Stochastic Comparisons for Performability of Telecommunication Systems

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


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.


Performability Stochastic comparisons Markov chains 


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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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