Server farms are popular architectures for computing infrastructures such as supercomputing centers, data centers and web server farms. As server farms become larger and their workloads more complex, designing efficient policies for managing the resources in server farms via trial-and error becomes intractable. In this thesis, we employ stochastic modeling and analysis techniques to understand the performance of such complex systems and to guide design of policies to optimize the performance. There is a rich literature on applying stochastic modeling to diverse application areas such as telecommunication networks, inventory management, production systems, and call centers, but there are numerous disconnects between the workloads and architectures of these traditional applications of stochastic modeling and how compute server farms operate, necessitating new analytical tools. To cite a few: (i) Unlike call durations, supercomputing jobs and file sizes have high variance in service requirements and this critically affects the optimality and performance of scheduling policies. (ii) Most existing analysis of server farms focuses on the First-Come- First-Served (FCFS) scheduling discipline, while time sharing servers (e.g., web and database servers) are better modeled by the Processor- Sharing (PS) scheduling discipline. (in) Time sharing systems typically exhibit thrashing (resource contention) which limits the achievable concurrency level, but traditional models of time sharing systems ignore this fundamental phenomenon. (iv) Recently, minimizing energy consumption has become an important metric in managing server farms. State-of-the-art servers come with multiple knobs to control energy consumption, but traditional queueing models don’t take the metric of energy consumption into account. In this thesis we attempt to bridge some of these disconnects by bringing the stochastic modeling and analysis literature closer to the realities of today’s compute server farms. We introduce new queueing models for computing server farms, develop new stochastic analysis techniques to evaluate and understand these queueing models, and use the analysis to propose resource management algorithms to optimize their performance.

This dissertation is a systematic study of electric power distribution system reliability evaluation and improvement. Reliability evaluation of electric power systems has traditionally been an integral part of planning and operation. Changes in the electric utility coupled with aging electric apparatus create a need for more realistic techniques for power system reliability modeling. This work presents a reliability evaluation technique that combines set theory and Graph Trace Analysis (GTA). Unlike the traditional Markov approach, this technique provides a fast solution for large system reliability evaluation by managing computer memory efficiently with iterators, assuming a single failure at a time. A reconfiguration for restoration algorithm is also created to enhance the accuracy of the reliability evaluation, considering multiple concurrent failures. As opposed to most restoration simulation methods used in reliability analysis, which convert restoration problems into mathematical models and only can solve radial systems, this new algorithm seeks the reconfiguration solution from topology characteristics of the network itself. As a result the new reconfiguration algorithm can handle systems with loops. In analyzing system reliability, this research takes into account time-varying load patterns, and seeks approaches that are financially justified. An exhaustive search scheme is used to calculate optimal locations for Distributed Generators (DG) from the reliability point of view. A Discrete Ascent Optimal Programming (DAOP) load shifting approach is proposed to provide low cost, reliability improvement solutions. As weather conditions have an important effect on distribution component failure rates, the influence of different types of storms has been incorporated into this study. Storm outage models are created based on ten years' worth of weather and power outage data. An observer is designed to predict the number of outages for an approaching or on going storm. A circuit corridor model is applied to investigate the relationship between power outages and lightning activity. / Ph. D.

A new approach to the evaluation of the reliability of electrical systems is presented. In this approach a Graph Trace Analysis based approach is applied to integrated system models and reliability analysis. The analysis zones are extended from the traditional power system functional zones. The systems are modeled using containers with iterators, where the iterators manage graph edges and are used to process through the topology of the graph. The analysis provides a means of computationally handling dependent outages and cascading failures. The effects of adverse weather, time-varying loads, equipment age, installation environment, operation conditions are considered. Sequential Monte Carlo simulation is used to evaluate the reliability changes for different system configurations, including distributed generation and transmission lines. Historical weather records and loading are used to update the component failure rates on-the-fly. Simulation results are compared against historical reliability field measurements. Given a large and complex plant to operate, a real-time understanding of the networks and their situational reliability is important to operational decision support. This dissertation also introduces using an Integrated System Model in helping operators to minimize real-time problems. A real-time simulation architecture is described, which predicts where problems may occur, how serious they may be, and what is the possible root cause. / Ph. D.