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Stochastic Comparisons for Performability of Telecommunication Systems

  • Hind Castel-Taleb
  • Idriss Ismael-Aouled
  • Nihal Pekergin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6148)

Abstract

In this paper, we study the performability of telecommunication systems. Performability verification may be very complex as it is the joint evaluation of performance and dependability. We consider the composite Erlang loss model representing a telecommunication switching system. In this model we suppose that each channel can be free/busy for the performance behavior, and also in a failure/repair state for the availability. We suppose that the system is represented by a multidimensional Markov chain whose size increases quickly with the number of channels.

We apply stochastic comparison methods in order to define bounding systems easier to analyze. Different approaches have been used. In the first one, we modify the exact system in order to obtain a bounding system having a product form solution. The other systems are obtained by reducing the size of the exact system, by aggregating the states in order to obtain bounding systems. We compute upper and lower bounds on the blocking probability, and we study the impact of parameters on the quality of the bounds.

Keywords

Performability Stochastic comparisons Markov chains 

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References

  1. 1.
    Cloth, L., Haverkort, B.R.: The performability tool P’ility. In: 5th International Conference on the Quantitative Evaluation of Systems (QEST) 2008, St Malo, France, September 14-17 (2008)Google Scholar
  2. 2.
    Castel-Taleb, H., Mokdad, L., Pekergin, N.: Aggregated bounding Markov processes applied to the analysis of tandem queues. In: Second International Conference on Performance Evaluation Methodologies and Tools, ACM Sigmetrics, ValueTools 2007, Nantes, France, October 23-25 (2007)Google Scholar
  3. 3.
    Doisy, M.: A coupling technique for stochastic comparison of functions of Markov processes. Journal of Applied Mathematics and Decision Sciences 4(1), 39–64 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Lindvall, T.: Lectures on the coupling method. Wiley series in Probability and Mathematical statistics (1992)Google Scholar
  5. 5.
    Massey, W.: Stochastic orderings for Markov processes on partially ordered spaces. Mathematics of Operations Research 12(2) (May 1987)Google Scholar
  6. 6.
    Mokdad, L., Castel-Taleb, H.: Stochastic comparisons: a methodology for the performance evaluation of fixed and mobile networks. Computer Communications 31(17) (2008)Google Scholar
  7. 7.
    Meyer, J.F.: On evaluating the performability of degradable computing systems. IEEE Transactions on Computers 29(8), 720–731 (1980)zbMATHCrossRefGoogle Scholar
  8. 8.
    Sahner, R.A., Trivedi, K.S., Puliato, A.: Performance and reliability analysis of computer system: an example-based approach using the SHARPE software package. Kluwer Academic Publishers, Boston (1996)zbMATHGoogle Scholar
  9. 9.
    Stoyan, D.: Comparison methods for queues and other stochastic models. J. Wiley and Sons, Chichester (1976)Google Scholar
  10. 10.
    Trivedi, K.S.: Probability and statistics with reliability, queueing and computer science applications. Wiley and Sons, Chichester (2002)Google Scholar
  11. 11.
    Trivedi, K.S., Ma, X., Dharmaraja, S.: Performability modelling of wireless communication systems. Int. J. Commun. Syst. 16, 561–577 (2003)CrossRefGoogle Scholar
  12. 12.
    Van Dijk, N.M.: Queueing networks and product forms, a system approach. John Wiley and Sons, Chichester (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hind Castel-Taleb
    • 1
  • Idriss Ismael-Aouled
    • 1
    • 2
  • Nihal Pekergin
    • 2
  1. 1.INSTITUT TELECOM, Telecom SudParisEvry CedexFrance
  2. 2.LACL, Université Paris-Est, Créteil Val de MarneCréteil CedexFrance

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