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

Abstract

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