlang and hyper-Erlang distributions are diffi cult to consider since they cause an increase in computational complexity when deriving a solution for the average waiting time. For the considered second-order distributions, the classical spectral decomposition method of solving the Lindley integral equation for G/G/1 systems allows obtaining a solution in closed form. The article presents the obtained spectral decomposition of the Lindley integral equation solution for the system in question and the formula for the average waiting time in the queue. The adequacy of the obtained results is confi rmed by the correctness of using the classical spectral decomposition method and the results of numerical simulation. The 22 / /1HE E system is applicable when the arrival intervals variation coeffi cient is greater than or equal to 1/ 2 and the service time variation coeffi cient is equal to 1/ 2. For practical application of the results obtained, the method of moments from probability theory is used. The results of Mathcad numerical simulation unequivocally confi rm that the average waiting time is related to the arrival intervals variation coeffi cient and the service time variation coeffi cient by a quadratic dependence.

The probabilistic-temporal characteristics of multi-packet message delivery over a logical point-topoint channel in a data transmission system with decision feedback are presented. The information exchange procedure between the data transmission equipment is determined by the X.25 protocol. The problem of analyzing the timeliness and reliability of multi-packet messaging in a data transmission system, as well as X.25 protocol key parameter synthesis, which ensures a given information delivery quality, is solved. To accomplish this, mathematical models of the multi-packet message delivery process in the considered data transmission system are constructed taking into account all system parameters of the logical data transmission channel based on absorbing fi nite Markov chains. These models serve as the basis for solving analysis and synthesis problems. On the basis of absorbing fi nite Markov chains, a scientifi c and methodological apparatus is presented that adequately describes the multi-packet messages delivery process in the considered X.25 data transmission system, while situational-bipartite graphs and invariant graphs are used. The developed approach allows us to fi nd the maximum allowable number of retries for each packet while taking into account the client’s requirements regarding the reliability and timeliness of the information delivery.

The relevance of this article is confi rmed by the ever-increasing role of digital information networks worldwide. The most important (and sometimes determining) characteristic for organizing the information exchange is the digital channel capacity. Signifi cant advances in technology have been marked by the emergence of the abovementioned communication channels. The eff ectiveness of the digital network design and operation is achieved through the use of mathematical algorithms, the development of which is phased and has its own specifi c features. The issues of theoretical change in data transmission network capacity are widely considered in the scientifi c literature. Practical methods and tools for studying the data transmission network capacity use the terminology for the development, implementation, manufacturing, construction, and operation of digital communication networks.

The third and fi nal part of the article is devoted to the main stage of the business process simulation - software implementation and a series of quasi-optimal control experiments. The essence of quasioptimization is to fi nd a non-rigorous optimal solution, which is the best for the given conditions, according to the expert. The prefabricated buildings construction rate was considered as a business process target value. This value is calculated as a percentage of completed requests relative to the total number of requests received in a given time. The quasi-optimal solution search is carried out by sequentially changing the parameters of random variables selected by expert evaluation and comparing the corresponding target values. The quasi-optimization criterion is to fi nd random variables parameter values that correspond to the maximum target value. The article provides a detailed algorithm for working with a simulation model, as well as an example of its application in the business process studied.

Based on the analysis of the requirements for modern mobile radio networks, the design method was developed for designing multi-frequency multiple-pass antenna systems for linear radio centers. The design method includes the choice of implementation options, design of a radiating system, development of a beamforming scheme and a matching device. An antenna system has been designed using this method. The aforementioned antenna consists of two circular antenna array tiers with antenna elements of the type of a log-periodic antenna synthesized for diff erent subbands. Experimental studies of multi-frequency emitters for multi-pass antenna systems of linear radio centers were performed. The obtained results of experimental studies lead to the conclusion that characteristics of the antenna array designed using the presented method correspond to the specifi ed technical requirements, which, in turn, indicates the effi ciency of the method for multi-frequency multi-input antenna systems design.

The paper discusses relationships between augmented reality and components of technicalorganizational complex system corporate security within the digital economy framework. Corporate security is divided into four components: economic, physical, consumer and operational, among which information and content security of the services provided to the population are distinguished. The «human factor» is an integral attribute of such a system. It includes personnel, customers, partners, and corporation’s competitors. The specifics of the corporate business performance analysis using statistical simulation are considered, taking into account verified and axiological knowledge of decision-makers in the field of AR. The differences are shown between the objective and subjective ontological approaches to the business development project’s expected utility analysis when augmented reality is involved. The important external and internal corporate security threats during the intensive formation period of the digital economy are considered.