## Section: New Results

### Analytical techniques in queueing models

Participants : Gerardo Rubino, Bruno Sericola.

In [25] , we expose a clear methodology to analyze maximum level and hitting probabilities in a Markov driven fluid queue for various initial condition scenarios and in both cases of infinite and finite buffers. Step by step we build up our argument that finally leads to matrix differential Riccati equations for which there exists a unique solution. The power of the methodology resides in the simple probabilistic argument used that permits to obtain analytic solutions of these differential equations. We illustrate our results by a comprehensive fluid model that we exactly solve.

In [66] , [64] and [30] we presented some preliminary results on two general and basic problems related to queueing systems. In [66] we extended results obtained some years ago, concerning a new queueing paradigm, better adapted to models of nodes in a communication network than standard queueing models. In the paper written some years ago, we basically developed a Mean Value Analysis of a M/GI/1 model when the data occupying the buffers is seen at the bit level. The extension proposed in [66] mainly consists in deriving results about other models (for instance, belonging to the G/M/1 family), and in deriving also analytical expressions for second moments of the metrics of interest. In [64] we discuss the concept of power of a queueing model proposed by Kleinrock in the 80s, we give some new results about it and underline some weaknesses of Kleinrock's definition. These results are extended in [30] , where alternative definitions are explored.