On the Use of Analytic Matric Functions in Queueing Theory,

Abstract

In the thesis the author defines an analytic matric function F(.) by F(X) = the summation from N = 0 to infinity of ((F sub N)(X sup N)) where F sub n, X are mxm complex matrices. In chapter 1 the author discusses a fixed point theorem for such functions and then in subsequent chapters he analyzes various queueing models where these occur. The basic problem in each of the queueing models analyzed reduces to the solution of a non-linear matrix integral equation of Volterra type. By use of the fixed point theorem of Chapter 1 the author shows that the non-linear integral equation has a unique solution. The complete transient behavior of each queue may be expressed in terms of the solution of the integral equation. For each model, the equilibrium condition is also determined. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1972
Accession Number
AD0737251

Entities

People

  • Peter Purdue

Organizations

  • Purdue University

Tags

DTIC Thesaurus Topics

  • Arrhenius Equation
  • Equations
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Point Theorem
  • Queueing Theory
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra
  • Statistical inference.