AN ALTERNATIVE PROOF OF A THEOREM OF TAKACS ON THE GI/M/1 QUEUE.

Abstract

An analytic proof is given of the fact that the stationary distribution for the imbedded Markov chain in a GI/M/1 queue is geometric. A generating function for the stationary transition probabilities is obtained as the unique solution to an integro-differential equation, which may be solved by reduction to a Wiener-Hopf equation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1965
Accession Number
AD0618530

Entities

People

  • Marcel F. Neuts

Organizations

  • Purdue University

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Markov Chains
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Probability
  • Real Variables
  • Stationary
  • Transitions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.