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

Abstract

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 ill-conditioned problem and usual numerical methods of inversion fail to give accurate error bounds. A new method to address this old problem is afforded by the recently developed formal computing tools: exact computations can be done during the first steps of calculation, while usual floating point computations remain confined 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.