A numerical method for solving singular Brownian control problems

The Brownian approximation approach to developing dynamic control policies for multiclass queueing networks is useful when the limiting, usually singular, Brownian control problem can be solved. However, this problem can be rarely solved analytically. In this paper we present a method for numerically solving singular Brownian control problems. We adapt finite element methods to iteratively solve the Hamilton-Jacobi-Bellman equation associated with the Brownian control problem. A key feature of our method is that the presence of singular controls simplifies the procedure. The solution to the Hamilton-Jacobi-Bellman equation is then used to construct an optimal control for the Brownian system. We illustrate the method on two examples of singular Brownian control problems