Aggregate Matrix Analytic Techniques: Theory and Applications Evgenia Smirni (College of William and Mary)

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Aggregate Matrix Analytic Techniques Theory and
ApplicationsEvgenia Smirni (College of William
and Mary)
Seminar Series23th January
Abstract 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. McBryde 655 ,at 4 p.m.