Efficient Timeout Synthesis in Fixed-Delay CTMC Using Policy Iteration

TL;DR

This paper introduces a symbolic algorithm for fixed-delay synthesis in fdCTMCs that significantly reduces memory usage and speeds up computation by avoiding large action spaces and using polynomial root-finding techniques.

Contribution

The paper presents a novel symbolic fixed-delay synthesis algorithm that efficiently identifies promising actions without explicit large action space construction.

Findings

Achieves three orders of magnitude speedup over previous methods

Reduces memory consumption significantly

Effectively computes optimal fixed-delays using polynomial root-finding

Abstract

We consider the fixed-delay synthesis problem for continuous-time Markov chains extended with fixed-delay transitions (fdCTMC). The goal is to synthesize concrete values of the fixed-delays (timeouts) that minimize the expected total cost incurred before reaching a given set of target states. The same problem has been considered and solved in previous works by computing an optimal policy in a certain discrete-time Markov decision process (MDP) with a huge number of actions that correspond to suitably discretized values of the timeouts. In this paper, we design a symbolic fixed-delay synthesis algorithm which avoids the explicit construction of large action spaces. Instead, the algorithm computes a small sets of "promising" candidate actions on demand. The candidate actions are selected by minimizing a certain objective function by computing its symbolic derivative and extracting a univariate polynomial whose roots are precisely the points where the derivative takes zero value. Since roots of high degree univariate polynomials can be isolated very efficiently using modern mathematical software, we achieve not only drastic memory savings but also speedup by three orders of magnitude compared to the previous methods.