ETD

• G-network
• Iterative Methods
• Newton-Raphson Iteration.
• Nonnegative Matrices
• Numerical Analysis
• Queueing Network

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. Negative customers have the capability to destroy a positive customer present in a queue, thus reducing the workload. Under ergodicity condition the steady-state distribution of the network is given as the product of the marginal distributions of each queue, but unlike classical queueing network the equation yelding the steady-state distribution are non-linear. In this thesis we develeop two new numerical methods for the computation of the steady-state distribution. Rewriting the problem as a fixed point matrix equation, we study a fixed point iteration and a Newton-Raphson iteration. We prove that both the methods converge, with linear and quadratic rate respectively, choosing the starting value in a neighbourhood of the fixed point. We then compare these methods with an existing algorithm develped by Fourneau, concluding that the Newton-Raphson iteration is preferable for moderate-sized G-networks.