Estimating Customer and Time Averages

Abstract

In this paper we establish a joint central limit theorem for customer and time averages by applying a martingale central limit theorem in a Markov framework. The limiting values of the two averages appear in the translation terms. This central limit theorem helps to construct confidence intervals for estimators and perform statistical tests. It thus helps determine which finite average is a more asymptotically efficient estimator of its limit. As a basis for testing for PASTA (Poisson arrivals see time averages), we determine the variance constant associated with the central limit theorem for the difference between the two averages when PASTA holds.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1991
Accession Number
ADA249105

Entities

People

  • Benjamin Melamed
  • Peter W. Glynn
  • Ward Whitt

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Covariance
  • Data Science
  • Estimators
  • Information Science
  • Intervals
  • Markov Chains
  • Markov Processes
  • New York
  • Operations Research
  • Probability
  • Random Variables
  • Simulations
  • Standards
  • Stationary Processes
  • Statistical Inference
  • Stochastic Processes
  • Systems Engineering

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Mathematical Modeling and Probability Theory.