Extreme Values of Queue Lengths in M/G/1 and GI/M/1 Systems.

Abstract

This document states the limiting behavior of maximum queue lengths in the M/G/1 and GI/M/1 service systems. When the system are positive recurrent, the distributions of their maximum queue lengths, under standards linear normalizations, either do not converge or they converge to degenerate limits. Consequently, one cannot use classical extreme value theory to characterize their limiting behavior. It is shown, however, that by varying the system parameters in a certain way as the time interval grows, these maxima do indeed have three possible limit distributions. Two of them are classical extreme value distributions and the third one is a new distribution. The latter distribution is the best one for practical approximations. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 30, 1986
Accession Number
ADA177117

Entities

People

  • Richard F. Serfozo

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Classification
  • Convergence
  • Industrial Plants
  • Integrals
  • Intervals
  • North Carolina
  • Numbers
  • Order Statistics
  • Probability
  • Random Variables
  • Real Numbers
  • Scientific Research
  • Security
  • Standards
  • Stochastic Processes

Readers

  • Mathematical Modeling and Probability Theory.
  • Spectroscopy.
  • Statistical inference.