Section: New Results

Analytical fluid models

Participants : Raymond Marie, Bruno Sericola.

In [34] we published a chapter introducing fluid models, devoted to the practitioners in the field of telecommunications.

On the basis of the simple formulae and precise algorithms that we had obtained for the distribution of the buffer content of a finite or infinite capacity fluid queue  [138] fed by a Markovian queue or by an M/M/1 queue  [112] , we have obtained in [36] an algorithm to compute the transient distribution of a fluid queue driven by a birth and death process whose birth and death rates are suggested by a chain sequence, for which the stationary probabilities do not exist.

The transient analysis of a fluid queue driven by an M/M/1 queue has been considered in [41] and the general case of the birth and death process has been studied in [65] by means of results from spectral theory.