Moment Formulas for the Markov Renewal Branching Process.

Abstract

There are many queueing models in which there appears a semi-Markov matrix G(.), whose entries are absorption time distributions in a Markov renewal branching process. The role of G(.) is similar to that of the busy period in the simple M/G/1 model. The computation of various quantities associated with G(.) is however much more complicated. The moment matrices, and particularly the mean matrix of G(.), are essential in the construction of general and mathematically well-justified algorithms for the steady-state distributions of such queues. This paper discusses the moment matrices of G(.) and algorithms for their numerical computation. Its contents are basic to the algorithmic solutions to several queueing models, which are to be presented in follow-up papers.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1975
Accession Number
ADA017615

Entities

People

  • Marcel F. Neuts

Organizations

  • Purdue University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Absorption
  • Algorithms
  • Computations
  • Construction
  • Mathematical Analysis
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Parallel and Distributed Computing.
  • Statistical inference.