# Markov Automata with Multiple Objectives

## TL;DR

This paper develops algorithms for analyzing multiple, possibly dependent objectives in Markov automata, enabling the approximation of Pareto curves and trade-offs in complex stochastic systems.

## Contribution

It introduces methods to analyze several objectives simultaneously in Markov automata, including trade-offs and combined criteria, extending beyond single-objective verification.

## Key findings

- Algorithms successfully approximate Pareto curves.
- Approach handles multiple, dependent objectives.
- Experimental results demonstrate scalability.

## 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.