OSA's Digital Library

Journal of Optical Communications and Networking

Journal of Optical Communications and Networking

  • Editors: K. Bergman and V. Chan
  • Vol. 1, Iss. 6 — Nov. 1, 2009
  • pp: 530–542

Exact Analysis of Single-Wavelength Optical Buffers With Feedback Markov Fluid Queues

Huseyin Emre Kankaya and Nail Akar  »View Author Affiliations


Journal of Optical Communications and Networking, Vol. 1, Issue 6, pp. 530-542 (2009)
http://dx.doi.org/10.1364/JOCN.1.000530


View Full Text Article

Enhanced HTML    Acrobat PDF (305 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Optical buffering via fiber delay lines is used for contention resolution in optical packet and optical burst switching nodes. This article addresses the problem of exactly finding the blocking probabilities in an asynchronous single-wavelength optical buffer. Packet lengths are assumed to be variable and modeled by phase-type distributions, whereas the packet arrival process is modeled by a Markovian arrival process that can capture autocorrelations in interarrival times. The exact solution is based on the theory of feedback fluid queues for which we propose numerically efficient and stable algorithms. We not only find the packet blocking probabilities but also the entire distribution of the unfinished work in this system from which all performance measures of interest can be derived.

© 2009 Optical Society of America

OCIS Codes
(060.1155) Fiber optics and optical communications : All-optical networks
(060.4259) Fiber optics and optical communications : Networks, packet-switched

ToC Category:
Research Papers

History
Original Manuscript: June 10, 2009
Revised Manuscript: September 15, 2009
Manuscript Accepted: September 19, 2009
Published: October 15, 2009

Citation
Huseyin Emre Kankaya and Nail Akar, "Exact Analysis of Single-Wavelength Optical Buffers With Feedback Markov Fluid Queues," J. Opt. Commun. Netw. 1, 530-542 (2009)
http://www.opticsinfobase.org/jocn/abstract.cfm?URI=jocn-1-6-530


