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