Diffusion Approximations

Abstract

This paper provides a survey of some of the basic applications of the theory of diffusion approximation to queueing theory. The paper starts with a brief description of the theory of weak convergence of stochastic processes. This theory is then applied to the study of networks of queues in heavy traffic. The resulting approximations involve diffusion processes with reflecting boundaries. Queues in which both the number of servers and number of customers are large are also studied. In this case, the queueing processes are best approximated by Gaussian processes. The paper is intended to give the non-specialist a self-contained introduction to what is a rapidly developing area of applied probability. Keywords: Queueing theory; Diffusion approximations; Gaussian approximations; Weak convergence.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1989
Accession Number
ADA212581

Entities

People

  • Peter W. Glynn

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Convergence
  • Differential Equations
  • Gaussian Processes
  • Markov Processes
  • New York
  • Operations Research
  • Partial Differential Equations
  • Probability
  • Probability Distributions
  • Queueing Theory
  • Random Variables
  • Random Walk
  • Stochastic Processes
  • Surveys
  • Theorems
  • Weak Convergence

Readers

  • Computer Networking
  • Materials Science and Engineering.
  • Statistical inference.