Transient Reward Approximation for Continuous-Time Markov Chains

TL;DR

This paper introduces a symblicit analysis method for large continuous-time Markov chains, enabling efficient reward approximation without multi-terminal decision diagrams, demonstrated on practical case studies.

Contribution

The paper presents a novel symblicit approach combining abstraction and algorithms for reward bounds in large CTMCs, avoiding multi-terminal decision diagrams.

Findings

Efficient reward bounds computation for large CTMCs.

Practical applicability demonstrated on case studies.

Circumvents limitations of multi-terminal decision diagrams.

Abstract

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.