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## Stability Analysis of Multi-Server Discrete-Time Queueing Systems with Interruptions and Regenerative Input Flow

Ch. 1. P. 13-26.

Tkachenko A., L.G. Afanasyeva

This paper is focused on a discrete-time multichannel queueing system with heterogeneous servers, regenerative input
ow and interruptions. The breakdowns of servers may occur at any time even if they are not occupied by customers. Consecutive moments of breakdowns are dened by a renewal process. We consider the preemptive repeat dierent service discipline. Exploiting coupling method the necessary and sucient stability condition for the system is established.

### In book

Athens: ISAST: International Society for the Advancement of Science and Technology, 2015

Tkachenko A., L.G. Afanasyeva, Theory of Probability and Its Applications 2019 Vol. 63 No. 4 P. 507-531

This paper is focused on the multichannel queueing system with heterogeneous servers, regenerative input flow, and a regenerative process of interruptions. Two service disciplines are studied: preemptive-repeat-different service discipline and preemptive resume service discipline. We consider discrete as well as continuous-time cases. We introduce an auxiliary service flow, which does not depend on the input ...

Added: March 3, 2020

Mikheev A. V., Известия Санкт-Петербургского государственного электротехнического университета ЛЭТИ 2013 № 10 С. 3-5

The question of local stability of cylindrical shells of medium length with elastic filling for three methods of fixing the edges: rigid fixing at both ends, rocker bearing - rigid fixing, rocker bearing at both ends is considered. The dependence of critical load parameter on the stiffness parameter for three types of boundary conditions in ...

Added: January 3, 2014

Mikheev A. V., Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия 2007 № 2 С. 128-133

In this work we consider the task of stability of shallow orthotropic shell on elastic base. The dependence of critical load parameter on constants of shell’s elasticity and rigidity of base is considered. As example we analyse the case of spherical shell made of unidirectional glass-fiber material. ...

Added: January 31, 2013

Grishunina S., , in: IX Moscow International Conference on Operations Research (ORM2018) Moscow, October 22–27, 2018. .: [б.и.], 2018.. P. 333-337.

We study stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one. We consider two models: the system where service time is the same on all occupied servers and equals a constant b and the system where service times ...

Added: December 9, 2018

Shalimova E., Burov A. A., Technische Mechanik 2017 Vol. 37 No. 2-5 P. 129-138

Dynamics of a massive point on a rotating wire or surface under dry friction force action is considered. Existence, stability and bifurcations of non-isolated relative equilibria sets of the point located - on a sphere uniformly rotating about an inclined fixed axis; - on a thin circular hoop rotating about an inclined fixed axis; - ...

Added: December 7, 2017

Bratersky M., С.В. Голунов, А.Л. Зеличенко et al., М.: МГИМО-Университет, 2009

В сборнике представлены доклады и выступления, сделанные на секции «Будущее стабильности и безопасности в регионе Центральной Азии, проведенной в рамках V Конвента Российской ассоциации международных исследований (РАМИ) «Мировая политика: взгляд из будущего» (МГИМО (У) МИД России, сентябрь 2008 г.) ...

Added: February 10, 2013

Pardalos P. M., Rassias T. undefined., Springer, 2014

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional ...

Added: May 30, 2014

Zlotnik A.A., Lomonosov T.A., Computational Mathematics and Mathematical Physics 2019 Vol. 59 No. 3 P. 452-464

Explicit two-level in time and symmetric in space finite-difference schemes constructed by approximating the 1D barotropic quasi-gas-/quasi-hydrodynamic systems of equations are studied. The schemes are linearized about a constant solution with a nonzero velocity, and, for them, necessary and sufficient conditions for the L2-dissipativity of solutions to the Cauchy problem are derived depending on the Mach number. These conditions ...

Added: March 11, 2019

Zotov M., Качество. Инновации. Образование 2014 № 10 С. 42-45

The article focuses attention on the problems related to practical application of classic Michailov and Nyquist frequency-domain stability criteria and offers the ways to modify them to eliminate the issues. The examples are provided. ...

Added: March 20, 2015

Andrey Alexandrovich Altukhov, Zakharchenko K. V., Kolyubin V. et al., Journal of Physics: Conference Series 2016 Vol. 675 No. 4 P. 042027

The article describes the device for selective registration of electrons, protons and heavy ions fluxes from the solar and galactic cosmic rays in the twelve energy ranges, built on a base of diamond detector. The use of the diamond detectors allowed for the creation a device for registration of cosmic particles fluxes at the external ...

Added: June 22, 2016

Buzmakov A. V., Kuznetsov S., Amedeo Napoli, , in: 2017 IEEE 17th International Conference on Data Mining (ICDM). .: New Orleans: IEEE, 2017.. Ch. 89. P. 757-762.

A scalable method for mining graph patterns stable under subsampling is proposed.
The existing subsample stability and robustness measures are not antimonotonic according to definitions known so far.
We study a broader notion of antimonotonicity for graph patterns, so that measures of subsample stability become antimonotonic. Then we propose gSOFIA for mining the most subsample-stable graph patterns.
The ...

