Optimal Control of Markov Processes with Age-Dependent Transition Rates

TL;DR

This paper develops a framework for optimal control of Markov processes with age-dependent transition rates, using semi-Markov decision processes to characterize optimal policies for infinite horizon costs.

Contribution

It introduces a novel approach to control Markov processes with age-dependent rates by formulating an equivalent semi-Markov decision process and characterizing optimal controls.

Findings

Characterized the value function for discounted and average costs.

Derived optimal control policies for age-dependent Markov processes.

Established the equivalence between age-dependent Markov control and semi-Markov decision processes.

Abstract

We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterize the value function and optimal controls for both discounted and average cost cases.