Extreme Values of Birth and Death Processes and Queues,

Abstract

This document studies the asymptotic behavior of maximum values of birth and death processes over large time intervals. In most cases, the distributions of these maxima, under standard linear normalizations, either do not converge or they converge to a degenerate distribution. However, by allowing the birth and death rates to vary in a certain manner as the time interval increases, we show that the maxima do indeed have three possible limit distributions. Two of these are classical extreme value distributions and the third one is a new distribution. This third distribution is the best one for practical applications. Our results are for transient as well as recurrent birth and death processes and related queues. For transient processes, the focus is on the maxima conditioned that they are finite. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 25, 1986
Accession Number
ADA169932

Entities

People

  • Richard F. Serfozo

Organizations

  • Georgia Tech

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Analogs
  • Convergence
  • Discrete Distribution
  • Industrial Plants
  • Inequalities
  • Intensity
  • Intervals
  • Markov Processes
  • Numbers
  • Numerical Integration
  • Probability
  • Random Variables
  • Random Walk
  • Standards
  • Stochastic Processes
  • Time Intervals
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Neuroscience