ETAQA: an efficient technique for the analysis of QBD-processes by aggregation

In this paper we present ETAQA, an Efficient Technique for the Analysis of QBD-processes by Aggregation. We concentrate on procyesses satisfying a particular repetitive structure that frequently occurs in modeling of computer and communication 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.