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@dm.unipi.it _______________________________________________ Settimanale mailing list Settimanale@mail.dm.unipi.it https://mail.dm.unipi.it/mailman/listinfo/settimanale