# Discrete and Continuous Models and Applied Computational Science

**Editor-in-Chief**: Yuriy P. Rybakov, Doctor of Science (Physics and Mathematics), Professor, Honored Scientist of Russia

**ISSN: **2658-4670 (Print). **ISSN: **2658-7149 (Online)

**Founded in **1993. ** Publication frequency**: quarterly.

**Peer-Review**: double blind. **Publication language:** English.

**APC**: no article processing charge. **Open Access**: Open Access , DOAJ SEAL

**PUBLISHER**: Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)

**See the Journal History **to get information on previous journal titles.

**Indexation**: Russian Index of Science Citation, Scopus, VINITI RAS, DOAJ, Google Scholar, Ulrich's Periodicals Directory, WorldCat, Cyberleninka, East View, Dimensions, ResearchBib, Lens, Research4Life, JournalTOCs

Discrete and Continuous Models and Applied Computational Science was created in 2019 by renaming RUDN Journal of Mathematics, Information Sciences and Physics. RUDN Journal of Mathematics, Information Sciences and Physics was created in 2006 by combining the series "Physics", "Mathematics", "Applied Mathematics and Computer Science", "Applied Mathematics and Computer Mathematics".

Discussed issues affecting modern problems of physics, mathematical modeling, computer science. The widely discussed issues Teletraffic theory, queuing systems design, software and databases design and development.

Discussed problems in physics related to quantum theory, nuclear physics and elementary particle physics, astrophysics, statistical physics, the theory of gravity, plasma physics and the interaction of electromagnetic fields with matter, radio physics and electronics, nonlinear optics.

Journal has a high qualitative and quantitative indicators. The Editorial Board consists of well-known scientists of world renown, whose works are highly valued and are cited in the scientific community. Articles are indexed in the Russian and foreign databases. Each paper is reviewed by at least two reviewers, the composition of which includes PhDs, are well known in their circles. Author's part of the magazine includes both young scientists, graduate students and talented students, who publish their works, and famous giants of world science.

Subject areas:

- Mathematics
- Modeling and Simulation
- Mathematical Physics

- Computer Science
- Computer Science (miscellaneous)

## Current Issue

### Vol 31, No 4 (2023)

**Year:**2023**Articles:**7**URL:**https://journals.rudn.ru/miph/issue/view/1728**DOI:**https://doi.org/10.22363/2658-4670-2023-31-4

#### Full Issue

#### Articles

##### Chronology of the development of Active Queue Management algorithms of RED family. Part 1: from 1993 up to 2005

###### Abstract

This work is the first part of a large bibliographic review of active queue management algorithms of the Random Early Detection (RED) family, presented in the scientific press from 1993 to 2023. The first part will provide data on algorithms published from 1993 to 2005.

**Discrete and Continuous Models and Applied Computational Science**. 2023;31(4):305-331

##### On the algorithmization of construction of the transition intensity matrix in systems with a large number of same elements

###### Abstract

In this article, using the example of a multi-channel exponential queueing system with reordering of requests, we study the problem of computer construction of the state space and coefficient matrix of a system of equilibrium equations. As a result, general principles for solving problems of this type are formulated.

**Discrete and Continuous Models and Applied Computational Science**. 2023;31(4):332-344

##### Evaluation of firewall performance metrics with ranging the rules for Poisson incoming packet flow and exponential filtering time

###### Abstract

The given article is a continuation of a number of works devoted to the development of models and methods for ranging the filtration rules to prevent a decrease in the firewall performance caused by the use of a sequential scheme for checking packet compliance with the rules, as well as by the heterogeneity and variability of network traffic. The article includes a description of a firewall mathematical model given in the form of a complex system and a queuing system with a phase-type discipline for request servicing, which formalizes the network traffic filtering process with the functionality of ranging the rules. The purpose of modeling is to obtain estimates for major firewall performance metrics for various network traffic behavior scenarios, as well as to evaluate an increase in the firewall performance due to ranging a filtration rule set. Calculation of estimates for the firewall (FW) performance metrics was made using the analytical method for a Poisson request flow. Based on the analysis of the modeling results, conclusions were drawn on the effectiveness of ranging the filtration rules in order to improve the firewall performance for traffic scenarios that are close to real ones.

