TWO WORKLOAD PROPERTIES FOR BROWNIAN NETWORKS
M. Bramson and R. J. Williams
Abstract
As one approach to dynamic scheduling problems for open stochastic
processing networks, J. M. Harrison has proposed the use of formal
heavy traffic approximations known as Brownian networks.
A key step in this approach is a reduction
in dimension of a Brownian network, due to
Harrison and Van Mieghem, in which the "queue length" process
is replaced by a "workload" process.
In this paper,
we establish two properties of these workload processes.
Firstly, we derive a formula for
the dimension of such
processes.
For a given Brownian network, this dimension
is unique.
However, there are infinitely many
possible choices for
the workload process.
Harrison
has proposed a "canonical" choice, which
reduces the possibilities to a finite number.
Our second result provides sufficient conditions for this
canonical choice to be valid and for it to yield a non-negative workload process.
The assumptions and proofs for our
results involve only first-order model parameters.
In Queueing Systems, 45 (2003), 191-221. The original publication is available by clicking here.
For a copy of a preprint
for personal scientific non-commercial use only, click
here for postscript or
here for pdf.
Last updated August 4, 2006.