Multi-service resource queue with the multy-component Poisson arrivals

In many papers devoted to telecommunication systems, multiservice queueing models with heterogeneous customer arrivals are given. As a rule, there is streaming traffic, corresponding to the audio and video conference, and elastic traffic, corresponding to the data and file transmission. Different types of traffic require different quality of service, therefore the multi-service systems are also differentiated service systems. Such papers are aimed at developing a framework for estimating the quality of service indicators in new generation multi-service networks. This paper considers a multiservice resource queueing system with three Poisson arrivals, one of which is splitting. The equation for the probabilities distribution of the total resource amounts on the system blocks is compiling by the dynamic screening method, and using the characteristic function of the stationary distribution, the solution is obtaining. The numerical characteristics of the system performance are obtained by the method of moments using characteristic function. A numerical example shows that arrivals intensity growing increases optimal total resource amounts on system blocks in the system with limited resources, and the splitting arrivals affect the correlation between total resource amounts

Modeling of the process of preparing future teachers of informatics to resource-saving activities based on european experience

The article describes the model for the preparation of future teachers of informatics for resource-saving activities, the stages of modeling are considered. The developed model, which is a structural interconnection of the target, content, technological, technical and effective components, will allow not only to form the teachers' readiness for introduction of innovative teaching methods in the educational process of the school on the basis of green information technologies, but also to develop a culture of resource saving

Infinite-server resource queueing systems with different types of Markov-modulated poisson process and renewal arrivals

In this paper, we propose models that significantly expand the scope of practical applications, namely, queueing systems with various nodes for processing heterogeneous data that require arbitrary resource capacities for their service. When a customer arrives in the system, the customer typeis randomly selected according to a set of probabilities. Then the customer goes to the server of the corresponding device type, where its service is performed during a random time period with a distribution function depending on the type of customer. Moreover, each customer requires a random amount of resources, of which the distribution function also depends on the customer type, but is independent of its service time. The aim of this research was to develop a heterogeneous queueing resource system with an unlimited number of servers and an arrival process in the form of a Markov-modulated Poisson process or stationary renewal process, and with requests for a random number of heterogeneous resources. We have performed analysis under conditions of growing intensity of the arrival process. Here we formulate the theorems and prove that under high-load conditions, the joint asymptotic probability distribution of the n-dimensional process of the total amounts of the occupied resources in the system is a multidimensional Gaussian distribution with parameters that are dependent on the type of arrival process. As a result of numerical and simulation experiments, conclusions are drawn on the limits of the applicability of the obtained asymptotic results. The dependence of the convergence of experimental results on the type of distribution of the system parameters (including the distributions of the service time and of the customer capacity) are also studied. The results of the approximations may be applied to estimating the optimal total number of resources for a system with a limited amount of resources

Multiclass GI/GI/∞ Queueing Systems with Random Resource Requirements

In the paper we consider a GI/GI/∞ queuing system with n types of customers under the assumptions that customers arrive at the queue according to a renewal process and occupy random resource amounts, which are independent of their service times. Since, in general, the analytical solution of the corresponding Kolmogorov differential equations is not available, we focus on the amount of resources occupied by each class of customers under the assumption of infinitely growing arrival rate, and derive its first and second-order asymptotic approximations. In more detail, we show that the n-dimensional probability distribution of the total resource amount is asymptotically n-dimensional Gaussian, and we verify the accuracy of the asymptotics (in terms of Kolmogorov distance) by means of discrete event simulation

Using infinite‑server resource queue with splitting of requests for modeling two‑channel data transmission

New Radio Access Technology 3GPP New Radio has become the fundamental wireless technology in the fifth-generation networks, which allows us to achieve high data rates due to the ability to work in the millimeter-wave band. But the key feature and the main problem of 5G New Radio networks is that people themselves, cars, buildings, etc. are signal blockers, while the base stations of the fourth generation networks have widescreen broadcasting and such small obstacles do not cause loss of connection. Service providers and mobile operators are already testing the proposed technology. In this connection, the scientific community has the task of analyzing the performance of these systems and increasing it in the future. Currently, there are known studies of “basic” mathematical models of such networks. By this term, we mean models built in the simplest possible assumptions. However, due to the justified necessity of introducing new technology into the daily lives of subscribers, service providers pose the scientific community with the task of analyzing the effectiveness of the most appropriate mathematical models. For example, a technology of splitting transmitted data into two streams using as 5G and both 4G transmission technologies is considered now by 3GPP Project Coordination Group. The paper is devoted to such a problem. We consider a mathematical model of the message transmitting with the implementation of the splitting function in the communication networks of New Radio technology in the form of a resource queueing system with a renewal arrival process and non-exponential service. For this problem, an approximation of a stationary two-dimensional probability distribution of the number of occupied resources in parallel service units is obtained. It is shown that this approximation coincides with the Gaussian distribution, and its area of applicability is shown

Ресурсные неоднородные СМО MMPP/GI(2)/∞

A heterogeneous queuing system with an infinite number of servers is considered in this paper. Customers arrive in the system according to a Markov Modulated Poisson Process. The type of incoming customer is defined as i-type with probability pi (i = 1, 2). Each customer carries a random quantity of work (capacity of the customer). In this study service time does not depend on the customers capacities. It is shown that the joint probability distribution of the customers number and total capacities in the system is multidimensional Gaussian distribution under the asymptotic condition of an infinitely growing service time. Simulation results allow us to determine an applicability area of the asymptotic result

Crystal Growth and Spectroscopy of Yb²⁺-Doped CsI Single Crystal

The single crystals of CsI-Yb2+ were grown, and their spectroscopic studies were conducted. The observed luminescence in CsI-Yb2+ is due to 5d–4f transitions in Yb2+ ions. Using time-resolved spectroscopy, spin-allowed and spin-forbidden radiative transitions of ytterbium ions at room temperature were found. The excitation spectra of Yb2+ luminescence bands were obtained in the range of 3–45 eV. The mechanism of charge compensation of Yb2+ ions in a CsI crystal was also studied, the spectrum of the thermally stimulated depolarization current was measured, and the activation energies of the two observed peaks were calculated. These peaks belong to impurity–vacancy complexes in two different positions. The charge compensation of Yb2+ occurs via cation vacancies in the nearest-neighbor and next-nearest-neighbor positions.The Yb2+ ions are promising dopants for CsI scintillators and X-ray phosphors in combination with SiPM photodetectors

Asymptotic analysis of resource heterogeneous QS (MMPP + 2M)(2,ν)/GI(2)/∞ under equivalently increasing service time

We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total amount of resources occupied by each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources