Markov Automata with Multiple Objectives

  • Tim QuatmannEmail author
  • Sebastian Junges
  • Joost-Pieter Katoen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10426)


Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and stochastic scheduling. Their verification so far focused on single objectives such as (timed) reachability, and expected costs. In practice, often the objectives are mutually dependent and the aim is to reveal trade-offs. We present algorithms to analyze several objectives simultaneously and approximate Pareto curves. This includes, e.g., several (timed) reachability objectives, or various expected cost objectives. We also consider combinations thereof, such as on-time-within-budget objectives—which policies guarantee reaching a goal state within a deadline with at least probability p while keeping the allowed average costs below a threshold? We adopt existing approaches for classical Markov decision processes. The main challenge is to treat policies exploiting state residence times, even for untimed objectives. Experimental results show the feasibility and scalability of our approach.


Markov Automata (MAs) Markov Decision Process (MDPs) Approximate Pareto Curve Achievement Points Multi-objective Model Checking 
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.



This work was supported by the CDZ project CAP (GZ 1023).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tim Quatmann
    • 1
    Email author
  • Sebastian Junges
    • 1
  • Joost-Pieter Katoen
    • 1
  1. 1.RWTH Aachen UniversityAachenGermany

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