A Brownian control problem for a simple queueing system in the Halfin-Whitt regime

摘要

We consider a formal diffusion limit for a control problem of a multi-type multi-server queueing system, in the regime proposed by Halfin and Whitt. This takes the form of a control problem where the dynamics are driven by a Brownian motion. In one dimension, a pathwise minimum is obtained and is characterized as the solution to a stochastic differential equation. The pathwise solution to a special multi-dimensional problem (corresponding to a multi-type system) follows. (C) 2003 Elsevier B.V. All rights reserved. [References: 13]