On the numerical solution of a structured nonsymmetric algebraic Riccati equation

A class of nonsymmetric algebraic Riccati equation, where one of the two linear coefficients is block diagonal, is studied. These equations arise in the modeling of an adaptive MMAPK]/PHK]/1$MMAPK]/PHK]/1$ queue. Some theoretical results are proved, and two new algorithms are introduced that exploit the diagonal structure of the linear coefficient.