  Reflected diffusions naturally arise in many problems from applications
ranging from economics and mathematical biology to queueing theory. In this
paper we consider a class of infinite time-horizon singular stochastic control
problems for a general one-dimensional diffusion that is reflected at zero. We
assume that exerting control leads to a state-dependent instantaneous reward,
whereas reflecting the diffusion at zero gives rise to a proportional cost with
constant marginal value. The aim is to maximize the total expected reward,
minus the total expected cost of reflection. We show that depending on the
properties of the state-dependent instantaneous reward we can have
qualitatively different kinds of optimal strategies. The techniques employed
are those of stochastic control and of the theory of linear diffusions.
