Optimal Control of a Two-Station Brownian Network

Harrison [7] has introduced a model called a Brownian network, which approximates a multiclass queueing network with dynamic scheduling capability. In the present paper, a particular Brownian network control problem is considered that approximates a mathematically intractable scheduling problem for a two-station multiclass queueing network. A reformulation of the Brownian network control problem is solved. Linear programming is used to reduce the reformulated problem to a singular control problem for a one-dimensional Brownian motion. The objective of the singular control problem is to minimize the long-run expected average holding cost of the controlled process, subject to constraints on the long-run expected average amount of control exerted.