Applications of Functional Analytical Methods to Problems in Queueing Network Theory and Reliability Theory
Abstract
The diffusion approximation for queueing networks is proved via the Trotter-kato Theorem. This involves delicate calculations involving the domains of certain operators some of which have been successful and some not. One tries t solve the martingale problem instead of characterizing the domain and hopes to use the Stroock-Varadham approach in order to prove the corresponding limit theorem. For example, we solve the martingale problem for a class of Markov processes whose infinite simal generators are integro-differential operators. Extensions of these results to more complicated queueing systems are currently in progress. Publications: (1) On the Accuracy of Kingman's Heavy Traffic Approximation in the Theory of Queues; (2) Limit theorems for Markov processes via a variant of the Trotter-Kato theorem; and (3) On a integro-differential equation occurring in Queueing and Storage theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1980
- Accession Number
- ADA208736
Entities
People
- Walter A. Rosenkrantz
Organizations
- University of Massachusetts Amherst