Photonic Network Communications

, Volume 21, Issue 1, pp 64–77 | Cite as

The effect of partial conversion and fiber delay lines in an OBS switch with a large number of wavelengths

  • Juan F. Pérez
  • Benny Van Houdt


In this paper, we analyze an optical burst switching (OBS) switch endowed with both wavelength converters (WCs) and fiber delay lines (FDLs) to resolve contention. We consider the case where the number of wavelengths is large by introducing a mean field model that provides exact results when the number of wavelengths tends to infinity. We have confirmed through simulations that the mean field model provides accurate approximations for switches with a large but finite number of wavelengths, which are of interest in view of wavelength division multiplexing (WDM). Furthermore, our model allows a very general behavior for the arrival process and the packet size distribution, as well as two different wavelength allocation policies: minimum horizon and minimum gap. Our results include a detailed analysis of the effect that these parameters have on the burst loss rate, and on the minimum number of WCs required to attain a zero loss rate as the number of wavelengths becomes large. We have found that at high loads there is little value in adding FDLs and, if included, shorter granularities result in fewer WCs required to achieve a zero loss rate. The inclusion of FDLs becomes more significant under mid loads and bursty traffic, where the addition of several FDLs may reduce the conversion requirements. Also, increasing the number of WCs under the minimum horizon policy may worsen the loss rate, while this is never the case for the minimum gap policy.


Optical switch Partial wavelength conversion Mean field 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akar N., Karasan E., Dogan K.: Wavelength converter sharing in asynchronous optical packet/burst switching: an exact blocking analysis for markovian arrivals. IEEE J. Select. Areas Commun. 24, 69–80 (2006)CrossRefGoogle Scholar
  2. 2.
    Akar N., Karasan E., Rafaelli C.: Fixed point analysis of limited range share per node wavelength conversion in asynchronous optical packet switching systems. Photon. Netw. Commun. 18, 255–263 (2009)CrossRefGoogle Scholar
  3. 3.
    Callegati F.: Approximate modeling of optical buffers for variable length packets. Photon. Netw. Commun. 3, 383–390 (2001)CrossRefGoogle Scholar
  4. 4.
    Callegati F., Cerroni W., Corazza G., Develder C., Pickavet M., Demeester P.: Scheduling algorithms for a slotted packet switch with either fixed or variable lengths packets. Photon. Netw. Commun. 8, 163–176 (2004)CrossRefGoogle Scholar
  5. 5.
    Callegati F., Cerroni W., Rafaelli C., Zaffoni P.: Wavelength and time domain exploitation for QoS management in optical packet switches. Comput. Netw. 44, 569–582 (2004)CrossRefGoogle Scholar
  6. 6.
    Dogan K., Gunulay Y., Akar N.: A comparative study of limited range wavelength conversion policies for asynchronous optical packet switching. J. Opt. Netw. 6, 134–145 (2007)CrossRefGoogle Scholar
  7. 7.
    Gauger C.M.: Optimized combination of converter pools and FDL buffers for contention resolution in optical burst switching. Photon. Netw. Commun. 8, 139–148 (2004)CrossRefGoogle Scholar
  8. 8.
    Latouche G., Ramaswami V.: Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM Series on Statistics and Applied Probability. SIAM, Philadelphia, PA (1999)Google Scholar
  9. 9.
    Laevens K., Moeneclaey M., Bruneel H.: Queueing analysis of a single-wavelength fiber-delay-line buffer. Telecommun. Syst. 31, 259–287 (2006)CrossRefGoogle Scholar
  10. 10.
    Lambert J., Van Houdt B., Blondia C.: Queues with correlated inter-arrival and service times and its application to optical buffers. Stoch. Models 22(2), 233–251 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Le Boudec, J., McDonald, D., Mundinger, J.: A generic mean field convergence result for systems of interacting objects. In: Proceedings of the 4th International Conference on the Quantitative Evaluation of SysTems (QEST 2007), pp. 3–15. Edinburgh, UK (2007)Google Scholar
  12. 12.
    Michiel, H., Laevens, K.: Teletraffic engineering in a broad-band era. In: Proceedings of the IEEE, vol. 85, pp. 2007–2033 (1997)Google Scholar
  13. 13.
    Pérez, J.F., Van Houdt, B.: Dimensioning an OBS switch with partial wavelength conversion and fiber delay lines via a mean field model. In: Proceedings of the IEEE Infocom 2009, Rio de Janeiro, Brazil, pp. 2651–2655 (2009)Google Scholar
  14. 14.
    Pérez J.F., Van Houdt B.: Wavelength allocation in an optical switch with a fiber delay line buffer and limited-range wavelength conversion. Telecommun. Syst. 41(1), 37–49 (2009)CrossRefGoogle Scholar
  15. 15.
    Puttasubbapa V., Perros H.: Performance analysis of limited-range wavelength conversion in an OBS switch. Telecommun. Syst. 31, 227–246 (2006)CrossRefGoogle Scholar
  16. 16.
    Qiao J., Yoo M.: Optical burst switching: A new paradigm for an optical Internet. J. High-Speed Netw. 8, 69–84 (1999)Google Scholar
  17. 17.
    Robertazzi T.: Computer Networks and Systems. Springer, Berlin (2000)Google Scholar
  18. 18.
    Turner J.: Terabit burst switching. J. High-Speed Netw. 8, 3–16 (1999)Google Scholar
  19. 19.
    Van Houdt, B., Laevens, K., Lambert, J., Blondia, C., Bruneel, H.: Channel utilization and loss rate in a single-wavelength Fibre Delay Line (FDL) buffer. In: Proceedings of IEEE Globecom 2004, vol. 3, pp. 1900–1906 (2004)Google Scholar
  20. 20.
    Xu, L., Perros, H., Rouskas, G.N.: A queueing network model of an edge optical burst switching node. In: Proceedings of the IEEE Infocom 2003, pp. 2019–2029 (2003)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Performance Analysis of Telecommunication Systems (PATS), Department of Mathematics and Computer ScienceUniversity of Antwerp-IBBTAntwerpBelgium

Personalised recommendations