On An Exact Solution Of The Rate Matrix Of Quasi-Birth-Death Process With Small Number Of Phases

Abstract

A new method of obtaining exact solution for the rate matrix R in the Matrix-Analytic method in case of the phase state of dimension two is proposed. The method is based on symbolic solution of the determinental polynomial equation, and obtaining a linear matrix equation for the unknown rate matrix R by Cayley-Hamilton theorem. The method is applied to analyze the Energy-Performance tradeoff of an Internet-of-Things device. A new randomized regime switching scheme is proposed, which, as it is shown by means of numerical experiment, provides significant decrease of energy consumption of the system under study.