Abstract
G-networks are a class of queueing networks introduced by E. Gelembe in 1989, which are characterized by the presence of positive and negative customers. Unlike classical queueing networks, the equations yielding the steady-state distribution of a G-network are nonlinear, resulting in the need of developing efficient numerical methods for their solution. In this talk we present two numerical methods for the computation of the steady-state distribution, namely a fixed point and a Newton-Raphson iteration. Using tools from nonnegative matrix theory, we prove that both methods are locally convergent to the fixed point, with linear and quadratic rate of convergence, respectively.We compare these methods with an existing algorithm, concluding that the Newton-Raphson iteration is a preferable choice for G-networks with a moderate number of queues. We conclude by suggesting a possible application for future research.