In the analysis and design of computer systems and communication networks, difficulties often arise due to the so-called "Curse of Dimensionality"--prohibitive computational requirements for large size systems. When the system is small, we can often get accurate results. As the system size grows, the computational burdens become overwhelming. In this dissertation, we propose a unified approach, Global Rational Approximation (GRA), to tackle this "Curse of Dimensionality" problem from the standpoint of systems analysis. We observe that quite often the accurate evaluation of such systems is feasible when the system size is small. On the other hand, an impressive amount of knowledge has been accumulated in the past decade regarding the qualitative behavior such as monotonicity, convexity, boundedness and the asymptotic properties of the performance functions for very general computer/communication systems. The central idea of our approach is to take advantage of the knowledge of the down-sized systems, as well as the asymptotic properties, and to finally yield good estimates of performance for large size systems. The performance values of down-sized systems can be obtained either from analytic methods or from simulations. This work establishes the theoretical foundation for the GRA approach. Two types of rational approximants are proposed. An approximation scheme of generating sequence of approximants is also proposed. As an important application of the GRA approach, the dissertation discusses the issue of supporting quality-of-service (QoS) guarantees, in specific, calculation of cell loss probabilities, in ATM networks. The dissertation also discusses the applications of the GRA approach in many other computer/communication systems. In an example of multiprocessor systems, we consider a model of a particular architecture with single bus and distributed common memory. For the queue inference engine problem, the mean queue length area is obtained using GRAs. For large Markov chain with certain regularity (with the stochastically monotone transition matrix), we also apply the GRA approach to obtain the stationary probability distribution. The theoretical and numerical results indicate that the GRA approach could be a promising tool for many applications in many computer systems and communication networks.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-7544 |
| Date | 01 January 1996 |
| Creators | Yang, Hong |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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