Markov Automata with Multiple Objectives

Abstract

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.