Estimating Bottlenecks of Very Large Models

Queueing theory has been extensively used since 70’s to carry out performance evaluations of complex computer systems. However, handling the complexity of modern computer networks with thousands of servers and millions of customers is still a challenge. Indeed, although the identification of product-form queueing networks has promoted the development of computationally tractable exact solution techniques, the dimensionality of “very large” models makes it difficult to meet the requirements of either exact and approximate algorithms. In this paper we focus on the bottleneck analysis as a technique that may provide answers to many capacity planning questions (e.g., “which is the maximum number of transactions per second the computer system is able to process?” or “which is the minimum response time that can be achieved per transaction?”) for “very large” computer installations with a limited complexity. The problem to be solved with this technique is the identification of the set of resources that may saturate among the thousands of components. We show some results concerning the application of the theory of convex polyhedra to bottleneck analysis that can sensibly reduce the complexity of the analysis. The connections between this technique and the behavior of closed and open models are also investigated.