Applications of Functional Analytical Methods to Problems in Queueing Network Theory and Reliability Theory

摘要

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 to 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. (jhd)