Relations Between Arrival and Time Averages of a Process in Discrete-Time Systems and Some applications.

Abstract

The fact that Poisson Arrivals See Time Averages (PASTA) has been repeatedly in the analysis of queueing systems. Various authors provided proofs of PASTA under varying assumptions on the observed process and its relationship to the Poisson arrivals. In an earlier publication it was shown that PASTA is essentially a sample path property. The basic condition is that the observed process cannot anticipate future jumps of the Poisson process. This paper considers discrete-time systems. These systems arise naturally in the study of sychronized communication networks and can also be considered as approximations of assumed by an underlying denumberable Markov chain and that the observed process cannot anticipate future arrivals if the current state of the Markov chain is known. The relation between the time average of the observed process and the average of the process as observed by the arrivals is derived. The results can be applied even if the observing process has a role different than arrival.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1986
Accession Number
ADA174551

Entities

People

  • Leonidas Georgiadis

Organizations

  • University of Virginia

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Applied Mathematics
  • Business Administration
  • Classification
  • Computer Science
  • Electrical Engineering
  • Engineering
  • Markov Chains
  • Materials Science
  • Mathematics
  • Military Research
  • Operations Research
  • Probability
  • Random Variables
  • Security
  • Statistics
  • Steady State
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Joint Military Operations and Doctrine.
  • Mathematical Modeling and Probability Theory.