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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 326830, 17 pages
http://dx.doi.org/10.1155/2012/326830
Research Article

Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

Institute of Informatics, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Received 10 July 2012; Accepted 12 November 2012

Academic Editor: Joao B. R. Do Val

Copyright © 2012 Andrzej Chydzinski and Blazej Adamczyk. 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. http://www.internettrafficreport.com/.
  2. H. Takagi, Queueing Analysis—Finite Systems, vol. 2, North-Holland Publishing, Amsterdam, The Netherlands, 1993.
  3. N. K. Kim and K. C. Chae, “Transform-free analysis of the GI/G/1/K queue through the decomposed Little's formula,” Computers & Operations Research, vol. 30, no. 3, pp. 353–365, 2003. View at Publisher · View at Google Scholar
  4. D. R. Manfield and P. Tran-Gia, “Analysis of a finite storage system with batch input arising out of message packetization,” IEEE Transactions on Communications, vol. 30, no. 3, pp. 456–463, 1982. View at Scopus
  5. A. Chydzinski, R. Wojcicki, and G. Hryn, “On the number of losses in an MMPP queue,” in Next Generation Teletraffic and Wired/Wireless Advanced Networking, vol. 4712 of Lecture Notes in Computer Science, pp. 38–48, 2007.
  6. F. N. Gouweleeuw, “The loss probability in finite-buffer queues with batch arrivals and complete rejection,” Probability in the Engineering and Informational Sciences, vol. 8, pp. 221–227, 1994.
  7. H. C. Tijms, “Heuristics for finite-buffer queues,” Probability in the Engineering and Informational Sciences, vol. 6, no. 3, pp. 227–285, 1992.
  8. M. Bratiychuk and A. Chydzinski, “On the loss process in a batch arrival queue,” Applied Mathematical Modelling, vol. 33, no. 9, pp. 3565–3577, 2009. View at Publisher · View at Google Scholar
  9. A. Baiocchi and B. MElazzi, “Steady-state analysis of the MMPP/G/1/K queue,” IEEE Transactions on Communications, vol. 41, no. 4, pp. 531–534, 1993. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Nagarajan, J. F. Kurose, and D. Towsley, “Approximation techniques for computing packet loss in finite-buffered voice multiplexers,” IEEE Journal on Selected Areas in Communications, vol. 9, no. 3, pp. 368–377, 1991. View at Publisher · View at Google Scholar · View at Scopus
  11. N. B. Shroff and M. Schwartz, “Improved loss calculations at an ATM multiplexer,” IEEE/ACM Transactions on Networking, vol. 6, no. 4, pp. 411–421, 1998. View at Scopus
  12. A. N. Dudin, A. A. Shaban, and V. I. Klimenok, “Analysis of a queue in the BMAP/G/1/N system,” International Journal of Simulation, vol. 6, no. 1-2, pp. 13–23, 2005.
  13. D. M. Lucantoni, “New results on the single server queue with a batch Markovian arrival process,” Communications in Statistics, vol. 7, no. 1, pp. 1–46, 1991. View at Publisher · View at Google Scholar
  14. L. Breuer, “An EM algorithm for batch Markovian arrival processes and its comparison to a simpler estimation procedure,” Annals of Operations Research, vol. 112, pp. 123–138, 2002. View at Publisher · View at Google Scholar
  15. A. Klemm, C. Lindemann, and M. Lohmann, “Modeling IP traffic using the batch Markovian arrival process,” Performance Evaluation, vol. 54, no. 2, pp. 149–173, 2003. View at Publisher · View at Google Scholar · View at Scopus
  16. P. Salvador, A. Pacheco, and R. Valadas, “Modeling IP traffic: Joint characterization of packet arrivals and packet sizes using BMAPs,” Computer Networks, vol. 44, no. 3, pp. 335–352, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Chakravarthy, “The batch markovian arrival process: a review and future work,” in Advances in Probability and Stochastic Processes, A. Krishnamoorthy, et al., Ed., pp. 21–49, Notable Publications, Neshanic Station, NJ, USA, 2001.
  18. A. Chydzinski, “The oscillating queue with finite buffer,” Performance Evaluation, vol. 57, no. 3, pp. 341–355, 2004.
  19. A. Chydzinski, “Time to reach buffer capacity in a BMAP queue,” Stochastic Models, vol. 23, no. 2, pp. 195–209, 2007. View at Publisher · View at Google Scholar
  20. J. Abate, G. L. Choudhury, and W. Whitt, “An introduction to numerical transform inversion and its application to probability models,” in Computational Probability, W. Grassman, Ed., pp. 257–323, Kluwer, Boston, Mass, USA, 2000.
  21. http://www.omnetpp.org/.