UC San Diego
Two workload properties for Brownian networks
- Author(s): Bramson, M
- Williams, R J
- et al.
Published Web Locationhttp://www.springerlink.com/app/home/contribution.asp?wasp=0ab57809559c48cca41812eb5f83b89a&referrer=parent&backto=issue,2,4;journal,13,63;linkingpublicationresults,1:101752,1
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.