DISCRETE AND CONTINUOUS MODELS AND APPLIED COMPUTATIONAL SCIENCE

The article describes a method for calculating interpolation coefficients of expansion using Chebyshev polynomials. The method is valid when the desired function is bounded and has a finite number of maxima and minima in a finite domain of interpolation. The essence of the method is that the interpolated desired function can be represented as an expansion in Chebyshev polynomials; then the expansion coefficients are determined using the collocation method by reducing the problem to solving a well-conditioned system of linear algebraic equations for the required coefficients. Using the well-known useful properties of Chebyshev polynomials can significantly simplify the solution of the problem of function interpolation. A technique using the Clenshaw algorithm for summing the series and determining the expansion coefficients of the interpolated function, based on the discrete orthogonality of Chebyshev polynomials of the 1st kind, is outlined.

In this paper, we study a queuing system with a single-capacity storage device and queue updating. An update is understood as the following mechanism: an application that enters the system and finds another application in the drive destroys it, taking its place in the drive. It should be noted that systems with one or another update mechanism have long attracted the attention of researchers, since they have important applied significance. Recently, interest in systems of this kind has grown in connection with the tasks of assessing and managing the age of information. A system with a queue update mechanism similar to the one we are considering has already been studied earlier in the works of other authors. However, in these works we were talking about the simplest version of the system with Poisson flow and exponential maintenance. In this paper, we consider a phase-type flow and maintenance system. As a result of our research, we developed a recurrent matrix algorithm for calculating the stationary distribution of states of a Markov process describing the stochastic behavior of the system in question, and obtained expressions for the main indicators of its performance.

This article continues the cycle of works by the authors devoted to the problem of the age of information (AoI), a metric used in information systems for monitoring and managing remote sources of information from the control center. The theoretical analysis of information transmission systems requires a quantitative assessment of the “freshness” of information delivered to the control center. The process of transferring information from peripheral sources to the center is usually modeled using queuing systems. In this paper, a queuing system with phase-type distributions is used to estimate the maximum value of the information age, called the peak age. This takes into account the special requirement of the transmission protocol, which consists in the fact that information enters the system in groups of random size. For this case, an expression is obtained for the Laplace–Stieltjes transformation of the stationary distribution function of the peak age of information and its average value. Based on the results of analytical modeling, a numerical study of the dependence of the average value of the peak age of information on the system load was carried out. The correctness of the expressions obtained was verified by comparing the analytical results with the results of simulation modeling.