**Discrete and Continuous Models and Applied Computational Science**. 2023;31(4):345-358

##### Demographic indicators, models, and testing

###### Abstract

The use of simple demographic indicators to describe mortality dynamics can obscure important features of the survival curve, particularly during periods of rapid change, such as those caused by internal or external factors, and especially at the oldest or youngest ages. Therefore, instead of the generally accepted Gompertz method, other methods based on demographic indicators are often used. In human populations, chronic phenoptosis, in contrast to age-independent acute phenoptosis, is characterized by rectangularization of the survival curve and an accompanying increase in average life expectancy at birth, which can be attributed to advances in society and technology. Despite the simple geometric interpretation of the phenomenon of rectangularization of the survival curve, it is difficult to notice one, detecting changes in the optimal coefficients in the Gompertz-Makeham law due to high computational complexity and increased calculation errors. This is avoided by calculating demographic indicators such as the Keyfitz entropy, the Gini coefficient, and the coefficient of variation in lifespan. Our analysis of both theoretical models and real demographic data shows that with the same value of the Gini coefficient in the compared cohorts, a larger value of the Keyfitz entropy indicates a greater proportion of centenarians relative to average life expectancy. On the contrary, at the same value of the Keyfitz entropy, a larger value of the Gini coefficient corresponds to a relatively large mortality at a young age. We hypothesize that decreases in the Keyfitz entropy may be attributable to declines in background mortality, reflected in the Makeham term, or to reductions in mortality at lower ages, corresponding to modifications in another coefficient of the Gompertz law. By incorporating dynamic shifts in age into survival analyses, we can deepen our comprehension of mortality patterns and aging mechanisms, ultimately contributing to the development of more reliable methods for evaluating the efficacy of anti-aging and geroprotective interventions used in gerontology.

**Discrete and Continuous Models and Applied Computational Science**. 2023;31(4):359-374

##### On application of solution continuation method with respect to the best exponential argument in solving stiff boundary value problems

###### Abstract

The problematic of solving stiff boundary value problems permeates numerous scientific and engineering disciplines, demanding novel approaches to surpass the limitations of traditional numerical techniques. This research delves into the implementation of the solution continuation method with respect to the best exponential argument, to address these stiff problems characterized by rapidly evolving integral curves. The investigation was conducted by comparing the efficiency and stability of this novel method against the conventional shooting method, which has been a cornerstone in addressing such problems but struggles with the erratic growth of integral curves. The results indicate a marked elevation in computational efficiency when the problem is transformed using the exponential best argument. This method is particularly pronounced in scenarios where integral curves exhibit exponential growth speed. The main takeaway from this study is the instrumental role of the regularization parameter. Its judicious selection based on the unique attributes of the problem can dictate the efficiency of the solution. In summary, this research not only offers an innovative method to solve stiff boundary value problems but also underscores the nuances involved in method selection, potentially paving the way for further refinements and applications in diverse domains.

**Discrete and Continuous Models and Applied Computational Science**. 2023;31(4):375-386

##### On a set of tests for numerical methods of integrating differential equations, based on the Calogero system

###### Abstract

Based on the completely integrable Calogero dynamical system, which describes the one-dimensional many-body problem, a tool for testing difference schemes has been developed and implemented in the original fdm package integrated into the Sage computer algebra system. This work shows how the developed tools can be used to examine the behavior of numerical solutions near the collision point and how to study the conservatism of the difference scheme. When detecting singularities using Alshina’s method, a difficulty was discovered associated with false order fluctuations. One of the main advantages of this set of tests is the purely algebraic nature of the solutions and integrals of motion.

**Discrete and Continuous Models and Applied Computational Science**. 2023;31(4):387-398

##### Methodological derivation of the eikonal equation

###### Abstract

Usually, when working with the eikonal equation, reference is made to its derivation in the monograph by Born and Wolf. The derivation of this equation was done rather carelessly. Understanding this derivation requires a certain number of implicit assumptions. For a better understanding of the eikonal approximation and for methodological purposes, the authors decided to repeat the derivation of the eikonal equation, explicating all possible assumptions. Methodically, the following algorithm for deriving the eikonal equation is proposed. The wave equation is derived from Maxwell’s equation. In this case, all conditions are explicitly introduced under which it is possible to do this. Further, from the wave equation, the transition to the Helmholtz equation is carried out. From the Helmholtz equation, with the application of certain assumptions, a transition is made to the eikonal equation. After analyzing all the assumptions and steps, the transition from the Maxwell’s equations to the eikonal equation is actually implemented. When deriving the eikonal equation, several formalisms are used. The standard formalism of vector analysis is used as the first formalism. Maxwell’s equations and the eikonal equation are written as three-dimensional vectors. After that, both the Maxwell’s equations and the eikonal equation use the covariant 4-dimensional formalism. The result of the work is a methodically consistent description of the eikonal equation.

**Discrete and Continuous Models and Applied Computational Science**. 2023;31(4):399-418