Maximal Cost-Bounded Reachability Probability on Continuous-Time Markov Decision Processes

2013/10/09 by Hongfei Fu, Fu, Hongfei
Computer Science · #FOS: Electrical engineering #Formal Methods in Verification #Petri Nets in System Modeling #Real-Time Systems Scheduling #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1310.2514

openalex publication_date 2013/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider multi-dimensional maximal cost-bounded reachability probability over continuous-time Markov decision processes (CTMDPs). Our major contributions are as follows. Firstly, we derive an integral characterization which states that the maximal cost-bounded reachability probability function is the least fixed point of a system of integral equations. Secondly, we prove that the maximal cost-bounded reachability probability can be attained by a measurable deterministic cost-positional scheduler. Thirdly, we provide a numerical approximation algorithm for maximal cost-bounded reachability probability. We present these results under the setting of both early and late schedulers.

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