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Gambini, M. Renaud, C. Guillemot, F. Callegati, I. Andonovic, B. Bostica, D. Chiaroni, G. Corazza, S. L. Danielsen, P. Gravey, P. B. Hansen, M. Henry, C. Janz, A. Kloch, R. Krahenbuhl, C. Raffaelli, M. Schilling, A. Talneau, L. Zucchelli, “Transparent optical packet switching: network architecture and demonstrators in the KEOPS project,” IEEE J. Sel. Areas Commun., vol. 16, pp. 1245–1259, 1998. [CrossRef]
  2. C. Qiao, M. Yoo, “Optical burst switching (OBS)—a new paradigm for an optical Internet,” J. High Speed Networks (JHSN), vol. 8, no. 1, pp. 69–84, 1999.
  3. R. Barry, P. Humblet, “Models of blocking probability in all-optical networks with and without wavelength changers,” IEEE J. Sel. Areas Commun., vol. 14, no. 5, pp. 858–867, June 1996. [CrossRef]
  4. I. Chlamtac, A. Fumagalli, L. Kazovsky, P. Melman, W. Nelson, P. Poggiolini, M. Cerisola, A. Choudhury, T. Fong, R. Hofmeister, C.-L. Lu, A. Mekkittikul, D. J. M. Sabido, C.-J. Suh, E. Wong, “Cord: contention resolution by delay lines,” IEEE J. Sel. Areas Commun., vol. 14, no. 5, pp. 1014–1029, June 1996. [CrossRef]
  5. T. Zhang, K. Lu, J. Jue, “Shared fiber delay line buffers in asynchronous optical packet switches,” IEEE J. Sel. Areas Commun., vol. 24, no. 4, pp. 118–127, 2006. [CrossRef]
  6. F. Callegati, “Optical buffers for variable length packets,” IEEE Commun. Lett., vol. 4, no. 9, pp. 292–294, Sept. 2000. [CrossRef]
  7. R. C. Almeida, J. Pelegrini, H. Waldman, “A generic-traffic optical buffer modeling for asynchronous optical switching networks,” IEEE Commun. Lett., vol. 9, no. 2, pp. 175–177, Feb. 2005. [CrossRef]
  8. W. Rogiest, K. Laevens, D. Fiems, H. Bruneel, “A performance model for an asynchronous optical buffer,” Perform. Eval., vol. 62, no. 1–4, pp. 313–330, 2005. [CrossRef]
  9. W. Rogiest, J. Lambert, D. Fiems, B. V. Houdt, H. Bruneel, C. Blondia, “A unified model for synchronous and asynchronous FDL buffers allowing closed-form solution,” Perform. Eval., vol. 66, no. 7, pp. 343–355, 2009. [CrossRef]
  10. Z. Liang, S. Xiao, “Performance evaluation of single-wavelength fiber delay line buffer with finite waiting places,” J. Lightwave Technol., vol. 26, no. 5, pp. 520–527, Mar. 2008. [CrossRef]
  11. J. Liu, T. T. Lee, X. Jiang, S. Horiguchi, “Blocking and delay analysis of single wavelength optical buffer with general packet size distribution,” J. Lightwave Technol., vol. 27, no. 8, pp. 955–966, 2009. [CrossRef]
  12. M. Mandjes, D. Mitra, W. Scheinhardt, “Models of network access using feedback fluid queues,” Queueing Syst., vol. 44, no. 4, pp. 2989–3002, 2003. [CrossRef]
  13. H. E. Kankaya, N. Akar, “Solving multi-regime feedback fluid queues,” Stoch. Models, vol. 24, no. 3, pp. 425–450, July 2008. [CrossRef]
  14. M. F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications. New York: Marcel Dekker, 1989.
  15. D. M. Lucantoni, “New results for the single server queue with a batch Markovian arrival process,” Stoch. Models, vol. 7, pp. 1–46, 1991. [CrossRef]
  16. V. Paxson, S. Floyd, “Wide-area traffic: the failure of Poisson modeling,” IEEE/ACM Trans. Netw., vol. 3, pp. 226–244, 1995. [CrossRef]
  17. L. Muscariello, M. Mellia, M. Meo, R. L. Cigno, M. A. Marsan, “An MMPP-based hierarchical model of Internet traffic,” in 2004 IEEE Int. Conf. Communications, vol. 4, June 2004, pp. 2143–2147. [CrossRef]
  18. M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models. Baltimore, MD: Johns Hopkins U. Press, 1981.
  19. S. Asmussen, O. Nerman, M. Olsson, “Fitting phase-type distributions via the EM algorithm,” Scand. J. Stat., vol. 23, pp. 419–441, 1996.
  20. D. Anick, D. Mitra, M. M. Sondhi, “Stochastic theory of a data handling system with multiple sources,” Bell Syst. Tech. J., vol. 61, pp. 1871–1894, 1982. [CrossRef]
  21. R. Tucker, “Accurate method for analysis of a packet speech multiplexer with limited delay,” IEEE Trans. Commun., vol. 36, no. 4, pp. 479–483, 1988. [CrossRef]
  22. I. Adan, E. van Doorn, J. Resing, W. Scheinhardt, “Analysis of a single-server queue interacting with a fluid reservoir,” Queueing Syst., vol. 29, pp. 313–336, 1998. [CrossRef]
  23. W. Scheinhardt, “Markov modulated and feedback fluid queues,” Ph.D. dissertation, University of Twente, Enschede, The Netherlands, 1998.
  24. B. R. Haverkort, Performance of Computer and Communication Systems: A Model-based Approach. Wiley, 1998. [CrossRef]
  25. S. Kang, D. Sung, “Two-state MMPP modeling of ATM superposed traffic streams based on the characterization of correlated interarrival times,” in IEEE Global Telecommunications Conf., 1995. GLOBECOM ’95, vol. 2, Nov. 1995, pp. 1422–1426.
  26. G. H. Golub, C. F. van Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins U. Press, 1996.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited