핵심 개념
This paper presents a computational method for solving singular stochastic control problems motivated by queueing theory applications. The method approximates the original singular control problem by a drift control problem, which can be solved efficiently using a recently developed simulation-based approach.
초록
The paper considers two classes of singular stochastic control problems with a d-dimensional state process W evolving as a reflected Brownian motion. In the first formulation, the system is subject to exogenous reflection at the boundary, while in the second formulation, the reflection is endogenous.
The authors propose approximating the original singular control problem by a drift control problem, where the control is restricted to have a specific form. This approximation can be solved efficiently using a recently developed computational method. The authors conjecture that the solution obtained from the drift control problem is nearly optimal for the original singular control problem as the upper bound on the drift rates becomes large.
The paper presents several examples to demonstrate the viability of the proposed approach:
A one-dimensional singular control problem with known analytical solution, which is used to compare the approximation accuracy for different upper bound values.
A multi-dimensional singular control problem with a decomposable structure, which can be solved efficiently using the proposed method.
Two queueing network examples - a tandem queue network and a criss-cross network - where the singular control approximation is used to derive near-optimal policies for the original discrete-flow queueing models.
The authors show that the policies derived from the singular control approximation perform very close to the optimal policies obtained by solving the original Markov decision process formulations.