Dynamic control of Brownian networks: state space collapse and equivalent workload formulations

Brownian networks are a class of linear stochastic control systems arise as heavy traffic approximations in queueing theory. Such Brownian models have been used to approximate problems of dynamic routing, sequencing and dynamic input control for queueing networks. A number of examples have been analyzed in recent years, and in each case the network has been successfully reduced to an "equivalent workload" of lower dimension. In this article we explain that reduction in terms, using an orthogonal decomposition that distinguishes between and irreversible controls.