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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 809460, 9 pages
Several Types of Convergence Rates of the M/G/1 Queueing System
1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
2School of Science, North China University of Technology, Beijing 100144, China
Received 25 October 2012; Accepted 31 December 2012
Academic Editor: Xiaochen Sun
Copyright © 2013 Xiaohua Li and Jungang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springe, London, UK; Beijing World Publishing Corporation, Beijing, China, 1999.
- P. Tuominen and R. L. Tweedie, “Subgeometric rates of convergence of -ergodic Markov chains,” Advances in Applied Probability, vol. 26, no. 3, pp. 775–798, 1994.
- D. Bakry, P. Cattiaux, and A. Guillin, “Rate of convergence for ergodic continuous Markov processes: lyapunov versus Poincaré,” Journal of Functional Analysis, vol. 254, no. 3, pp. 727–759, 2008.
- Z. Hou and Y. Liu, “Explicit criteria for several types of ergodicity of the embedded and queues,” Journal of Applied Probability, vol. 41, no. 3, pp. 778–790, 2004.
- Y. Y. Liu and Z. T. Hou, “Several types of ergodicity for -type Markov chains and Markov processes,” Journal of Applied Probability, vol. 43, no. 1, pp. 141–158, 2006.
- Z. T. Hou and X. H. Li, “Ergodicity of quasi-birth and death processes (I),” Acta Mathematica Sinica, vol. 23, no. 2, pp. 201–208, 2007.
- Z. T. Hou and X. H. Li, “Ergodicity of quasi-birth and death processes (II),” Chinese Annals of Mathematics A, vol. 26, no. 2, pp. 181–192, 2005.
- Q.-L. Li and Y. Q. Zhao, “Heavy-tailed asymptotics of stationary probability vectors of Markov chains of type,” Advances in Applied Probability, vol. 37, no. 2, pp. 482–509, 2005.
- Q.-L. Li and Y. Q. Zhao, “Light-tailed asymptotics of stationary probability vectors of Markov chains of type,” Advances in Applied Probability, vol. 37, no. 4, pp. 1075–1093, 2005.
- S. F. Jarner and G. O. Roberts, “Polynomial convergence rates of Markov chains,” The Annals of Applied Probability, vol. 12, no. 1, pp. 224–247, 2002.
- S. F. Jarner and R. L. Tweedie, “Necessary conditions for geometric and polynomial ergodicity of random-walk-type Markov chains,” Bernoulli, vol. 9, no. 4, pp. 559–578, 2003.
- R. Douc, G. Fort, E. Moulines, and P. Soulier, “Practical drift conditions for subgeometric rates of convergence,” The Annals of Applied Probability, vol. 14, no. 3, pp. 1353–1377, 2004.
- R. B. Lund and R. L. Tweedie, “Geometric convergence rates for stochastically ordered Markov chains,” Mathematics of Operations Research, vol. 21, no. 1, pp. 182–194, 1996.