Uniform Limit Theorems for Synchronous Processes with Applications to Queues

Abstract

In the present paper we investigate conditions under which the Cesaro averaged functionals. We show that to obtain uniform convergence requires placing further conditions on the Positive Recurrence Process (PRS). This is in sharp contrast to both classical regenerative processes and discrete time Harris recurrent Markov chains (where renewal theory can be applied) where such uniform convergence holds without any further conditions. For continuous time positive Harris recurrent Markov processes (where renewal theory can not be applied) we show that these further conditions are in fact automatically satisfied. In this context, applications to queueing models are given. Synchronous process, Cesaro convergence, Limit theorems, Point processes.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1989
Accession Number
ADA220224

Entities

People

  • Karl Sigman
  • Peter W. Glynn

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Engineering
  • Industrial Engineering
  • Markov Chains
  • Markov Processes
  • Military Research
  • Operations Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Sequences
  • Stationary
  • Stationary Processes
  • Steady State
  • Stochastic Processes
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.