Aggregate Matrix Analytic Techniques: Theory and Applications
                    Evgenia Smirni
              College of William and Mary 
              http://www.cs.wm.edu/~esmirni

Over the last two decades, considerable effort has been put into the
development of matrix analytic techniques for the exact analysis of 
a general and frequently encountered class of queuing models. In these 
models, the embedded Markov chains are two-dimensional
generalizations of elementary GI/M/1 and M/G/1 queues, and
their intersection, i.e., quasi-birth-death (QBD) processes. GI/M/1 and M/G/1
queues model systems with  interarrival and service times characterized,
respectively,  by general distributions rather than simple exponentials
and are often used as the modeling tool of choice in modern computer and
communication systems. 

In the first part of this talk, I will present a new methodology, called 
ETAQA, for the analysis of queuing systems subjected to general distributions. 
ETAQA uses basic, well-known results for Markov chains
by exploiting the structure of the repetitive portion of the chain and
recasting the overall problem into the computation of the solution of a
finite linear system.  The proposed methodology is exact, numerically stable,
and can yield significantly less expensive solutions when compared with
other methods.
In the second part of the talk, I will present the use of ETAQA for 
evaluating load balancing policies in clustered web servers and conclude
with a discussion of on-going research projects.