Timed, Distributed, Probabilistic, Typed Processes

  • Martin Berger
  • Nobuko Yoshida
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4807)


This paper studies types and probabilistic bisimulations for a timed π-calculus as an effective tool for a compositional analysis of probabilistic distributed behaviour. The types clarify the role of timers as interface between non-terminating and terminating communication for guaranteeing distributed liveness. We add message-loss probabilities to the calculus, and introduce a notion of approximate bisimulation that discards transitions below a certain specified probability threshold. We prove this bisimulation to be a congruence, and use it for deriving quantitative bounds for practical protocols in distributed systems, including timer-driven message-loss recovery and the Two-Phase Commit protocol.


Distribute System Type Process Weak Transition Linear Output Linear Input 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Martin Berger
    • 1
  • Nobuko Yoshida
    • 1
  1. 1.Department of Computing, Imperial College London 

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