Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 834731, 11 pages
http://dx.doi.org/10.1155/2013/834731
Research Article

A Discrete-Time Retrial Queue with Vacations and Two Types of Breakdowns

College of Science, North University of China, Taiyuan 030051, China

Received 12 July 2013; Revised 21 September 2013; Accepted 21 September 2013

Academic Editor: Ram N. Mohapatra

Copyright © 2013 Feng Zhang and Zhifeng Zhu. 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. T. Yang and J. G. C. Templeton, “A survey of retrial queues,” Queueing Systems. Theory and Applications, vol. 2, no. 3, pp. 201–233, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. Gómez-Corral, “A bibliographical guide to the analysis of retrial queues through matrix analytic techniques,” Annals of Operations Research, vol. 141, pp. 163–191, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. G. Falin, “A survey of retrial queues,” Queueing Systems. Theory and Applications, vol. 7, no. 2, pp. 127–167, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. Yang and H. Li, “On the steady-state queue size distribution of the discrete-time Geo /G/1 queue with repeated customers,” Queueing Systems. Theory and Applications, vol. 21, no. 1-2, pp. 199–215, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. I. Atencia and P. Moreno, “A discrete-time Geo/G/1 retrial queue with general retrial times,” Queueing Systems. Theory and Applications, vol. 48, no. 1-2, pp. 5–21, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. I. Atencia and P. Moreno, “A discrete-time Geo/G/1 retrial queue with server breakdowns,” 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. I. Atencia and P. Moreno, “A discrete-time Geo/G/1 retrial queue with the server subject to starting failures,” Annals of Operations Research, vol. 141, pp. 85–107, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. 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
  9. J. Wang and Q. Zhao, “Discrete-time Geo/G/1 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
  10. J. Wang, “On the single server retrial queue with priority subscribers and server breakdowns,” Journal of Systems Science & Complexity, vol. 21, no. 2, pp. 304–315, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. 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
  12. 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
  13. H. Li and T. Yang, “A single-server retrial queue with server vacations and a finite number of input sources,” European Journal of Operational Research, vol. 85, no. 1, pp. 149–160, 1995. View at Google Scholar · View at Scopus
  14. B. K. Kumar and D. Arivudainambi, “The M/G/1 retrial queue with Bernoulli schedules and general retrial times,” Computers & Mathematics with Applications, vol. 43, no. 1-2, pp. 15–30, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. B. K. Kumar, R. Rukmani, and V. Thangaraj, “An M/M/C retrial queueing system with Bernoulli vacations,” Journal of Systems Science and Systems Engineering, vol. 18, no. 2, pp. 222–242, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. G. Choudhury, “A two phase batch arrival retrial queueing system with Bernoulli vacation schedule,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1455–1466, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. R. Artalejo, “Analysis of an M/G/1 queue with constant repeated attempts and server vacations,” Computers & Operations Research, vol. 24, no. 6, pp. 493–504, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. F.-M. Chang and J.-C. Ke, “On a batch retrial model with J vacations,” Journal of Computational and Applied Mathematics, vol. 232, no. 2, pp. 402–414, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. J.-C. Ke and F.-M. Chang, “Modified vacation policy for M/G/1 retrial queue with balking and feedback,” Computers and Industrial Engineering, vol. 57, no. 1, pp. 433–443, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. J.-C. Ke and F.-M. Chang, “M[x]/G1,G2/1 retrial queue under Bernoulli vacation schedules with general repeated attempts and starting failures,” Applied Mathematical Modelling, vol. 33, no. 7, pp. 3186–3196, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Wu and X. Yin, “An M/G/1 retrial G-queue with non-exhaustive random vacations and an unreliable server,” Computers & Mathematics with Applications, vol. 62, no. 5, pp. 2314–2329, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. J. Wang, “Discrete-time Geo/G/1 retrial queues with general retrial time and Bernoulli vacation,” Journal of Systems Science & Complexity, vol. 25, no. 3, pp. 504–513, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. T. Li, Z. Wang, and Z. Liu, “Geo/Geo/1 retrial queue with working vacations and vacation interruption,” Journal of Applied Mathematics and Computing, vol. 39, no. 1-2, pp. 131–143, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  24. Z. Liu and Y. Song, “Geo/Geo/1 retrial queue with non-persistent customers and working vacations,” Journal of Applied Mathematics and Computing, vol. 42, no. 1-2, pp. 103–115, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  25. F. Zhang, D. Q. Yue, and Z. F. Zhu, “A discrete time Geo/G/1 retrial queue with second multi-optional service and server vacation,” ICIC Express Letters, vol. 6, pp. 1871–1876, 2012. View at Google Scholar