Défense de thèse de doctorat par Eleonora DEIANA

Sojourn time distribution in fluid queues with reactions at boundaries

In this thesis we analyse different fluid queues with complex behaviours, inspired by applications.

Intuitively, a fluid queue is composed by a buffer or recipient, filled up and emptied out with some fluid. The content of the buffer varies through time depending on an underlying continuous time Markov process. We talk about a reactive fluid queue if the fluid queue changes its behaviour when the buffer content reaches particular levels. In this thesis we present different example of reactive fluids, such as fluid with jumps in level 0, vacation servers, finite buffer with general behaviour, and more.

Traditionally, the focus of the analysis of a fluid queue is on the characterisation of the joint stationary distribution of the level and phase, used to obtain performance measures of the system. This allows to analyse the fluid queue from the point of view of the system. But another perspective is possible, and in this thesis, we also analyse the fluid queue from the point of view of the users, through the analysis of the sojourn time distribution.

This is obtained through a two-step approach. First, we obtain the distribution of the buffer content at arrival epochs. We then consider the time needed for a unit of fluid to leave the buffer when only considering the output rates.

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