# [CvGmt News] [Notiziario] [Settimanale] Avviso di Seminario

Giulia Curciarello curciare at dm.unipi.it
Wed Dec 10 08:36:03 CET 2003

Martedi' 16 dicembre, ore 10, Sala dei Seminari
Evgenia Smirni, College of William and Mary, Williamsburg

TITOLO:
Exact Aggregate Solutions for Infinite Markov Processes with Repetitive
Structure

ABSTRACT:
We introduce a new methodology for the exact analysis of M/G/1 and
GI/M/1-type processes, and their intersection, i.e., quasi-birth-death
processes.

The proposed methodology exploits the repetitive structure of the infinite
portion of the chain and derives a finite system of linear equations.

In contrast to the classic techniques for the solution of such systems,
the solution of this finite linear system {\em does not} provide the
entire probability distribution of the state space but simply allows for
the calculation of the aggregate probability of a finite set of classes of
states from the state space, appropriately defined.

Nonetheless, these aggregate probabilities allow for the computation of a
rich set of measures of interest such as the system queue length or any of
its higher moments.

The proposed methodology is exact and, for the case of M/G/1-type
processes, it compares favorably to the classic methods as shown by
detailed time and space complexity analysis. Detailed experimentation
further corroborates that the proposed methodology provides significantly
less expensive solutions when compared to the classic methods.

Examples that show how this method can be used to model load balancing
policies in clustered web servers will be presented as well as some
discussion of on-going projects.

Giulia Curciarello
Segreteria Didattica
tel: 050-2213219
e-mail curicare at dm.unipi.it
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