Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 536982, 13 pages
http://dx.doi.org/10.1155/2012/536982
Research Article

Stochastic Approximations and Monotonicity of a Single Server Feedback Retrial Queue

1Laboratory of Modeling and Optimization of Systems, University of Béjaïa, Béjaïa 06000, Algeria
2Department of Mathematics, University of Annaba, Annaba 23000, Algeria

Received 30 October 2011; Accepted 16 January 2012

Academic Editor: M. D. S. Aliyu

Copyright © 2012 Mohamed Boualem 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. J. R. Artalejo, “Accessible bibliography on retrial queues: progress in 2000–2009,” Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1071–1081, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. J. R. Artalejo and A. Gómez-Corral, Retrial queueing system: A Computation Approach, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar
  3. G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman and Hall, London, UK, 1997.
  4. G. Ayyappan, A. Muthu Ganapathi Subramanian, and G. Sekar, “M/M/1 retrial queueing system with loss and feedback under non-pre-emptive priority service by matrix geometric method,” Applied Mathematical Sciences, vol. 4, no. 45–48, pp. 2379–2389, 2010. View at Google Scholar · View at Zentralblatt MATH
  5. 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
  6. D. Stoyan, Comparison Methods for Queues and Other Stochastic Models, John Wiley & Sons, Chichester, UK, 1983.
  7. M. Shaked and J. G. Shanthikumar, Stochastic Orders, Springer, New York, NY, USA, 2007. View at Publisher · View at Google Scholar
  8. M. Shaked and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, Boston, Mass, USA, 1994.
  9. N. Oukid and A. Aissani, “Bounds on busy period for queues with breakdowns,” Advances and Applications in Statistics, vol. 11, no. 2, pp. 137–156, 2009. View at Google Scholar · View at Zentralblatt MATH
  10. M. Boualem, N. Djellab, and D. Aïssani, “Stochastic inequalities for M/G/1 retrial queues with vacations and constant retrial policy,” Mathematical and Computer Modelling, vol. 50, no. 1-2, pp. 207–212, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. Taleb and A. Aissani, “Unreliable M/G/1 retrial queue: monotonicity and comparability,” Queueing Systems. Theory and Applications, vol. 64, no. 3, pp. 227–252, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. N. Djellab, “On the M/G/1 retrial queue with feedback,” in Proceedings of the International Conference on Mathematical Methods of Optimization of Telecommunication Networks, pp. 32–35, Minsk, Byelorussia, 2005.
  13. L. Takács, “A single-server queue with feedback,” The Bell System Technical Journal, vol. 42, pp. 505–519, 1963. View at Google Scholar
  14. B. Heidergott and F. J. Vázquez-Abad, “Measure-valued differentiation for Markov chains,” Journal of Optimization Theory and Applications, vol. 136, no. 2, pp. 187–209, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. B. Heidergott and F. J. Vázquez-Abad, “Measure-valued differentiation for random horizon problems,” Markov Processes and Related Fields, vol. 12, no. 3, pp. 509–536, 2006. View at Google Scholar · View at Zentralblatt MATH
  16. B. Heidergott, A. Hordijk, and H. Weisshaupt, “Measure-valued differentiation for stationary Markov chains,” Mathematics of Operations Research, vol. 31, no. 1, pp. 154–172, 2006. View at Publisher · View at Google Scholar