The minimal positive solution of nonsymmetric algebraic Riccati equations arising from transport theory, can be obtained by computing the one of two vector equations. Some existing methods such as simple iteration method, converge slowly in the singular case, but this drawback can be improved with the shift technique. When using the shift technique, a parameter will be used. In this paper, the parameter's effects on the convergence rate of four existing methods for solving the vector equations and its optimal value in a given interval is given. Numerical results are presented to demonstrate theoretical analysis.