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Queueing analysis of a single-wavelength Fiber-Delay-Line buffer

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Abstract

We present in rather mathematical detail the queueing analysis of a single-wavelength Fiber-Delay-Line buffer. Such optical buffer system cannot realize all possible delay values, but only a limited set, typically multiple integers of some basic unit called the granularity. This leads to an under-utilization of the available channel capacity, and a bad design choice for the granularity can seriously impair performance.

The analysis makes extensive use of generating functions and focusses on the scheduling horizon as seen by arriving bursts and the waiting time these incur in an infinite system. From the expressions obtained, several measures of interest are derived, notably heuristics for the burst loss probability and the mean waiting time in finite systems, which can be used to evaluate performance for any given value of the input load. The model we propose allows for rather general burst-size distributions, but for special instances thereof, the formulae can be made more explicit. A number of numerical examples highlight some of the peculiar aspects of Fiber-Delay-Line buffers.

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References

  1. A. Agarwal, L. Wang, Y. Su and P. Kumar, All-optical erasable storage buffer based on parametric nonlinearity in fiber, in: Proceedings OFC01 (2001).

  2. R. Almeida, J. Pelegrini and H. Waldman. Optical buffer modelling for performance evaluation considering any packet inter-arrival time distribution, in: Proceedings ICC 2004 (2004).

  3. R. Almeida, J. Pelegrini and H. Waldman, A generic-traffic optical buffer modeling for asynchronous optical switching networks, IEEE Communications Letters 9(2) (2005) 175–177.

    Article  Google Scholar 

  4. S. Bregni, G. Guerra and A. Pattavina, State of the art of optical switching technology for all-optical networks, in: N. Mastorakis (Ed.), Communications World. WSES Press (2001).

  5. H. Bruneel, and B. Kim, Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic Publishers (Boston) (1993).

  6. P. Cadro, A. Gravey and C. Guillemot, Performance evaluation of an optical transparent packet switch, in: Proceedings ITC 15 (1997).

  7. F. Callegati, Optical buffers for variable length packets, IEEE Communications Letters 4(9) (2000) 292–294.

    Article  Google Scholar 

  8. F. Callegati, Approximate modeling of optical buffers for variable length packets, Photonic Network Communications 3(4) (2001) 383–390.

    Article  Google Scholar 

  9. I. Chlamtac, A. Fumagalli, L. Kazovsky, P. Melman, et al., CORD: Contention resolution by delay lines. IEEE Journal on Selected Areas in Communications 14(5) (1996) 1014–1029.

    Google Scholar 

  10. L. Dittmann, C. Develder, D. Chiaroni, F. Neri, et al., The European IST project DAVID: A viable approach toward optical packet switching. IEEE Journal on Selected Areas in Communications 21(7) (2003) 1026–1040.

    Article  Google Scholar 

  11. T. El-Bawab and J.-D. Shin, Optical packet switching in core networks: between vision and reality. IEEE Communications Magazine 40(9) (2002) 60–65.

    Article  Google Scholar 

  12. P. Flajolet and A. Odlyzko, Singularity analysis of generating functions. SIAM Journal on Discrete Mathematics 3(2) (1990) 216–240.

    Article  Google Scholar 

  13. R. Geldenhuys, F. Leuschner, Y. Liu, G. Khoe, N. Calabretta and H. Dorren, Selecting fibre delay line distributions for travelling buffers in an all-optical packet switched cross-connect, in: Proceedings of the IEEE Canadian Conference on Electrical and Computer Engineering (2003).

  14. C. Guillemot, M. Renaud, P. Gambini, C. Janz, et al., Transparent optical packet switching: the European ACTS KEOPS project approach. IEEE/OSA Journal of Lightwave Technology 16(12) (1998) 2117–2134.

    Article  Google Scholar 

  15. D. Hong, F. Poppe, J. Reynier, F. Baccelli and G. Petit, The impact of burstification on TCP throughput in optical burst switching networks, in: Proceedings ITC 18 (2003).

  16. D. Hunter, W. Cornwel, T. Gilfedder, A. Franzen and I. Andonovic, SLOB: A switch with large optical buffers for packet switching. Journal of Lightwave Technology 16(10) (1998) 1725–1736.

    Article  Google Scholar 

  17. D. Hunter, M. Nizam, M. Cia, I. Andonovic, et al., WASPNET: A wavelength switched packet network. IEEE Communications Magazine 37(3) (1999) 120–129.

