The Renewal Equation for Markov Renewal Processes with Applications to Storage Models.

Abstract

For Markov renewal process in which the sojourn times are controlled by an imbedded, denumerable state Markov chain, it is shown that there exist a random time at which the Markov renewal process regenerates. The basic renewal theorem is applied to determine the limiting behavior of the Markov renewal process. These results are then applied to a particular two compartment storage model to determine the limiting behavior of the amounts in storage. Keywords: Markov Renewal Process; Semi-Markov Process; Renewal Equation; Coupling; Storage Model.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1986
Accession Number
ADA172688

Entities

People

  • Eric S. Tollar

Organizations

  • Florida State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Couplings
  • Equations
  • Ergodic Processes
  • Markov Chains
  • Markov Processes
  • Military Research
  • New York
  • Probability
  • Random Variables
  • Sequences
  • Stationary
  • Statistics
  • Stochastic Processes
  • Theorems
  • Transitions

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.