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Arbitrarily accurate approximation of numerical characteristics of stationary ALOHA Channels
Ch. 9470700. P. 1–8.
The development of the Internet of Things technology in cellular networks is considered within the framework of massive machine-type communications with the use of random multiple access algorithms such as ALOHA and its modifications. Despite the fact that this class of algorithms has been studied for a long time, there are no numerical methods for obtaining with a given accuracy such characteristics of the system as the average delay and the average number of transmissions per user. We propose a method for calculating upper and lower bounds for these characteristics, which converge to each other (and the exact value) as the computational complexity increases. The proposed method allows one to obtain these characteristics with an arbitrary accuracy.
Anton Karamyshev, Artem Krasilov, Evgeny Khorov, IEEE Transactions on Network Science and Engineering 2026 P. 1–18
Modern communication networks shall support mission-critical and real-time applications that demand high data rates, low latency, and ultra-high reliability, which is known as Ultra-reliable Low-latency Communications (URLLC). In URLLC systems, the effective capacity, i.e., the maximum traffic rate at which latency and reliability constraints are satisfied, is a key metric for resource management. Its estimations ...
Added: April 17, 2026
Alexeeva T., Shirokov N. A., St Petersburg Mathematical Journal 2025 Vol. 36 No. 1 P. 25–39
Let L be a chord-arc curve in R3. We introduce a functional class Hr+ω(L) where a modulus of continuity ω satisfies the Dini condition and r≥1. We define neighborhoods of L Ωδ(L)=⋃M∈LBδ(M), Bδ(M)={X∈R3:∥XM∥<δ} and set HarmΩδ(L) for harmonic functions in Ωδ(L). The Theorem 1 states that if f∈Hω+r(L) then there exist functions vδ∈HarmΩδ(L) such that ∣∣f(X)−vδ(M)∣∣≤cfδrω(δ), M∈L, and ∣∣∂αvδ(M)∣∣≤cfω(δ)δ, M∈Ωδ(L), |α|=r+1. The Theorem 2 states that if a function f defined on L satisfies claim of Theorem 1 then f∈Hω+r(L). ...
Added: March 16, 2026
Сильванович О. В., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 Т. 545 С. 179–205
Let ak < bk < ak+1, k ∈ Z, Ik = (ak, bk), Jk = [bk, ak+1]. We assume that |Ik| |Jk|, ak −−−−−→ k→+∞ ∞, ak −−−−−→ k→−∞ −∞ and |Jk| 1 |ak|α , |k| → ∞, α > 0. The distribution of {Jk} satisfies some regularity conditions, E = S k∈Z ...
Added: March 16, 2026
Медведев А. Н., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2025 № 545 С. 157–167
Let D be a bounded domain on the complex plain C with sufficiently smooth boundary. We denote by Λ αpDq, 0 α 1, the class of analytic functions in D satisfying the α-H¨older condition in D . Each function f P Λ αpDq can be factored as f F I with F ...
Added: March 16, 2026
Monakhova E., Monakhov O., Edward R. Rzaev et al., IEEE Access 2025 Vol. 13 P. 104716–104727
Based on the analysis of a large dataset for optimal undirected double-loop networks, we studied the problem of finding families of optimal double-loop graphs with the minimal possible diameter. Optimal double-loop networks are of practical interest as graph models for reliable, low-delay communication in computer systems and networks-on-chip, due to their advantageous networking properties. A ...
Added: June 30, 2025
Alexander Lazarev, Nikolay Pravdivets, Barashov E., Mathematics 2024 Vol. 12 No. 5 Article 699
The problem of the approximation of the coefficients of the objective function of a scheduling problem for a single machine is considered. It is necessary to minimize the total weighted completion times of jobs with unknown weight coefficients when a set of problem instances with known optimal schedules is given. It is shown that the ...
Added: May 16, 2024
Шагай М. А., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2023 Т. 527 С. 242–255
Let sk, 1 6 k 6 m, m > 2, be disjoint segments lying in a parallelogram Q. We denote by ℘(z) a doubly periodic Weierstrass function with the fundamental parallelogram Q. Let fk : sk → C be functions, and let f 0 k ∈ L pk (sk), 1 6 k 6 m, 1 ...
Added: February 10, 2024
Sintsova K. A., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2023 Vol. 56 No. 1 P. 46–56
The approximation-theory problem to describe classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, and splines arose over 100 years ago; it still remains topical. Among many problems related to approximation, we consider the two-variable polynomial approximation problem for a function defined on the continuum of an ...
Added: February 10, 2024
Alexeeva T., Shirokov N. A., Алгебра и анализ 2024 Т. 36 № 1 С. 40–59
On the chord-arc curve in R^3 classes of functions similar to Hölder functions with smoothness greater than unity are defined. A constructive description of these classes is obtained in terms of the rate of approximation of functions from them by functions that are harmonic in neighborhoods contracting to the curve. The choice of defining these classes ...
Added: January 10, 2024
Бурков А. А., Tyurlikov A., Информационно-управляющие системы 2020 Vol. 3 P. 79–85
Introduction: Currently, the first versions of 5G communication standard networks are being deployed and discussions are underway on the further development of cellular networks and the transition to the 6G standard. The work of the currently popular idea of the Internet of Things (IoT) is supposed to be in the framework of a Massive Machine-Type ...
