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Journal of Applied Mathematics
Volume 2013, Article ID 821684, 11 pages
http://dx.doi.org/10.1155/2013/821684
Research Article

A Novel Analytic Technique for the Service Station Reliability in a Discrete-Time Repairable Queue

1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
2School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China

Received 13 February 2013; Accepted 11 May 2013

Academic Editor: Zhijun Liu

Copyright © 2013 Renbin Liu and Yinghui Tang. 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.

Linked References

  1. J. Wang and Q. Zhao, “Discrete-time Geo/G/1 retrial queue with general retrial queue with general retrial times and starting failures,” Mathematical and Computer Modelling, vol. 45, no. 7-8, pp. 853–863, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. Wang and Q. Zhao, “A discrete-time Geo/G/1 retrial queue with starting failures and second optional service,” Computers & Mathematics with Applications, vol. 53, no. 1, pp. 115–127, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. I. Atencia, I. Fortes, and S. Sánchez, “A discrete-time retrial queueing system with starting failures, Bernoulli feedback and general retrial times,” Computers and Industrial Engineering, vol. 57, no. 4, pp. 1291–1299, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Wang and P. Zhang, “A discrete-time retrial queue with negative customers and unreliable server,” Computers and Industrial Engineering, vol. 56, no. 4, pp. 1216–1222, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. P. Moreno, “A discrete-time retrial queue with unreliable server and general server lifetime,” Journal of Mathematical Sciences, vol. 132, no. 5, pp. 643–655, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  6. I. Atencia and P. Moreno, “A discrete-time retrial queue with server breakdown,” Asia-Pacific Journal of Operational Research, vol. 23, no. 2, pp. 247–271, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z. M. Liu and S. Gao, “Reliability indices of a Geo/G/1/1 Erlang loss system with active breakdowns under Bernoulli schedule,” International Journal of Management Science and Engineering Management, vol. 5, no. 6, pp. 433–438, 2010. View at Google Scholar
  8. Y. H. Tang, M. M. Yu, and C. L. Li, “Geom/G1, G2/1/1 repairable Erlang loss system with catastrophe and second optional service,” Journal of Systems Science and Complexity, vol. 24, no. 3, pp. 554–564, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. H. B. Yu, “The discrete-time repairable queue MAP/geometric (geometric/PH)/1,” Hong Kong: Clobal-Link, pp. 1044–1050, 2000. View at Google Scholar
  10. H.-b. Yu, Z.-k. Nie, and J.-w. Yang, “The MAP/PH/(PH/PH)/1 discrete-time queuing system with repairable server,” Chinese Quarterly Journal of Mathematics, vol. 16, no. 2, pp. 59–63, 2001. View at Google Scholar · View at MathSciNet
  11. Y. H. Tang, X. Yun, and S. J. Huang, “Discrete-time GeoX/G/1 queue with unreliable server and multiple adaptive delayed vacations,” Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 439–455, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. H. Tang, M. M. Yu, X. Yun, and S. J. Huang, “Reliability indices of discrete-time GeoX/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations,” Journal of Systems Science and Complexity, vol. 25, no. 6, pp. 1122–1135, 2012. View at Google Scholar
  13. J. J. Hunter, Mathematical Techniques of Applied Probability, Vol. II, Discrete Time Models: Techniques and Applications, Academic Press, New York, NY, USA, 1983. View at MathSciNet
  14. N. S. Tian and Z. G. Zhang, Vacation Queueing Models-Theory and Applications, Springer, New York, NY, USA, 2006. View at MathSciNet
  15. S. W. Fuhrmann and R. B. Cooper, “Stochastic decompositions in the M/G/1 queue with generalized vacations,” Operations Research, vol. 33, no. 5, pp. 1117–1129, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. H. Cao and K. Cheng, Introduction to Reliability Mathematics, Higher Education Press, Beijing, China, 1986.
  17. J.-C. Ke, K.-B. Huang, and W. L. Pearn, “The performance measures and randomized optimization for an unreliable server M[x]/G/1 vacation system,” Applied Mathematics and Computation, vol. 217, no. 21, pp. 8277–8290, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Y. H. Tang and X. W. Tang, Queueing Theories—Foundations and Analysis Techniques, Science Press, Beijing, China, 2006.
  19. Z. Niu, Y. Takahashi, and N. Endo, “Performance evaluation of SVC-based IP-over-ATM networks,” IEICE Transactions on Communications, vol. E81-B, no. 5, pp. 948–955, 1998. View at Google Scholar · View at Scopus