Analysis of a Queueing System of the Type Ek / El / 1 / R With a Pair of Incoming Flows of Requests, Absolute Priority, Limited Bufer and Waiting Time
Authors:   International Research and Training Center for Information Technologies and Systems of the National Academy of Science and Ministry of Education and Science of Ukraine., IVANESHKIN O.I. 
Published: November 2024

Introduction. The modern pace of industrialization of society and the integration of knowledge from various spheres of human activity have led to constantly growing volumes of collectively used and geographically distributed information. These circumstances were the reason for the creation of information networks and systems of various purposes, which not only became the main means of satisfying the demand for information and caused the need for global digitalization of almost all spheres of scientific and applied human activity, but also transferred to a new, larger-scale level understanding of the very problem of information interactions. The stochastic nature of the processes occurring in networks has greatly complicated their work, turning nodes into the main and most numerous places of “concentration” of overloads, delays and other undesirable moments. Significantly reducing the efficiency of the software and hardware included in the nodes, they became capable of not only completely blocking the operation of the nodes themselves, but also of networks as a whole. Transitions to new generations of network protocols, of course, solve this problem, but not for a long period of time. With the exponential growth in the volume of information circulating in networks, such an approach is unlikely to become an universal panacea that can permanently and completely solve the problem. The need for prompt delivery to the consumer of information that has not lost its value (due to its aging over time) and significantly lower resource costs during implementation are constantly attracting more and more attention to another approach to improving the efficiency of information exchange components. The main principles of this approach are the construction of the appropriate type of adequate models, their analysis, obtaining a set of required characteristics and parameters and subsequent modification, development and implementation of new generations of software as structural and functional elements of the nodes themselves. In most cases, another component is included in this chain - optimization (based on the principle of situational adaptation to existing conditions) using additive cost quality criteria. The foundations of this version of the campaign were laid in the works of L. Takach, A.N. Kolmogorov, A.Y. Khinchin, B.V.Gnedenko, I.M. Kovalenko, a number of their students and researchers in other areas of scientific activity [1 – 6]. The purpose of the paper is to develop of models of new types of random access protocols in nodes of information networks and systems, the operation of which can be described and analyzed by means and methods of the theory of probability and stochastic processes. Studying models and obtaining a number of stationary and non-stationary characteristics that are important in practical terms, to solve problems of increasing the efficiency of nodes by reducing various types of losses of applications, the cost of temporary stay in the buffer and obtaining the ability to optimize the process of their functioning using dynamic programming methods. Methods. Methods and means of the apparatus of the theory of probability and stochastic processes. Result. A model of a new type of random access protocol in nodes of information networks and systems has been developed, the operation of which is described and analyzed by means and methods of the theory of probability and stochastic processes. A number of practically important stationary and non-stationary characteristics have been obtained to solve the problems of increasing the efficiency of nodes by reducing various types of losses of applications and the costs of their temporary stay in a buffer pool of a finite volume, as well as optimizing the process of their functioning using dynamic programming methods. Conclusions. A model of a random access protocol in nodes of information networks and systems has been developed, the operation of which has been described and analyzed by methods and techniques of probability theory and stochastic processes. Expressions have been obtained for a number of practically important chr.c.t.s.s that serve as a basis for solving the problem of increasing the efficiency of node operation by reducing the loss of requests and the costs of their temporary stay in a finite-volume buffer, as well as optimizing the process of functioning of the QS by dynamic programming methods. Keywords: information networks and systems, nodes, random access protocols, stochastic processes.