Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 587269, 10 pages
http://dx.doi.org/10.1155/2013/587269
Research Article

The Discrete-Time Bulk-Service Geo/Geo/1 Queue with Multiple Working Vacations

1School of Mathematics & Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China
2College of Computer Science and Technology, Southwest University for Nationalities, Chengdu, Sichuan 610041, China
3School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China

Received 3 July 2012; Accepted 14 December 2012

Academic Editor: Alvaro Valencia

Copyright © 2013 Jiang Cheng et al. 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. L. D. Servi and S. G. Finn, “M/M/1 queues with working vacations (M/M/1/WV),” Performance Evaluation, vol. 50, no. 1, pp. 41–52, 2002. View at Publisher · View at Google Scholar · View at Scopus
  2. D. A. Wu and H. Takagi, “M/G/1 queue with multiple working vacations,” Performance Evaluation, vol. 63, no. 7, pp. 654–681, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. Baba, “Analysis of a GI/M/1 queue with multiple working vacations,” Operations Research Letters, vol. 33, no. 2, pp. 201–209, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Li and N. Tian, “Analysis of the discrete time Geo/Geo/1 queue with single working vacation,” Quality Technology & Quantitative Management, vol. 5, pp. 77–89, 2008. View at Google Scholar
  5. N. Tian, Z. Ma, and M. Liu, “The discrete time Geo/Geo/1 queue with multiple working vacations,” Applied Mathematical Modelling, vol. 32, no. 12, pp. 2941–2953, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. K. C. Chae, D. E. Lim, and W. S. Yang, “The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation,” Performance Evaluation, vol. 66, no. 7, pp. 356–367, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. J. H. Li, N. S. Tian, and W. Y. Liu, “Discrete-time GI/Geo/1 queue with multiple working vacations,” Queueing Systems, vol. 56, no. 1, pp. 53–63, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. J. H. Li and N. S. Tian, “The discrete-time GI/Geo/1 queue with working vacations and vacation interruption,” Applied Mathematics and Computation, vol. 185, no. 1, pp. 1–10, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. V. Goswami and G. B. Mund, “Analysis of a discrete-time GI/Geo/1/N queue with multiple working vacations,” Journal of Systems Science and Systems Engineering, vol. 19, no. 3, pp. 367–384, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. U. C. Gupta and V. Goswami, “Performance analysis of finite buffer discrete-time queue with bulk service,” Computers and Operations Research, vol. 29, no. 10, pp. 1331–1341, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. M. L. Chaudhry and S. H. Chang, “Analysis of the discrete-time bulk-service queue Geo/GY/1/N+B,” Operations Research Letters, vol. 32, no. 4, pp. 355–363, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. A. S. Alfa and Q. M. He, “Algorithmic analysis of the discrete time GIX/GY/1 queueing system,” Performance Evaluation, vol. 65, no. 9, pp. 623–640, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. X. W. Yi, N. K. Kim, B. K. Yoon, and K. C. Chae, “Analysis of the queue-length distribution for the discrete-time batch-service Geo/GY/1/N+B queue,” European Journal of Operational Research, vol. 181, no. 2, pp. 787–792, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Banerjee, K. Sikdar, and U. C. Gupta, “Computing system length distribution of a finite-buffer bulk-arrival bulk-service queue with variable server capacity,” International Journal of Operational Research, vol. 12, no. 3, pp. 294–317, 2011. View at Publisher · View at Google Scholar
  15. A. Banerjee and U. C. Gupta, “Reducing congestion in bulk service queueing system using batch dependent service,” Performance Evaluation, vol. 69, pp. 53–70, 2012. View at Google Scholar
  16. D. Claeys, J. Walraevens, K. Laevens, and H. Bruneel, “Analysis of threshold-based batch-service queueing systems with batch arrivals and general service times,” Performance Evaluation, vol. 68, no. 6, pp. 528–549, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Claeys, B. Steyaert, J. Walraevens, K. Laevens, and H. Bruneel, “Tail distribution of the delay in a general batch-service queueing model,” Computers and Operations Research, vol. 39, no. 11, pp. 2733–2741, 2012. View at Publisher · View at Google Scholar
  18. B. D. Choi and D. H. Han, “GI/M(a,b)/1 queues with server vacations,” Journal of Operations Research Society of Japan, vol. 37, pp. 171–181, 1994. View at Google Scholar
  19. S. H. Chang and T. Takine, “Factorization and stochastic decomposition properties in bulk queues with generalized vacations,” Queueing Systems, vol. 50, no. 2-3, pp. 165–183, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. K. Sikdar and U. C. Gupta, “Analytic and numerical aspects of batch service queues with single vacation,” Computers and Operations Research, vol. 32, no. 4, pp. 943–966, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. M. M. Yu, Y. H. Tang, and Y. H. Fu, “Steady state analysis and computation of the GI[x]/Mb/1/L queue with multiple working vacations and partial batch rejection,” Computers and Industrial Engineering, vol. 56, no. 4, pp. 1243–1253, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Vijaya Laxmi and O. M. Yesuf, “Renewal input infinite buffer batch service queue with single exponential working vacation and accessibility to batches,” International Journal of Mathematics in Operational Research, vol. 3, no. 2, pp. 219–243, 2011. View at Publisher · View at Google Scholar
  23. V. Goswami and G. B. Mund, “Analysis of discrete-time batch service renewal input queue with multiple working vacations,” Computers and Industrial Engineering, vol. 61, no. 3, pp. 629–636, 2011. View at Publisher · View at Google Scholar
  24. M. R. Spiegel, Schaum's Outline of Theory and Problems of Calculus of Finite Differences and Difference Equations, McGraw-Hill, New York, NY, USA, 1971.
  25. J. J. Hunter, “Mathematical techniques of applied probability,” in Discrete-Time Models: Techniques and Applications, vol. 2, Academic Press, New York, NY, USA, 1983. View at Google Scholar
  26. N. S. Tian and Z. Y. Ma, Discrete Time Queue Theory, Science Press, Beijing, China, 2007.