Weak Convergence of a Sequence of Queueing and Storage Processes to a Singular Diffusion.

Abstract

It has been known for a long time that heavy traffic limit theorems in queueing theory are but a special case of the so-called diffusion approximation in Physics and Genetics. Take for example Kingman's (1962) heavy traffic approximation for the stationary waiting time distribution for a sequence of GI/GI/1 queues Q(sigma) depending on a parameter sigma. Denote the waiting time, excluding service, or the nth customer by W(n,sigma) and let U(n,sigma) = S(n,sigma) - T(n,sigma) where S(n,sigma) = service time of the nth cutstomer and T(n,sigma) = inter arrival time between the nth and (n + 1)st customer and assume E(U(n,sigma)) = variance of U(n,sigma) = sigma squared, sigma > 0.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1984
Accession Number
ADA150655

Entities

People

  • W. A. Rosenkrantz

Organizations

  • University of Massachusetts Amherst

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Banach Space
  • Classification
  • Convergence
  • Differential Equations
  • Diffusion
  • Equations
  • Functional Analysis
  • Information Science
  • Intensity
  • Mathematics
  • Notation
  • Security
  • Sequences
  • Standards
  • Stochastic Processes
  • Theorems
  • Weak Convergence

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Biotechnology