    Article  Google Scholar 

  18. A. Jajszczyk, Optical networks – the electro-optic reality. Optical Switching and Networking 1(1) (2005) 3–18.

    Article  Google Scholar 

  19. A. Jourdan, D. Chiaroni, E. Dotaro, G. Eilenberger, F. Masetti and M. Renaud, The perspective of optical packet switching in IP-dominant backbone and metropolitan networks. IEEE Communications Magazine 39(3) (2001) 136–141.

    Article  Google Scholar 

  20. L. Kleinrock, Queueing Systems, Volume 1: Theory. John Wiley & Sons (1975).

  21. P. Ku, C. Chang-Hasnain and S. Chuang, Variable semiconductor all-optical buffer. Electronics Letters 38(24) (2002) 1581–1583.

    Article  Google Scholar 

  22. K. Laevens and H. Bruneel, Analysis of a single-wavelength optical buffer, in: Proceedings Infocom 2003 (2003).

  23. K. Laevens, B. Van Houdt, C. Blondia and H. Bruneel, Sustainable load of Fibre-Delay-Line buffers. Electronics Letters 40(2) (2004) 137–138.

    Article  Google Scholar 

  24. M. Listanti, V. Eramo and R. Sabella, Architectural and technological issues for future optical internet networks. IEEE Communications Magazine 38(9) (2000) 82–92.

    Google Scholar 

  25. A. Liu, C. Wu, M. Lim, Y. Gong and P. Shum, Optical buffer configuration based on a 3x3 collinear fibre coupler. Electronics Letters 40(16) (2004) 1017–1019.

    Article  Google Scholar 

  26. F. Masetti, J. Benoit, F. F. Brillouet, J. Gabriagues, et al., High speed, high capacity ATM optical switches for future telecommunication transport networks. IEEE Journal on Selected Areas in Communications 14(5) (1996) 979–998.

    Article  Google Scholar 

  27. M. Murata and K. Kitayama, Ultrafast photonic label switch for asynchronous packets of variable length, in: Proceedings Infocom 02 (2002).

  28. L. Nieminen and E. Hyytiä, Delay line configurations in optical burst switching with JET protocol, in: Proceedings Sixteenth Nordic Teletraffic Seminar (2002).

  29. W. Rogiest, K. Laevens, D. Fiems and H. Bruneel, Analysis of an asynchronous single-wavelength FDL buffer, in: Proceedings ITC 19 (2005a).

  30. W. Rogiest, K. Laevens, D. Fiems and H. Bruneel, A performance model for an asynchronous optical buffer, in: Proceedings Performance 2005 (2005b).

  31. J. Turner, Terabit burst switching progress report (9/98-12/98). Technical report, Washington University at St. Louis (1998).

  32. B. Van Houdt, K. Laevens, J. Lambert, C. Blondia and H. Bruneel, Channel utilization and loss rate in a single-wavelength Fiber Delay Line (FDL) buffer, in: Proceedings Globecom 2004 (2004).

  33. Van Ommeren, J., Asymptotic analysis of queueing systems. Ph. D. thesis, Vrije Universiteit te Amsterdam (1989).

  34. K. Vlachos, I. Monroy, A. Koonen, C. Peucheret and P. Jeppesen, STOLAS: Switching technologies for optically labeled signals. IEEE Communications Magazine 41(11) (2003) S9–S15.

    Article  Google Scholar 

  35. H. Waldman, R. Almeida and J. Pelegrini, An infinite granularity bound on the performance of delay-line buffering, in: Proceedings ONDM'03 (2003).

  36. M. Xiaohua, Optical switching technology comparison: optical MEMS vs. other technologies. IEEE Communications Magazine 41(11) (2003) S16–S23.

    Google Scholar 

  37. Y. Xiong, M. Vandenhoute and H. Cankaya, Control architecture in optical burst-switched WDM networks. IEEE Journal on Selected Areas in Communications 18(10) (2000) 1838–1851.

    Google Scholar 

  38. T. Yamaguchi, K. Baba, M. Murata and K. Kitayama, Scheduling algorithm with consideration to void space reduction in photonic packet switch. IEICE Transactions on Communications (8) (2003) 2310–2318.

    Google Scholar 

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Authors and Affiliations

  1. Department of Telecommunications and Information Processing, Ghent University, Belgium

    K. Laevens, M. Moeneclaey & H. Bruneel

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  1. K. Laevens
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  2. M. Moeneclaey
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  3. H. Bruneel
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Correspondence to K. Laevens.

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Laevens, K., Moeneclaey, M. & Bruneel, H. Queueing analysis of a single-wavelength Fiber-Delay-Line buffer. Telecommun Syst 31, 259–287 (2006). https://doi.org/10.1007/s11235-006-6524-8

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  • DOI: https://doi.org/10.1007/s11235-006-6524-8

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