Associated Events

- Excursion to Lucca (a medioeval town close to Pisa), and social dinner on Wednesday from 15:00 to 23:00.

- Business meeting on thursday afternoon at 16:30.

- Short course on Matrix Analytic Methods for Fluid Flow Models by V. Ramaswami in Aula Faedo on Friday afternoon (15:00-17:00).

Abstract of the course.

Stochastic fluid flow models have been used extensively in a variety of areas such as dam and storage theories, insurance risk, and performance modeling. The canonical model of this type assumes a random environment governed by a finite state Markov chain which modulates the linear rate of change of the fluid level such that when the Markov chain is in state i, the fluid changes at rate ci per unit time.

Noting the model's similarity to a QBD, in 1999 I developed a steady state analysis of fluid flow models pursuing ideas similar to those in matrix geometric methods for Quasi-birth-and-death processes. Subsequently this theory has been developed further by me in several papers with Soohan Ahn. Overall, the approach has proven to be quite powerful in a variety of ways: (a) it reduces the continuous time, continuous state space problem to the consideration of a discrete state space QBD in discrete time; (b) it provides powerful algorithms that do not appear to suffer from the numerical instabilities of other types of methods; (c) it provides a systematic framework to analyze fluid flows and is based on probabilistic methods and path properties. The method is particularly interesting as it offers a potential for significant generalization and thereby opens up several interesting areas for further research.

The goal of this tutorial is to review the basic ideas and methods behind the matrix-geometric approach to fluid flow models. While key results can be derived by elementary methods, a rigorous approach justifying the steps necessitates some advanced tools like stochastic discretization, stochastic coupling, and stochastic process limits; we shall therefore also provide an intuitive understanding of this interplay with probability enabling an easier reading of the set of our papers in this area.

You can download here the presentation of the tutorial.

List of References