Queueing Systems

, Volume 56, Issue 3–4, pp 203–212 | Cite as

Analyzing a degenerate buffer with general inter-arrival and service times in discrete time

  • W. Rogiest
  • K. Laevens
  • J. Walraevens
  • H. Bruneel


In novel switching approaches such as Optical Burst Switching, the involved buffers can only provide a degenerate waiting room, with delays restricted to multiples of a basic value, the granularity. Although the resulting performance loss was already studied analytically, previous work is either limited by the assumption of independent arrivals, or it involves a matrix with size growing fast with buffer size or arrival process complexity.

Overcoming this, we developed a generic and accurate loss performance model for a degenerate GI/G/1 buffer in discrete time, that yields results instantly for any constellation of burst sizes, inter-arrival times, granularity, load and buffer size. This paper presents our model and compares its results to simulations, illustrating the impact of different types of correlation in the arrival process on loss performance. Our basic model is general and accurate, it can thus serve as a basic tool for optical switch design.


Degenerate buffer Optical buffer FDL buffer Cyclic waiting Lakatos-type queueing system Correlated traffic Granularity Discrete-time queueing Generating functions 

Mathematics Subject Classification (2000)



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  1. 1.
    Lakatos, L.: On a simple continuous cyclic-waiting problem. Ann. Univ. Sci. Budapest. Sect. Comp. 14, 105–113 (1994) Google Scholar
  2. 2.
    Lakatos, L.: On a simple discrete cyclic-waiting queueing problem. J. Math. Sci. New York 4(92), 4031–4034 (1998) CrossRefGoogle Scholar
  3. 3.
    Mykhalevych, K.V.: A comparison of a classical retrial M/G/1 queueing system and a Lakatos-Type M/G/1 cyclic-waiting time queueing system. Ann. Univ. Sci. Budapest. Sect. Comp. 23 (2003) Google Scholar
  4. 4.
    Artalejo, J.R.: A classical bibliography of research on retrial queues: progress in 1990–1999. TOP 7, 187–211 (1999) CrossRefGoogle Scholar
  5. 5.
    Atencia, I., Moreno, P.: A discrete-time Geo/G/1 retrial queue with general retrial times. Queueing Syst. 48(1–2), 5–21 (2004) CrossRefGoogle Scholar
  6. 6.
    Qiao, C., Yoo, M.: Optical Burst Switching–a new paradigm for an optical Internet. J. High-Speed Netw. 8, 69–84 (1999) Google Scholar
  7. 7.
    Callegati, F.: Optical buffers for variable length packets. IEEE Commun. Lett. 4(9), 292–294 (2000) CrossRefGoogle Scholar
  8. 8.
    Murata, M., Kitayama, K.: Ultrafast photonic label switch for asynchronous packets of variable length. In: Proceedings of INFOCOM 2002, New York, June 2002 Google Scholar
  9. 9.
    Laevens, K., Bruneel, H.: Analysis of a single-wavelength optical buffer. In: Proceedings of Infocom 2003, San Francisco Google Scholar
  10. 10.
    Rogiest, W., Laevens, K., Fiems, D., Bruneel, H.: A performance model for an asynchronous optical buffer. Perform. Eval. 62(1–4), 313–330 (2005) Google Scholar
  11. 11.
    Laevens, K., Moeneclaey, M., Bruneel, H.: Queueing analysis of a single-wavelength Fiber-Delay-Line buffer. Telecommun. Syst. 31(2–3), 259–287 (2006) CrossRefGoogle Scholar
  12. 12.
    Almeida, R.C., Pelegrini, J.U., Waldman, H.: Optical buffer modelling for performance evaluation considering any packet inter-arrival time distribution. In: IEEE International Conference on Communications, vol. 3, pp. 1771–1775, 2004 Google Scholar
  13. 13.
    Almeida, R.C., Pelegrini, J.U., Waldman, H.: A generic-traffic optical buffer modeling for asynchronous optical switching networks. IEEE Commun. Lett. 9(2), 175–177 (2005) CrossRefGoogle Scholar
  14. 14.
    Bruneel, H., Kim, B.G.: Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic, Boston (1993) Google Scholar
  15. 15.
    Klimenok, V.I.: On the modification of Rouche’s theorem for the queueing theory problems. Queueing Syst. 38(4), 431–434 (2001) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • W. Rogiest
    • 1
  • K. Laevens
    • 1
  • J. Walraevens
    • 1
  • H. Bruneel
    • 1
  1. 1.SMACS Research GroupGhent UniversityGhentBelgium

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