Download PDFOpen PDF in browserQueueing Theory: Rouche's Theorem: Localization TheoremEasyChair Preprint 135506 pages•Date: June 5, 2024AbstractTraditionally, 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
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