The Modified Covering Problem (MCP) is introduced and theory is developed for solving it on paths and trees. First, the Modified Covering Problem is defined as a subset of the Conditional Covering Problem, and motivations are proposed for its study. Next, a literature review examines relevant, published material. The MCP is then formulated as a binary integer program, followed by an examination of the characteristics of its feasible solutions, optimality, and overall complexity. A polynomial algorithm is developed for the solving the MCP on paths with uniform link distances, and solving within 20% of optimality on paths with non-uniform link distances. Next, an exponential algorithm is developed to solve non-uniform link distance problems to optimality. The theory is then further expanded to construct an algorithm to develop strong upper and lower bounds for the optimal solution on trees with non-uniform link distances.

This thesis proposes a methodology for factory layout synthesis that combines the symbolic and numerical approaches. The layout model is represented as a loosely packed arrangement of rectangles with sides parallel to two orthogonal directions. Solutions must satisfy a set of qualitative and quantitative constraints and must optimize material handling costs. Qualitative constraints are specified using a rule based approach. Quantitative constraints and material handling costs are incorporated into a numerical, non linear-optimization problem. Optimal solutions are generated by inserting one device at the time in all admissible locations on the floorplan. The resulting partial layouts are optimized with respect to material handling costs. Then, the best partial solution obtained so far is the starting point for the next object insertion. The process stops when all devices have been placed. To illustrate the methodology, three case studies are presented.

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<p> Extreme risks associated with natural and man-made disasters involve disruptions in the production of goods or provision of services in interdependent systems. The reduced supply of critical goods and services will degrade "as planned" production outputs and create ripple effects of direct and indirect disruptions. Input-output modeling evaluates the propagation of disaster consequences by quantifying the associated economic risks of disruption, namely economic loss and inoperability, for multi-sectoral economic regions. The thesis enhances the reliability of these risk estimates by formulating a stochastic inventory-based risk assessment model using a multi-objective optimization framework for minimizing (i) economic losses, and (ii) sector inoperability. The research utilizes inventory-to-sales ratio data from the Bureau of Economic Analysis for modeling uncertainty in the levels of finished goods inventory and the beta distribution to integrate uncertainty in decision-maker preferences associated with the multi-objective framework. The framework focuses on the development of a holistic, flexible and scalable decision support system through a Dynamic Cross Prioritization Plot (DCPP) for identifying inventory enhancement opportunities among critically disrupted systems that is applicable to different regions and disaster scenarios. </p>

<p> With the advent of inexpensive computing and efficient power electronics, the load mix in commercial buildings has experienced a fundamental shift away from almost exclusively traditional alternating current (AC) loads toward primarily direct current (DC) loads&mdash;devices which use DC electricity either for end-use or as a power conditioning stage. Simultaneously, installations of DC distributed generation sources for commercial buildings, such as rooftop photovoltaic arrays, are accelerating. Despite this proliferation of DC devices, the basic design of building electrical distribution systems has changed very little in the past century: AC distribution remains the industry standard. The AC-DC electricity conversions required to connect DC sources and loads to the AC electric grid result in wasted energy. Partial replacement of AC distribution with DC distribution can improve overall building electrical energy efficiency; the result is a mixed AC-DC electrical distribution system. This dissertation develops a modeling framework, mathematical program, and global optimization algorithm which determine maximally energy efficient designs for mixed AC-DC building electrical distribution systems. The research approach precisely quantifies building electrical energy efficiency at a systems level, not simply the level of individual devices. The results of two case studies validate the power of the optimization algorithm and demonstrate that well designed mixed AC-DC building electrical distribution systems can achieve higher efficiency than either AC or DC distribution used alone.</p>