Added: September 26, 2023
Kulagin N. E., L.M. Lerman, Physica D: Nonlinear Phenomena 2023 Vol. 454 Article 133845
We study in this pap er the existence of periodically modulated in one variable and localized in another variable solutions to the cubic Swift-Hohenberg equation on the plane R2. In the first part we try to apply the method by Kirschgassner-Mielke to reduce the problem to the search of finite-dimensional submanifolds with periodic orbits on
them in some formal ...
Added: July 27, 2023
Shirokov N. A., Синцова К. А., Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия 2023 Т. 10 № 1 С. 61–72
The problem of describing classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, splines entered in the theory of approximation more than 100 years ago and still retains its relevance. Among a large number of problems related to approximation, we considered the problem of polynomial approximation in ...
Added: May 24, 2023
Шагай М. А., Флегонтов А. В., Иофе М. Д., Springer 2021
In our paper we seek to find of constructive describe functional classes defined on subsets of the period's parallelogram of doubly periodic Weierstrass functions using the integral norm. ...
Added: February 6, 2023
Tsarev A., Emil Khayrov, Medvedeva E. et al., , in: Internet of Things, Smart Spaces, and Next Generation Networks and Systems. 20th International Conference, NEW2AN 2020, and 13th Conference, ruSMART 2020, St. Petersburg, Russia, August 26–28, 2020, Proceedings, Part IIVol. 2: 20th International Conference, NEW2AN 2020, and 13th Conference, ruSMART 2020, St. Petersburg, Russia, August 26–28, 2020, Proceedings, Part II. Book 12526: LNCS.: Switzerland: Springer, 2020. Ch. 21 P. 240–258.
The paper provides a method for calculating characteristics of a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol to be used at the Medium Access Control (MAC) layer in an Industrial Internet of Things (IIoT) network. In particular, we consider a set of nodes equipped with sensors, deployed into an industrial machine, and having ...
Added: December 12, 2022
Lazarev A. A., Lemtyuzhnikova D. V., Tyunyatkin A. A. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 10 P. 2881–2886
This research extends the interpolation approach to approximating the objective function value for the minimization maximum lateness problem. The interpolation approach is defined using a special objective function Lmax(α), which is proven to be continuous and depends only on α transform coefficient. Such a function is proven to be monotonically increasing, and this property is ...
Added: December 5, 2022
Burkov A. A., Shneer S. V., A. M. Turlikov, Информационно-управляющие системы 2020 No. 3 P. 79–85
Currently, the first versions of 5G communication standard networks are being deployed and discussions are underway on further development of cellular networks and transition to the 6G standard. Once the Internet of Things is fully developed, it will function within the framework of Massive Machine-Type Communications. Its performance will need to satisfy a number of ...
Added: October 31, 2022
Salnikov A., Stepanova I., Gudkova T. et al., , in: 2021 14th International Conference Management of large-scale system development (MLSD).: IEEE, 2021. P. 1–3.
We have constructed an analytical model of the magnetic field over a region of the Martian surface using satellite raw data and S-approximations within the modified structural-parametric approach. The method mentioned above implies considering the environment features as a function included in an integral. We approximated the anomalous field by the sum of simple and ...
Added: October 30, 2022
Nesterenkov O., Chemodanov A., Turlikov A., , in: 2022 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF) 30 May - 3 June 2022, St. Petersburg, Russia.: IEEE, 2022. Ch. 180440 P. 1–5.
The number of devices transmitting any data is increasing rapidly every day, so modern wireless networks (especially sensor networks, where the number of sensors connected to one base station can be enormous) must adapt to new realities, and developers must change data transmission algorithms. In this article, we consider the problem of constructing the lower ...
Added: October 28, 2022
Borisovskayа A., Glebov A., Andrey Turlikov, , in: 2021 XVII International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY).: IEEE, 2021. P. 28–33.
In this paper, a model of the system with an unlimited number of users is considered. For data transmission in this model, unsourced random access is used. In case of successful transmission, multiple departure of users is carried out. For this system model, some hypotheses are formulated. Based on hypotheses, methods for constructing upper and ...
Added: October 27, 2022
Begishev V., Moltchanov D., Gaidamaka A. et al., Sensors 2022 Vol. 22 No. 3 Article 977
Unmanned aerial vehicles (UAV) are envisioned to become one of the new types of fifth/sixth generation (5G/6G) network users. To support advanced services for UAVs such as video monitoring, one of the prospective options is to utilize recently standardized New Radio (NR) technology operating in the millimeter-wave (mmWave) frequency band. However, blockage of propagation paths ...
Added: September 15, 2022
Chistopolskaia A., Podolskii V. V., Theory of Computing Systems 2022
In this paper we study decision tree models with various types of queries. For a given function it is usually not hard to determine the complexity in the standard decision tree model (each query evaluates a variable). However in more general settings showing tight lower bounds is substantially harder. Threshold functions often have non-trivial complexity ...
Added: September 13, 2022