Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 587163, 6 pages
http://dx.doi.org/10.1155/2013/587163
Research Article

On the Discrete-Time Queues under -Policy with Single and Multiple Vacations

1Department of Management Engineering, Sangmyung University, Cheonan 330-720, Republic of Korea
2Department of Industrial Engineering, Chonnam National University, Gwangju 500-757, Republic of Korea
3Department of Business Administration, Pai Chai University, Daejeon 302-735, Republic of Korea
4Department of Industrial and Systems Engineering, KAIST, Daejon 305-701, Republic of Korea
5Division of Business and Commerce, Baekseok University, Cheonan 330-704, Republic of Korea

Received 5 August 2013; Accepted 4 December 2013

Academic Editor: Alexander Timokha

Copyright © 2013 Sung J. Kim 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. B. T. Doshi, “Queueing systems with vacations-a survey,” Queueing Systems, vol. 1, no. 1, pp. 29–66, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. H. Takagi, Queueing Analysis, Vol. 1, North-Holland, Amsterdam, The Netherlands, 1991. View at MathSciNet
  3. H. Takagi, Queueing Analysis, Vol. 3, North-Holland, 1993.
  4. Z. G. Zhang and N. Tian, “Discrete time Geo/G/1 queue with multiple adaptive vacations,” Queueing Systems, vol. 38, no. 4, pp. 419–429, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Fiems and H. Bruneel, “Analysis of a discrete-time queueing system with timed vacations,” Queueing Systems, vol. 42, no. 3, pp. 243–254, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. S. Alfa, “Vacation models in discrete time,” Queueing Systems, vol. 44, no. 1, pp. 5–30, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. S. Lee, H. W. Lee, S. H. Yoon, and K. C. Chae, “Batch arrival queue with N-policy and single vacation,” Computers & Operations Research, vol. 22, pp. 173–189, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. W. Lee, S. S. Lee, J. O. Park, and K. C. Chae, “Analysis of the MX/G/1 queue with N-policy and multiple vacations,” Journal of Applied Probability, vol. 31, no. 2, pp. 476–496, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  9. G. Choudhury, “An MX/G/1 queueing system with a setup period and a vacation period,” Queueing Systems, vol. 36, no. 1–3, pp. 23–38, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-C. Ke, K.-B. Huang, and W. L. Pearn, “The randomized vacation policy for a batch arrival queue,” Applied Mathematical Modelling, vol. 34, no. 6, pp. 1524–1538, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T.-Y. Wang, “Random N-policy Geo/G/1 queue with startup and closedown times,” Journal of Applied Mathematics, vol. 2012, Article ID 793801, 19 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D.-E. Lim, D. H. Lee, W. S. Yang, and K.-C. Chae, “Analysis of the GI/Geo/1 queue with N-policy,” Applied Mathematical Modelling, vol. 37, no. 7, pp. 4643–4652, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J.-C. Ke, H.-I. Huang, and Y.-K. Chu, “Batch arrival queue with N-policy and at most J vacations,” Applied Mathematical Modelling, vol. 34, no. 2, pp. 451–466, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. B. Feyaerts, S. De Vuyst, H. Bruneel, and S. Wittevrongel, “The impact of the NT-policy on the behaviour of a discrete-time queue with general service times,” Journal of Industrial and Management Optimization, vol. 10, pp. 131–149, 2014. View at Google Scholar · View at Zentralblatt MATH
  15. N. Tian and Z. G. Zhang, Vacation Queueing Models, Springer, New York, NY, USA, 2006. View at MathSciNet
  16. D. E. Lim and T. S. Kim, “Modeling discovery and removal of security vulnerabilities in software system using priority queueing models,” submitted to Journal of Computer Virology and Hacking Techniques.
  17. J. J. Hunter, Mathematical Techniques of Applied Probability, Vol. 2, Operations Research and Industrial Engineering, Academic Press, New York, NY, USA, 1983. View at MathSciNet
  18. H. Bruneel and B. G. Kim, Discrete-Time Models for Communication System Including ATM, Kluwer Academic Publishers, 1993.
  19. R. W. Wolff, Stochastic Modeling and the Theory of Queues, Prentice Hall, Englewood Cliffs, NJ, USA, 1989. View at MathSciNet
  20. N. K. Kim, K. C. Chae, and M. L. Chaudhry, “An invariance relation and a unified method to derive stationary queue-length distributions,” Operations Research, vol. 52, no. 5, pp. 756–764, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet