The Unreliable M/M/1 Retrial Queue in a Random Environment

Abstract

We examine an M/M/1 retrial queue with an unreliable server whose arrival, service, failure repair, and retrial rates are all modulated by an exogenous random environment. Provided are conditions for stability, the (approximate) orbit size distribution, and mean queueing perfor- mance measures which are obtained via matrix-analytic methods. Additionally, we consider the problem of choosing arrival and service rates for each environment state with the objective of minimizing the steady state mean time spent in orbit by an arbitrary customer, subject to cost and revenue constraints. Two numerical examples illustrate the main results.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2012
Accession Number
ADA560766

Entities

People

  • James D. Cordeiro
  • Jeffrey P. Kharoufeh

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Environment
  • Equations
  • Failure Mode And Effect Analysis
  • Inequalities
  • Infinite Series
  • Lyapunov Functions
  • Markov Chains
  • Numbers
  • Probability
  • Probability Distributions
  • Random Variables
  • Stability Conditions
  • Standards
  • Steady State
  • Stochastic Processes

Readers

  • Electronics Engineering
  • Facility/Structural Engineering.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space