Compositional Design of Stochastic Timed Automata

  • Patricia Bouyer
  • Thomas Brihaye
  • Pierre CarlierEmail author
  • Quentin Menet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9691)


In this paper, we study the model of stochastic timed automata and we target the definition of adequate composition operators that will allow a compositional approach to the design of stochastic systems with hard real-time constraints. This paper achieves the first step towards that goal. Firstly, we define a parallel composition operator that (we prove) corresponds to the interleaving semantics for that model; we give conditions over probability distributions, which ensure that the operator is well-defined; and we exhibit problematic behaviours when this condition is not satisfied. We furthermore identify a large and natural subclass which is closed under parallel composition. Secondly, we define a bisimulation notion which naturally extends that for continuous-time Markov chains. Finally, we importantly show that the defined bisimulation is a congruence w.r.t. the parallel composition, which is an expected property for a proper modular approach to system design.


Composition Operator Parallel Composition Decidability Property Process Algebra Clock Variable 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Thomas Brihaye
    • 2
  • Pierre Carlier
    • 1
    • 2
    Email author
  • Quentin Menet
    • 2
  1. 1.LSV, CNRS, ENS Cachan, Université Paris-SaclayCachanFrance
  2. 2.Université de MonsMonsBelgium

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