Have a personal or library account? Click to login
Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services Cover

Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

Open Access
|Mar 2018

References

  1. Almasi, B., Roszik, J. and Sztrik, J. (2005). Homogeneous finite-source retrial queues with server subject to breakdowns and repairs, Mathematical and Computer Modelling 42(5): 673-682.10.1016/j.mcm.2004.02.046
  2. Chen, A., Pollett, P., Li, J. and Zhang, H. (2010). Markovian bulk-arrival and bulk-service queues with state-dependent control, Queueing Systems 64(3): 267-304.10.1007/s11134-009-9162-5
  3. Daleckij, J. and Krein,M. (1974). Stability of Solutions of Differential Equations in Banach Space, American Mathematical Society, Providence, RI.
  4. Doorn, E.V., Zeifman, A. and Panfilova, T. (2010). Bounds and asymptotics for the rate of convergence of birth-death processes, Theory of Probability and Its Applications 54(1): 97-113.10.1137/S0040585X97984097
  5. Granovsky, B. and Zeifman, A. (2000). The n-limit of spectral gap of a class of birthdeath Markov chains, Applied Stochastic Models in Business and Industry 16(4): 235-248.10.1002/1526-4025(200010/12)16:4<;235::AID-ASMB415>3.0.CO;2-S
  6. Granovsky, B. and Zeifman, A. (2004). Nonstationary queues: Estimation of the rate of convergence, Queueing Systems 46(3-4): 363-388.10.1023/B:QUES.0000027991.19758.b4
  7. Gudkova, I., Korotysheva, A., Zeifman, A., Shilova, G., Korolev, V., Shorgin, S. and Razumchik, R. (2016). Modeling and analyzing licensed shared access operation for 5g network as an inhomogeneous queue with catastrophes, 2016 8th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Lisbon, Portugal, pp. 282-287.10.1109/ICUMT.2016.7765372
  8. Kamiński, M. (2015). Symbolic computing in probabilistic and stochastic analysis, International Journal of Applied Mathematics and Computer Science 25(4): 961-973, DOI: 10.1515/amcs-2015-0069.10.1515/amcs-2015-0069
  9. Kartashov, N. (1985). Criteria for uniform ergodicity and strong stability of Markov chains with a common phase space, Theory of Probability and Mathematical Statistics 30(30): 71-89.
  10. Kartashov, N. (1996). Strong Stable Markov Chains, VSP, Utrecht. Kim, C., Dudin, A., Dudin, S. and Dudina, O. (2014). Analysis of an MMAP/PH1, PH2/N/∞ queueing system operating in a random environment, International Journal of Applied Mathematics and Computer Science 24(3): 485-501, DOI: 10.2478/amcs-2014-0036.10.2478/amcs-2014-0036
  11. Li, J. and Zhang, L. (2016). Decay property of stopped Markovian bulk-arriving queues with c-servers, Stochastic Models 32(4): 674-686.10.1080/15326349.2016.1196374
  12. Mitrophanov, A. (2003). Stability and exponential convergence of continuous-time Markov chains, Journal of Applied Probability 40(4): 970-979.10.1239/jap/1067436094
  13. Mitrophanov, A. (2004). The spectral GAP and perturbation bounds for reversible continuous-time Markov chains, Journal of Applied Probability 41(4): 1219-1222.10.1239/jap/1101840568
  14. Mitrophanov, A. (2005a). Ergodicity coefficient and perturbation bounds for continuous-time Markov chains, Mathematical Inequalities & Applications 8(1): 159-168.10.7153/mia-08-15
  15. Mitrophanov, A. (2005b). Sensitivity and convergence of uniformly ergodic Markov chains, Journal of Applied Probability 42(4): 1003-1014.10.1239/jap/1134587812
  16. Moiseev, A. and Nazarov, A. (2016a). Queueing network MAP − (GI/∞)K with high-rate arrivals, European Journal of Operational Research 254(1): 161-168.10.1016/j.ejor.2016.04.011
