ETAQA: An Efficient Technique for the Analysis of QBD-processes by Aggregation Gianfranco Ciardo, Evgenia Smirni 1 Department of Computer Science, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795 {ciardo,esmirni}@cs.wm.edu Abstract In this paper we present ETAQA, an Efficient Technique for the Analysis of QBD-processes by Aggregation. We concentrate on processes satisfying a particular repetitive structure that frequently occurs in modeling of computer and communica- tion systems. The proposed methodology exploits this special structure to evaluate the aggregate probability distribution of the states in each of the equivalence classes corresponding to a specific partitioning of the state space. Although the method does not compute the probability distribution of all states in the chain, not even in implicit recursive form, it provides the necessary information to easily compute an extensive set of Markov reward functions such as the queue length or any of its higher moments. The proposed technique has excellent computational and storage complexity and results in significant savings when compared with other traditional solution techniques such as the matrix geometric approach. Keywords: Markov chains; quasi-birth-death processes; matrix-geometric technique; computer system modeling. 1 Introduction Over the last two decades, considerable effort has been put into the develop- ment of techniques for the exact analysis of a general and frequently encoun- tered class of queuing models. In these models, the embedded Markov chains are two-dimensional generalizations of those arising from the embedding of elementary M/G/1 or G/M/1 queues [7]. The intersection of these two cases 1 This research was supported by a William and Mary Summer Research Grant. Preprint submitted to Elsevier Science 3 September 2002