Vol 30, No 1 (2022)


Performance analysis of queueing system model under priority scheduling algorithms within 5G networks slicing framework

Adou K.Y., Markova E.V., Zhbankova E.A.


A new era is opening for the world of information and communication technologies with the 5G networks’ release. Indeed 5G networks appear in modern wireless systems as solutions to “traditional” networks’ inflexibility and lack of radio resources problems. Using these networks the operators can expand their services’ range at will and, therefore, manage daily operations by monitoring ‘key performance indicators’ (KPIs) - helping meet the quality of service (QoS) requirements much easily. To meet the QoS requirements 5G networks can be implemented alongside priority scheduling algorithms. This paper considers the operation of a wireless network slicing model under two scheduling algorithms. A comparative analysis of main performance measures is provided.

Discrete and Continuous Models and Applied Computational Science. 2022;30(1):5-20
pages 5-20 views

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Bouchentouf A.A., Medjahri L., Boualem M., Kumar A.


In this paper, we analyze a multi-server queue with customers’ impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.

Discrete and Continuous Models and Applied Computational Science. 2022;30(1):21-38
pages 21-38 views

The quantization of the classical two-dimensional Hamiltonian systems

Belyaeva I.N.


The paper considers the class of Hamiltonian systems with two degrees of freedom. Based on the classical normal form, according to the rules of Born-Jordan and Weyl-MacCoy, its quantum analogs are constructed for which the eigenvalue problem is solved and approximate formulas for the energy spectrum are found. For particular values of the parameters of quantum normal forms using these formulas, numerical calculations of the lower energy levels were performed, and the obtained results were compared with the known data of other authors. It was found that the best and good agreement with the known results is obtained using the Weyl-MacCoy quantization rule. The procedure for normalizing the classical Hamilton function is an extremely time-consuming task, since it involves hundreds and even thousands of polynomials for the necessary transformations. Therefore, in the work, normalization is performed using the REDUCE computer algebra system. It is shown that the use of the Weyl-MacCoy and Born-Jordan correspondence rules leads to almost the same values for the energy spectrum, while their proximity increases for large quantities of quantum numbers, that is, for highly excited states. The canonical transformation is used in the work, the quantum analog of which allows us to construct eigenfunctions for the quantum normal form and thus obtain analytical formulas for the energy spectra of different Hamiltonian systems. So, it is shown that quantization of classical Hamiltonian systems, including those admitting the classical mode of motion, using the method of normal forms gives a very accurate prediction of energy levels.

Discrete and Continuous Models and Applied Computational Science. 2022;30(1):39-51
pages 39-51 views

On the many-body problem with short-range interaction

Gambaryan M.M., Malykh M.D.


The classical problem of the interaction of charged particles is considered in the framework of the concept of short-range interaction. Difficulties in the mathematical description of short-range interaction are discussed, for which it is necessary to combine two models, a nonlinear dynamic system describing the motion of particles in a field, and a boundary value problem for a hyperbolic equation or Maxwell’s equations describing the field. Attention is paid to the averaging procedure, that is, the transition from the positions of particles and their velocities to the charge and current densities. The problem is shown to contain several parameters; when they tend to zero in a strictly defined order, the model turns into the classical many-body problem. According to the Galerkin method, the problem is reduced to a dynamic system in which the equations describing the dynamics of particles, are added to the equations describing the oscillations of a field in a box. This problem is a simplification, different from that leading to classical mechanics. It is proposed to be considered as the simplest mathematical model describing the many-body problem with short-range interaction. This model consists of the equations of motion for particles, supplemented with equations that describe the natural oscillations of the field in the box. The results of the first computer experiments with this short-range interaction model are presented. It is shown that this model is rich in conservation laws.

Discrete and Continuous Models and Applied Computational Science. 2022;30(1):52-61
pages 52-61 views

Finite-difference methods for solving 1D Poisson problem

Ndayisenga S., Sevastianov L.A., Lovetskiy K.P.


The paper discusses the formulation and analysis of methods for solving the one-dimensional Poisson equation based on finite-difference approximations - an important and very useful tool for the numerical study of differential equations. In fact, this is a classical approximation method based on the expansion of the solution in a Taylor series, based on which the recent progress of theoretical and practical studies allowed increasing the accuracy, stability, and convergence of methods for solving differential equations. Some of the features of this analysis include interesting extensions to classical numerical analysis of initial and boundary value problems. In the first part, a numerical method for solving the one-dimensional Poisson equation is presented, which reduces to solving a system of linear algebraic equations (SLAE) with a banded symmetric positive definite matrix. The well-known tridiagonal matrix algorithm, also known as the Thomas algorithm, is used to solve the SLAEs. The second part presents a solution method based on an analytical representation of the exact inverse matrix of a discretized version of the Poisson equation. Expressions for inverse matrices essentially depend on the types of boundary conditions in the original setting. Variants of inverse matrices for the Poisson equation with different boundary conditions at the ends of the interval under study are presented - the Dirichlet conditions at both ends of the interval, the Dirichlet conditions at one of the ends and Neumann conditions at the other. In all three cases, the coefficients of the inverse matrices are easily found and the algorithm for solving the problem is practically reduced to multiplying the matrix by the vector of the right-hand side.

Discrete and Continuous Models and Applied Computational Science. 2022;30(1):62-78
pages 62-78 views

On methods of building the trading strategies in the cryptocurrency markets

Shchetinin E.Y.


The paper proposes a trading strategy for investing in the cryptocurrency market that uses instant market entries based on additional sources of information in the form of a developed dataset. The task of predicting the moment of entering the market is formulated as the task of classifying the trend in the value of cryptocurrencies. To solve it, ensemble models and deep neural networks were used in the present paper, which made it possible to obtain a forecast with high accuracy. Computer analysis of various investment strategies has shown a significant advantage of the proposed investment model over traditional machine learning methods.

Discrete and Continuous Models and Applied Computational Science. 2022;30(1):79-87
pages 79-87 views

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