  Motivated by a control problem of a certain queueing network we consider a
control problem where the dynamics is constrained in the nonnegative orthant
$\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the
reflections at the faces/boundaries. We define a discounted value function
associated to this problem and show that the value function is a viscosity
solution to a certain HJB equation in $\mathbb{R}_+$ with nonlinear Neumann
type boundary condition. Under certain conditions, we also characterize this
value function as the unique solution to this HJB equation.
