Computing Stochastical Bounds for the Tail Distribution of an M/GI/1 Queue

Packet switching networks lead mostly to M/GI/1 queue models. In this paper, computing methods are designed in order to get quickly approximate values for response time of these networks. Laplace transform is a powerful tool to study such queuing systems. But inversion of the Laplace transform on the real line is well known to be an illconditioned problem and usual numerical methods of inversion fail to give accurate error bounds. A new method to address this old problem is a orded by the recently developed formal computing tools: exact computations can be done during the rst steps of calculation, while usual oating point computations remain con ned to the last steps. Applying that method to an M/GI/1 queue, a formal approach is designed, leading to proven bounds, and several numerical improvements are proposed. Accurate bounds are obtained.