This paper describes a general type of stochastic system model that involves
three basic elements: activities, resources, and stocks of material.
A system manager chooses activity levels dynamically based on state
observations, consuming some materials as inputs and producing other
materials as outputs, subject to resource capacity constraints.
A generalized notion of heavy traffic is described, in which exogenous
input and output rates are approximately balanced with nominal activity
rates derived from a static planning problem. A Brownian network model
is then proposed as a formal approximation in the heavy traffic parameter
regime. The current formulation is novel, relative to models analyzed in
previous work, in that its definition of heavy traffic takes explicit
account of the system manager's economic objective.