Queueing Theory: Rouche's Theorem: Localization Theorem

EasyChair Preprint 13550

Abstract

Traditionally,  in   the  analysis  of  queueing  models  based  on  complex  analysis  method 

                and  the  associated   Skip  Free  Markov  chain  based  models, Rouche’s  Theorem  is 

                invoked  to  determine  the  eigenvalues  of  the  recursion  matrix,  called  rate  matrix     

                which  is  the  solution  of  a  matrix  polynomial/ matrix  power  series  equation.  In  this 

                research  paper,  we  provide  a  simple  proof  of  the  Localization  Theorem  using  the 

                linear  algebraic  arguments.  We  also,  prove  a  generalized   Perron  Theorem  associated 

                with  a  polynomial  matrix

Keyphrases: Localization Theorem, Matrix Polynomial Equation, Rate matrix, Rouche's Theorem, eigenvalues

@booklet{EasyChair:13550,
  author    = {Rama Garimella and Rumyantsev Alexander},
  title     = {Queueing  Theory: Rouche's  Theorem: Localization Theorem},
  howpublished = {EasyChair Preprint 13550},
  year      = {EasyChair, 2024}}