Added: September 26, 2017

Zlotnik A., Applied Mathematics Letters 2019 Vol. 92 P. 115-120

We deal with an explicit finite-difference scheme with a regularization for the 1D gas dynamics equations linearized at the constant solution. The sufficient condition on the Courant number for the $L^2$-dissipativity of the scheme is derived in the case of the Cauchy problem and a non-uniform spatial mesh. The energy-type technique is developed to this end, and ...

Added: January 20, 2019

Zlotnik A.A., Lomonosov T.A., Doklady Mathematics, Germany, Springer 2020 Vol. 101 No. 3 P. 198-204

We study an explicit two-level symmetric in space finite-difference scheme for the multi-dimensional barotropic gas dynamics system of equations with quasi-gasdynamic regularization linearized at a constant solution (with an arbitrary velocity). A criterion and both necessary and sufficient conditions for the $L^2$-dissipativity of the solutions to the Cauchy problem for the scheme are derived by the ...

Added: September 13, 2020

Zlotnik A., Zlotnik I. A., Доклады Академии наук 2012 Vol. 86 No. 3 P. 750-755

We consider the time-dependent 1D Schrödinger equation on the half-axis with variable coefficients becoming constant for large x. We study a two-level symmetric in time (i.e. the Crank-Nicolson) and any order finite element in space numerical method to solve it. The method is coupled to an approximate transparent boundary condition (TBC). We prove uniform in ...

Added: October 4, 2012

Mikheev A. V., В кн.: Материалы Международного молодежного научного форума "Ломоносов-2010". .: М.: МАКС Пресс, 2010.. С. 8-15.

Рассматривается задача локальной потери устойчивости тонкостенной круговой цилиндрической оболочки на упругом основании под действием комбинированного нагружения, состоящего из внешнего давления и осевого сжатия. При моделировании деформаций оболочки за основу взята классическая модель Кирхгофа – Лява. Для решения поставленной задачи применяется метод малых вариаций исследуемого напряженно - деформированного состояния в линейной постановке. Получена зависимость формы по ...

Added: February 4, 2013

М.: Издательство математико-механического факультета МГУ, 2009

В настоящий сборник вошли аннотации докладов участников XVI международной конференции «Ломоносов» по секции «Математика и механика». ...

Added: February 4, 2013

Bernard Ducomet, Zlotnik A., Zlotnik I. A., The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip / Cornell University. Series math "arxiv.org". 2013. No. arxiv: 1303.3471.

We consider an initial-boundary value problem for a generalized 2D time-dependent Schrödinger equation on a semi-infinite strip. For the Crank-Nicolson finite-difference scheme with approximate or discrete transparent boundary conditions (TBCs), the Strang-type splitting with respect to the potential is applied. For the resulting method, the uniform in time L2-stability is proved. Due to the ...

Added: March 16, 2013

Khasyanova S. Y., Проблемы управления 2017 № 4 С. 37-44

This research is devoted to the investigation of the changes in the nature of the largest Russian banks policies regarding the control of risks and capital adequacy caused by the implementation of the new international business standards. The dynamic analysis of indicators used by banks internally for the capital adequacy assessment was performed within this ...

Added: November 27, 2017

Boris Vexler, Zlotnik A., Philip Trautmann, Comptes Rendus Mathematique 2018 Vol. 356 No. 5 P. 523-531

The paper deals with the optimal control problems governed by the 1D wave equation with variable coefficients and the control spaces of either measure-valued functions or vector measures. Bilinear finite element discretizations are constructed and their stability and error analysis is accomplished. ...

Added: April 8, 2017

Povetkina N., Международное публичное и частное право 2018 № 1 С. 21-25

The article is devoted to the international legal understanding of the financial aspect of the Concept of sustainable development of states. The characteristic features of the Concept of Sustainable Development are given, the role and significance of the financial stability of states are determined in order to ensure the sovereignty of national entities and their ...

Added: November 9, 2020

IEEE, 2022

2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference) (STAB) is organized by V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
The conference is supported by
• Russian Academy of Sciences, Branch of Power Engineering, Mechanics, Machine-Building, and Control Sciences
Technical co-sponsoring
IEEE (Russia section)
Topics of the conference
General problems of stability and stabilization
Nonlinear oscillations: ...

Added: September 13, 2022

Mishchenko A. V., Логистика и управление цепями поставок 2010 № 6(41) С. 39-51

Models enabling to assess stability of solutions connected with the choice of the optimal production plan are presented in the article. The optimal production plan ensures the maximum profit for the company under input restraints. At the same time in the standard model supplementary variable is added which reflects inflation rate in the economy. Within ...

Added: October 26, 2012

Pardalos P. M., Rassias T. undefined., Springer, 2014

This volume consists of chapters written by eminent scientists and engineers from the international community and presents significant advances in several theories, and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, and Discrete Mathematics and Geometry, as well as several ...

Added: May 30, 2014

Zlotnik Alexander, On Error Estimates of the Crank-Nicolson-Polylinear Finite Element Method with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped / Cornell University. Series math "arxiv.org". 2015.

We deal with an initial-boundary value problem for the generalized time-dependent Schr\"odinger equation with variable coefficients in an unbounded $n$--dimensional parallelepiped ($n\geq 1$). To solve it, the Crank-Nicolson in time and the polylinear finite element in space method with the discrete transpa\-rent boundary conditions is considered. We present its stability properties and derive new error ...

Added: March 27, 2015