RAS PresidiumДоклады Российской академии наук. Математика, информатика, процессы управления Doklady Mathematics

  • ISSN (Print) 2686-9543
  • ISSN (Online) 3034-5049

ON ONE APPROACH TO OBTAINING THE BOUNDARIES OF PERTURBATION OF HOMOGENEOUS MARKOV PROCESSES

PII
S2686954325030072-1
DOI
10.31857/S2686954325030072
Publication type
Article
Status
Published
Authors
Volume/ Edition
Volume 523 / Issue number 1
Pages
35-43
Abstract
Homogeneous Markov chains with continuous time are considered. A new approach is proposed that makes it possible to obtain accurate estimates of stability for such chains with relation to perturbations of infinitesimal characteristics. The application of the results to stationary queuing systems of several classes, as well as to some non-stationary systems, is considered.
Keywords
системы массового обслуживания оценки устойчивости прямая система Колмогорова процессы рождения и гибели
Date of publication
07.05.2025
Year of publication
2025
Number of purchasers
0
Views
13

References

  1. 1. Капашников В.В. Качественный анализ сложных систем методом пробных функций. М.: Наука. 1978.
  2. 2. Штюйян Д. Качественные свойства и оценки стохастических моделей. М.: Мир. 1979.
  3. 3. Золотарев В.М. Количественные оценки свойства непрерывности систем массового обслуживания типа G/G/∞ // Теория вероятностей и ее применения. 1977. Т. 22. С. 700–711.
  4. 4. Золотарев В.М. Вероятностные метрики // Теория вероятностей и ее применения. 1983. Т. 28. С. 264–287.
  5. 5. Zeifman A.I., Korolev V.Y. On perturbation bounds for continuous-time Markov chains // Stat. & Prob. Let. 2014. V. 88. P. 66–72.
  6. 6. Mitrophanov A.Y. Connection between the rate of convergence to stationarity and stability to perturbations for stochastic and deterministic systems // In Proceedings of the 38th International Conference Dynamics Days Europe. Loughborough. UK. 2018. P. 3–7.
  7. 7. Mitrophanov A.Y. The Arsenal of Perturbation Bounds for Finite Continuous-Time Markov Chains: A Perspective // Mathematics. 2024. V. 12.
  8. 8. Zeifman A., Korolev V., Satin Y. Two approaches to the construction of perturbation bounds for continuous-time Markov chains // Mathematics. 2020. V. 8. P. 253.
  9. 9. Zeifman A.I. Stability for continuous-time nonhomogeneous Markov chains // Lecture Notes in Mathematics. 1985. V. 1155. P. 401–414.
  10. 10. Zeifman A.I., Korotysheva A.V. Perturbation bounds for queue with catastrophes // Stochastic models. 2012. V. 28. P. 49–62.
  11. 11. Mitrophanov A.Y. Sensitivity and convergence of uniformly ergodic Markov chains // Journal of Applied Probability. 2005. V. 42. P. 1003–1014.
  12. 12. Далецкий Ю.Л., Крейп М.Г. Устойчивость решений дифференциальных уравнений в банаховом пространстве. М.: Наука, 1970.
  13. 13. Сапиш Я.А., Крюкова А.Л., Ощущкова В.С., Зейдман А.И. О монотонности некоторых классов марковских цепей // Информ. и ее примеч. 2022. Т. 16. № 2. 27–34.
  14. 14. Cho G.E., Meyer C.D. Comparison of perturbation bounds for the stationary distribution of a Markov chain // Linear Algebra and its Applications. 2001. V. 335. P. 137–150.
  15. 15. Yuanyuan Liu. Perturbation Bounds for the Stationary Distributions of Markov Chains // SIAM Journal on Matrix Analysis and Applications. 2012. V. 33. P. 1057–1074.
  16. 16. Gaudio J., Saurabh A., Patrick J. Exponential convergence rates for stochastically ordered Markov processes under perturbation // Systems & Control Letters. 2019. V. 133.
  17. 17. Wang T., Plechac P. Steady-state sensitivity analysis of continuous time Markov chains // SIAM Journal on Numerical Analysis. 2019. V. 57. P. 192–217.
  18. 18. YuanYuan Liu. Perturbation analysis for continuous-time Markov chains // Science China Mathematics. 2015. V. 58. P. 2633–2642.
  19. 19. Altman E., Avrachenkov K., Nunez-Queija R. Perturbation analysis for denumerable Markov chains with application to queueing models // Advances in Applied Probability. 2004. V. 36. P. 839–853.
  20. 20. Shao J. Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes // Journal of Applied Probability. First View. 2023. P. 1–18.
  21. 21. Seidphan A.H., Kopouee B.IO., Pazywчик P.B., Camun Я.A., Koeauee H.A. O предельных характеристиках для систем обслуживания с исчезающими возмущениями // Доклады Российской академии наук. Математика, информатика, процессы управления. 2022. Т. 506. № 1. С. 83–88.
  22. 22. Zeifman A., Usov I., Kryukova A., Satin Y., Shilova G. On the Approach to Obtaining Perturbation Bounds for a Class of Birth-Death Processes // 7th International Conference on Information. Control, and Communication Technologies (ICCT). 2023. P. 1–6.
  23. 23. Zeifman A., Satin Y., Kovalev I., Razumchik R., Korolev V. Facilitating Numerical Solutions of Inhomogeneous Continuous Time Markov Chains Using Ergodicity Bounds Obtained with Logarithmic Norm Method // Mathematics. 2021.
  24. 24. Marin A., Rossi S. A queueing model that works only on the biggest jobs // In European Workshop on Performance Engineering. 2019. P. 118–132.
  25. 25. Chen A., Wu X., Zhang J. Markovian bulk-arrival and bulk-service queues with general state-dependent control // Queueing Syst. 2020. P. 1–48.
  26. 26. Van Doorn E. A. Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process // Advances in Applied Probability. 1985. V. 17. P. 514–530.
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