Abstraction for Stochastic Systems by Erlang’s Method of Stages

  • Joost-Pieter Katoen
  • Daniel Klink
  • Martin Leucker
  • Verena Wolf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5201)


This paper proposes a novel abstraction technique based on Erlang’s method of stages for continuous-time Markov chains (CTMCs). As abstract models Erlang-k interval processes are proposed where state residence times are governed by Poisson processes and transition probabilities are specified by intervals. We provide a three-valued semantics of CSL (Continuous Stochastic Logic) for Erlang-k interval processes, and show that both affirmative and negative verification results are preserved by our abstraction. The feasibility of our technique is demonstrated by a quantitative analysis of an enzyme-catalyzed substrate conversion, a well-known case study from biochemistry.


Model Check Poisson Process Stochastic System Goal State Markov Decision Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Joost-Pieter Katoen
    • 1
  • Daniel Klink
    • 1
  • Martin Leucker
    • 2
  • Verena Wolf
    • 3
  1. 1.RWTH Aachen University 
  2. 2.TU Munich 
  3. 3.EPF Lausanne 

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