Weak Stochastic Comparisons for Performability Verification

  • Hind Castel-Taleb
  • Nihal Pekergin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5513)


The probabilistic model checking provides a precise formalism for the performance and reliability verification of telecommunication systems modeled by Markov chains. We study a queueing system similar to a Jackson network except that queues have a finite capacity. We propose to study in this paper (state and path) formulas from the Continuous Stochastic Logic (CSL), in order to verify performability properties. Unfortunately, transient and stationary analysis is very complex for multidimensional Markov processes. So we propose to use the stochastic comparisons in the sense of weak orderings to define bounding processes. Bounding processes are represented by independent M/M/1 queues for which transient and stationary distributions can be computed as the product of probability distributions of each queue. We use the increasing set method, and we develop an intuitive formalism based on events to establish weak stochastic comparisons.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hind Castel-Taleb
    • 1
  • Nihal Pekergin
    • 2
  1. 1.INSTITUT TELECOM, Telecom et Management SudParisEvry CedexFrance
  2. 2.LACL, Université Paris-Est Val de MarneCréteil CedexFrance

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