  Due to a printing error the above mentioned article [Annals of Applied
Probability 10 (2000) 75--103, doi:10.1214/aoap/1019737665] had numerous
equations appearing incorrectly in the print version of this paper. The entire
article follows as it should have appeared. IMS apologizes to the author and
the readers for this error. A recent paper by Harrison and Van Mieghem
explained in general mathematical terms how one forms an ``equivalent workload
formulation'' of a Brownian network model. Denoting by $Z(t)$ the state vector
of the original Brownian network, one has a lower dimensional state descriptor
$W(t)=MZ(t)$ in the equivalent workload formulation, where $M$ can be chosen as
any basis matrix for a particular linear space. This paper considers Brownian
models for a very general class of open processing networks, and in that
context develops a more extensive interpretation of the equivalent workload
formulation, thus extending earlier work by Laws on alternate routing problems.
A linear program called the static planning problem is introduced to articulate
the notion of ``heavy traffic'' for a general open network, and the dual of
that linear program is used to define a canonical choice of the basis matrix
$M$. To be specific, rows of the canonical $M$ are alternative basic optimal
solutions of the dual linear program. If the network data satisfy a natural
monotonicity condition, the canonical matrix $M$ is shown to be nonnegative,
and another natural condition is identified which ensures that $M$ admits a
factorization related to the notion of resource pooling.
