Fixed-Delay Events in Generalized Semi-Markov Processes Revisited

  • Tomáš Brázdil
  • Jan Krčál
  • Jan Křetínský
  • Vojtěch Řehák
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)


We study long run average behavior of generalized semi-Markov processes with both fixed-delay events as well as variable-delay events. We show that allowing two fixed-delay events and one variable-delay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not exist). We use this observation to disprove several results from literature. Next we study GSMP with at most one fixed-delay event combined with an arbitrary number of variable-delay events. We prove that such a GSMP always possesses an invariant measure which means that the frequencies of states are always well defined and we provide algorithms for approximation of these frequencies. Additionally, we show that the positive results remain valid even if we allow an arbitrary number of reasonably restricted fixed-delay events.


Markov Chain Invariant Measure Model Check Transition Kernel Discrete Event System 
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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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tomáš Brázdil
    • 1
  • Jan Krčál
    • 1
  • Jan Křetínský
    • 1
  • Vojtěch Řehák
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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