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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1980
Accession Number
ADA208736

Entities

People

  • Walter A. Rosenkrantz

Organizations

  • University of Massachusetts Amherst

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Classification
  • Contracts
  • Differential Equations
  • Diffusion
  • Equations
  • Generators
  • Markov Processes
  • Mathematics
  • Network Science
  • Operations Research
  • Partial Differential Equations
  • Probability
  • Reliability
  • Security
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.