Workload Interpretation for Brownian Models of Stochastic Processing Networks

J. M. Harrison and R. J. Williams
Brownian networks are a class of stochastic system models that can arise as heavy traffic approximations for stochastic processing networks. In earlier work we developed the "equivalent workload formulation" of a generalized Brownian network: denoting by Z(t) the state vector of the generalized Brownian network at time t, one has a lower dimensional state descriptor W(t) = MZ(t) in the equivalent workload formulation, where M is an arbitrary basis matrix for a certain linear space. Here we use the special structure of a stochastic processing network to develop a more extensive interpretation of the equivalent workload formulation associated with its Brownian network approximation. In particular, we show how the basis matrix M can be constructed from the basic optimal solutions of a certain dual linear program, thus providing a mechanism for reducing the choices for M from an infinite set to a finite one (when the workload dimension exceeds one).

Appeared in Mathematics of Operations Research, November 2007, Vol. 32, 808--820.
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Last updated: December 4, 2005