To handle the growing demands of data intensive applications, storage consolidation is becoming an attractive organizational paradigm. The benefits of consolidation include universal data access, sharing among users, flexibility in allocation and provisioning, and economies of centralized infrastructure management. While high-end storage arrays deliver high performance and reliability, they generally lack support for providing quality of service (QoS) guarantees. Providing best effort service alone may no longer be sufficient in future shared storage systems serving diverse client workloads. Consequently, there is a growing need for storage systems to provide mechanisms for isolating applications from each other and providing differentiated QoS to them based on their needs. Existing approaches for QoS provisioning in storage servers fall into three different categories: (1) Bandwidth allocation mechanisms, (2) Time slicing at the devices, and (3) Control theoretic approaches. However all of these approaches have shortcomings that discourage their practical use. The challenges include dealing with bursty workloads, access locality, variable workload-dependent server capacity, and the impact of fairness mechanisms on overall throughput. This dissertation makes two major contributions towards making QoS in storage systems a reality and bridging the gap between theory and practice. First, we provide algorithms with stronger performance guarantees, robust behavior, and ability to handle storage specific issues such as bursts and variable capacity. Second, we provide a framework to evaluate and improve I/O efficiency of QoS mechanisms. Towards the first goal, we propose pClock, which has several benefits over existing approaches, namely (i) ability to handle bursts in workloads (ii) de-coupling bandwidth and latency allocation (iii) allocating spare capacity to background jobs in large chunks thereby increasing efficiency. To handle the variable system capacity of storage systems, we propose the Reservation Based Fair Queuing (RBFQ) algorithm, that guarantees a certain reserved capacity to each application, while allocating the remaining capacity in a proportionate manner. We also adapt RBFQ to work in distributed storage systems such as FAB [SFV+04] and IceCube [W +06]. The algorithm provides global bandwidth in proportion to application weights while avoiding starvation at any resource. QoS and efficiency are two strongly opposing forces when it comes to sharing of I/O devices, and it is a challenge to achieve both simultaneously. We explore this trade off in further detail, and propose an adaptive algorithm for improving the I/O efficiency of fair schedulers. We show the robustness of our model by analysis and by implementing and evaluating the algorithms on real systems.

This thesis introduces a new interpretation of the problems arising in robust model predictive control (MPC). In practice, MPC algorithms are typically embedded within a multi-level hierarchy of control functions. The MPC algorithm itself is usually implemented in two pieces: a steady-state target calculation followed by a dynamic optimization. It is shown in this thesis that some of the most promising methods of imparting robustness to MPC algorithms result in semi-infinite programs. These programs arise from the addition of semi-infinite constraints to the nominal MPC algorithms which come from theoretical arguments that guarantee stability of the closed loop system or from requiring existing constraints to hold for an infinite set of plants. While the number of constrained variables is finite, the constraint must hold over an infinite set. This infinite set corresponds to a continuous uncertainty description for the model parameters. In this dissertation it is also shown that the resulting optimization problems have a very unique structure. For some MPC algorithms the semi-infinite program (SIP) can be cast as an equivalent finite-dimensional nonlinear convex program. Primal-dual interior-point methods are used to efficiently solve the resulting optimization problem by exploiting its inherent convexity. Simulation examples illustrate the effects of uncertainty on nominal MPC algorithms and demonstrate the advantages of interior-point methods.

Parallel I/O architectures have become attractive in the context of high performance computing and services provided by high bandwidth data centers. It is challenging to provide a scheduling technique that maximizes throughput and can provide QoS guarantees. In this thesis we first introduce the problem of maximizing the throughput for a parallel I/O system that is simultaneously accessed by several concurrent applications. We show that the problem of obtaining a minimum length schedule is NP-complete. We present fairness metrics for parallel I/O and provide fair scheduling schemes for some representative situations. In particular we study schemes that support fairness at every I/O step (local fairness) and during a certain window of time (global fairness). We also present a more general algorithm for weighted allocation of disk system bandwidth to multiple reference strings. All the three algorithms have low polynomial time complexity and they are work conserving.

The commute by automobile, as it happens in Houston Texas, is a spatial envelope. This envelope widens and narrows based on a set of variables: position, traffic, speed, and time of day, and it changes from day to day. The project is a study of and an intervention into this spatial envelope of the commute. The intervention takes the form of a gas station located on a feeder road adjacent to a freeway. Video is both a means of study of the commute, and a tool for the design of the station.