Abstract: If it is going to have practical significance, the evaluation of overflow probabilities must be (1) precise, (2) computationaly stable and (3) real time compatible. The existing approximation expressions are gotten by using the traditional fluid-flow analytic techniques, which are mostly based on spectral analysis. The limitation of this approach comes from numerical difficulties caries by the spectral approach. In this paper, we suggested a fluid-flow approach in evaluating the overflow probability, which fully satisfies the above stated criteria, and removes the numerical difficulties of existing methods. The authors approach is based on the renewal argument and exploiting the similarity between fluid queues and Quasi-Birth-and-Death (QBD) processes.
Keywords: Fluid queues, Quasi-birth-and-death processes, Approximating method, ON/OFF model.