Approximate MVA Algorithms for Solving Queueing Network ModelsHai

As distributed systems such as Internet and Integrated Services Digital Networks (ISDN) become increasingly complex, the interactions among numerous components and workloads make system performance diicult to predict reliably. It is increasingly important to apply suitable performance evaluation tools to aid system analysis and design, system connguration and capacity planning, and resource management. Queueing network models are widely adopted for the performance evaluation of computer systems and communication networks. Approximate Mean Value Analysis (MVA) is a popular technique for analyzing queueing networks because of the eeciency and accuracy that it aaords. In this thesis, all of the existing approximate MVA algorithms for separable queue-ing networks are surveyed. New numerical and complexity analysis results for existing approximate MVA algorithms are presented. The relative merits and tradeoos of diier-ent implementations of the existing approximate MVA algorithms are examined quantitatively. Furthermore, two new approximate MVA algorithms, the Queue Line (QL) algorithm and the Fraction Line (FL) algorithm, for multiple class separable queueing networks are presented. Both the QL and FL algorithms are analyzed with respect to i their computational costs and accuracies. Based on theoretical and empirical results, the QL algorithm is always more accurate than, and yet has the same computational eeciency as, the Bard-Schweitzer Proportional Estimation (PE) algorithm, the most popular approximate MVA algorithm. The FL algorithm has the same computational cost and yet yields more accurate solutions than both the QL and PE algorithms for noncongested separable queueing networks. The existence, uniqueness, and convergence properties of the solutions of these two algorithms are also investigated. The QL algorithm can replace the PE algorithm in a spectrum based on the trade-oo between computational costs and accuracies of all of the approximate MVA algorithms. ii Acknowledgements I am deeply indebted to my supervisor, Professor K. C. Sevcik, for the guidance and encouragement that he has given me. His innuence on this work and my graduate career has been great. I would like to express my gratitude to Professor K. R. Jackson for his valuable suggestions that have helped to improve this thesis to a great extent, especially for his proof of the convergence rate. Many people have aided me over the years in ways both academic and personal. My thanks to all of them. I would like in particular to acknowledge the innuence of my grandparents and my parents. If there were to be a dedication of this work, it would be …