Optimal control of a stochastic network driven by a fractional Brownian motion input

TL;DR

This paper develops a stochastic control framework for a network driven by fractional Brownian motion, addressing various cost criteria and solving a constrained optimization problem, with insights into the relationships among different value functions.

Contribution

It introduces a novel control model for fractional Brownian motion-driven networks and provides solutions for multiple cost optimization problems, including a constrained minimization.

Findings

Solutions for long-run average, discounted, and finite horizon costs.

Established Abelian limit relationships among value functions.

Applied results to a constrained minimization problem.

Abstract

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an on-off input process. We study stochastic control problems associated with the long-run average cost, the infinite horizon discounted cost, and the finite horizon cost. In addition, we find a solution to a constrained minimization problem as an application of our solution to the long-run average cost problem. We also establish Abelian limit relationships among the value functions of the above control problems.