Numerical Methods for a Class of Markov Chains Arising in Queueing Theory.

Abstract

An algorithm is discussed for computing the stationary probability vector of an infinite-state Markov chain whose transition probability matrix has a block-partitioned structure. Such matrices arise in a wide variety of queueing models as well as generalized random walk problems. Traditionally, the analytic approach to this type of problem has been through complex variable methods. An alternate and unified treatment of this problem is presented and an algorithm is obtained which utilizes only real arithmetic computations. In addition, most of the intermediate steps of the algorithm have useful probabilistic interpretations.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1978
Accession Number
ADA055946

Entities

People

  • David Michael Lucantoni
  • Marcel F. Neuts

Organizations

  • University of Delaware

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Complex Variables
  • Computations
  • Computer Science
  • Eigenvalues
  • Equations
  • Geometric Forms
  • Markov Chains
  • Mathematics
  • Probability
  • Queueing Theory
  • Random Variables
  • Random Walk
  • Stationary
  • Statistics
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Operations Research