  17. Moiseev, A. and Nazarov, A. (2016b). Tandem of infinite-server queues with Markovian arrival process, Distributed Computer and Communication Networks: 18th International Conference, DCCN 2015, Moscow, Russia, pp. 323-333.10.1007/978-3-319-30843-2_34
  18. Nelson, R., Towsley, D. and Tantawi, A. (1987). Performance analysis of parallel processing systems, ACM SIGMETRICS Performance Evaluation Review 15(1): 93-94.10.1145/29904.29916
  19. Satin, Y., Zeifman, A. and Korotysheva, A. (2013). On the rate of convergence and truncations for a class of Markovian queueing systems, Theory of Probability&Its Applications 57(3): 529-539.10.1137/S0040585X97986151
  20. Schwarz, J., Selinka, G. and Stolletz, R. (2016). Performance analysis of time-dependent queueing systems: Survey and classification, Omega 63: 170-189.10.1016/j.omega.2015.10.013
  21. Whitt, W. (1991). The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increase, Management Science 37(3): 307-314.10.1287/mnsc.37.3.307
  22. Whitt, W. (2015). Stabilizing performance in a single-server queue with time-varying arrival rate, Queueing Systems 81(4): 341-378.10.1007/s11134-015-9462-x
  23. Zeifman, A. (1995a). On the estimation of probabilities for birth and death processes, Journal of Applied Probability 32(3): 623-634.10.2307/3215117
  24. Zeifman, A. (1995b). Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes, Stochastic Processes and Their Applications 59(1): 157-173.10.1016/0304-4149(95)00028-6
  25. Zeifman, A. and Korolev, V. (2014). On perturbation bounds for continuous-time Markov chains, Statistics & Probability Letters 88: 66-72.10.1016/j.spl.2014.01.031
  26. Zeifman, A. and Korolev, V. (2015). Two-sided bounds on the rate of convergence for continuous-time finite inhomogeneous Markov chains, Statistics & Probability Letters 103: 30-36.10.1016/j.spl.2015.04.013
  27. Zeifman, A., Korolev, V., Satin, Y., Korotysheva, A. and Bening, V. (2014a). Perturbation bounds and truncations for a class of Markovian queues, Queueing Systems 76(2): 205-221.10.1007/s11134-013-9388-0
  28. Zeifman, A., Korotysheva, A., Korolev, V. and Satin, Y. (2016a). Truncation bounds for approximations of inhomogeneous continuous-time Markov chains, Probability Theory and Its Applications 61(3): 563-569, (in Russian).10.1137/S0040585X97T988320
  29. Zeifman, A., Korotysheva, A., Satin, Y., Shilova, G., Razumchik, R., Korolev, V. and Shorgin, S. (2016b). Uniform in time bounds for “no-wait” probability in queues of Mt/Mt/S type, Proceedings of the 30th European Conference on Modelling and Simulation, ECMS 2016, Regensburg, Germany, pp. 676-684.10.7148/2016-0676
  30. Zeifman, A., Leorato, S., Orsingher, E., Satin, Y. and Shilova, G. (2006). Some universal limits for nonhomogeneous birth and death processes, Queueing Systems 52(2): 139-151.10.1007/s11134-006-4353-9
  31. Zeifman, A., Satin, Y., Korolev, V. and Shorgin, S. (2014b). n truncations for weakly ergodic inhomogeneous birth and death processes, International Journal of Applied Mathematics and Computer Science 24(3): 503-518, DOI: 10.2478/amcs-2014-0037.10.2478/amcs-2014-0037
  32. Zeifman, A., Satin, Y. and Panfilova, T. (2013). Limiting characteristics for finite birthdeath-catastrophe processes, Mathematical Biosciences 245(1): 96-102.10.1016/j.mbs.2013.02.00923458510
DOI: https://doi.org/10.2478/amcs-2018-0011 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 141 - 154
Submitted on: Apr 24, 2017
Accepted on: Aug 9, 2017
Published on: Mar 31, 2018
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2018 Alexander Zeifman, Rostislav Razumchik, Yacov Satin, Ksenia Kiseleva, Anna Korotysheva, Victor Korolev, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.