Photonic Network Communications

, Volume 14, Issue 2, pp 177–181 | Cite as

Analytical calculation of blocking probabilities in WDM rings with the first-fit algorithm

  • Divanilson R. Campelo
  • Raul C. AlmeidaJr
  • Helio Waldman


The estimation of blocking probabilities in optical path networks has been investigated mainly for the case in which wavelengths are chosen randomly among the available ones on a route. Even though algorithms that unbalance the load among wavelengths usually have a superior performance when compared with the random algorithm, the modeling complexity of these better-performance algorithms often limits their analytical analysis. This article proposes a per-wavelength plane blocking probability estimation for the first-fit algorithm in WDM rings with wavelength continuity constraint. Moreover, the estimation method allows the calculation of the probability distribution of the constellations of active wavelengths in the network links under the first-fit rule for a given blocking probability.


Blocking probability Reduced load approximation Wavelength assignment First-fit algorithm Rings WDM ring networks Call blocking 


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  1. Birman A. (1996). Computing approximate blocking probabilities for a class of all-optical networks. IEEE Journal of Selected Areas in Communications 14(5): 852–857 CrossRefGoogle Scholar
  2. Sridharan A. and Sivarajan K.N. (2004). Blocking in all-optical networks. IEEE/ACM Transactions on Networking 12(2): 384–397 CrossRefGoogle Scholar
  3. Zang H., Jue J.P. and Mukherjee B. (2000). A review of routing and wavelength assignment aproaches for wavelength-routed optical WDM networks. Optical Networks Magazine 1(1): 47–60 Google Scholar
  4. Karasan E. and Ayanoglu E. (1998). Effects of wavelength routing and selection algorithms on wavelengths conversion gain in WDM optical networks. IEEE/ACM Transactions on Networking 6(2): 186–196 CrossRefGoogle Scholar
  5. Harai H., Murata M. and Miyahara H. (1998). Performance analysis of wavelength assignment policies in all-optical networks with limited-range wavelength conversion. IEEE Journal of Selected Areas in Communications 16(7): 1051–1060 CrossRefGoogle Scholar
  6. Waldman H. and Campelo D.R. (2005). Asymptotic blocking probabilities in rings with single-circuit links. IEEE Communications Letters 9(6): 564–566 CrossRefGoogle Scholar
  7. Fonseca, I.E., Almeida R.C. Jr., Waldman, H., Ribeiro, M.R.N.: Meeting optical QoS requirements with reduced complexity in dynamic wavelength assignment. Proc. IEEE BROADNETS’04 (pp. 331–333). San Jose, CA, USA, October (2004)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Divanilson R. Campelo
    • 1
  • Raul C. AlmeidaJr
    • 2
  • Helio Waldman
    • 3
    • 4
  1. 1.Department of Electrical EngineeringUniversidade Presbiteriana MackenzieSao PauloBrazil
  2. 2.Department of Electronic Systems EngineeringUniversity of EssexColchesterUK
  3. 3.Universidade Federal do ABCSanto AndréBrazil
  4. 4.Universidade Estadual de CampinasCampinasBrazil

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