Lord Kelvin and Andrey Andreyevich Markov in a queue with single server

Lord Kelvin and Andrey Andreyevich Markov in a queue with single server

Автор: Bobrowski A.

Журнал: Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp

Рубрика: Математическое моделирование

Статья в выпуске: 3 т.11, 2018 года.

Бесплатный доступ

We use Lord Kelvin's method of images to show that a certain infinite system of equations with interesting boundary conditions leads to a Markovian dynamics in an L1-type space. This system originates from the queuing theory.

Queue, method of images, generation theorem, boundary conditions, markovian dynamics

Короткий адрес: https://sciup.org/147232897

IDR: 147232897   |   DOI: 10.14529/mmp180303

Список литературы Lord Kelvin and Andrey Andreyevich Markov in a queue with single server

  • Engel K.-J., Nagel R. One-Parameter Semigroups for Linear Evolution Equations. N.Y., Springer, 2000.
  • Batkai A., Piazzera S. Semigroups for Delay Equations. Wellesley, CRC Press, 2005.
  • Siegle P., Goychuk I., Talkner P., Hänggi P. Markovian Embedding of Non-Markovian Superdiffusion. Physical Review, 2010, vol. 81, Article ID 011136, 10 p.
  • Durbin R., Eddy S., Krogh A., Mitchison G. Biological Sequence Analysis. Probabilistic Models of Proteins and Nucleic Acids. Cambridge, Cambridge University Press, 1998.
  • Hoek J., Elliott R.J. Introduction to Hidden Semi-Markov Models. Cambridge, Cambridge University Press, 2018.
  • Goldstein S. On Diffusion by Discontinuous Movements, and on the Telegraph Equation. The Quarterly Journal of Mechanics and Applied Mathematics, 1986, vol. 4, no. 2, pp. 129-156.
  • Kac M. Some Stochastic Problems in Physics and Mechanics. N.Y., Literary Licensing, 1956.
  • Kisynski J. On M. Kac's Probabilistic Formula for the Solutions of the Telegraphist's Equation. Annales Polonici Mathematici, 1974, vol. 29, pp. 259-272.
  • Ethier S.N., Kurtz, T.G. Markov Processes. Characterization and Convergence. N.Y., Wiley, 1986.
  • Pinsky M.A. Lectures on Random Evolutions. Singapore, World Scientific, 1991.
  • Asmussen S. Applied Probability and Queues. N.Y., Springer, 2003.
  • Cox D.R. The Analysis of Non-Markovian Stochastic Processes by the Inclusion of Supplementary Variables. Mathematical Proceedings of the Cambridge Philosophical Society, 1955, vol. 51, no. 3, pp. 433-441.
  • Gwizdz P. Application of Stochastic Semigroups to Queueing Models. Annales Mathematicae Silesianae, 2018 (to appear).
  • DOI: 10.2478/amsil-2018-0007
  • Davis M.H.A. Lectures on Stochastic Control and Nonlinear Filtering. N.Y., Springer, 1984.
  • Davis M.H.A. Piece-Wise Deterministic Markov Processes. Journal of the Royal Statistical Society, 1984, vol. 46, no. 3, pp. 353-388.
  • Davis M.H.A. Markov Processes and Optimization. London, Chapman and Hall, 1993.
  • Rudnicki R., Tyran-Kaminska M. Piecewise Deterministic Processes in Biological Models. N.Y., Springer, 2017.
  • Greiner G. Perturbing the Boundary Conditions of a Generator. Houston Journal of Mathematics, 1987, vol. 13, no. 2, pp. 213-229.
  • Bobrowski A. Generation of Cosine Families via Lord Kelvin's Method of Images. Journal of Evolution Equations, 2010, vol. 10, no. 3, pp. 663-675.
  • Bobrowski A. Lord Kelvin's Method of Images in the Semigroup Theory. Semigroup Forum, 2010, vol. 81, no. 3, pp. 435-445.
  • Bobrowski A. Families of Operators Describing Diffusion Through Permeable Membranes. Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, 2015, vol. 250, pp. 87-105.
  • Bobrowski A., Gregosiewicz A. A General Theorem on Generation of Moments-Preserving Cosine Families by Laplace Operators in C[0,1]. Semigroup Forum, 2014, vol. 88, no. 3, pp. 689-701.
  • Bobrowski A., Gregosiewicz A., Murat M. Functionals-Preserving Cosine Families Generated by Laplace Operators in C[0,1]. Discrete and Continuous Dynamical System, 2015, vol. 20, no. 7, pp. 1877-1895.
  • Bobrowski A., Mugnolo D. On Moments-Preserving Cosine Families and Semigroups in C[0,1]. Journal of Evolution Equations, 2013, vol. 13, no. 4, pp. 715-735.
  • Bobrowski A. From Diffusions on Graphs to Markov Chains via Asymptotic State Lumping. Annales Henri Poincare, 2012, vol. 13, no. 6, pp. 1501-1510.
  • Bobrowski A., Kazmierczak B., Kunze M. An Averaging Principle for Fast Diffusions in Domains Separated by Semi-Permeable Membranes. Mathematical Models and Methods in Applied Sciences, 2017, vol. 27, no. 4, pp. 663-706.
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