Development of Planning And Evaluation Models For Superstreets

Despite the extensive implementation of Superstreets on congested arterials, reliable methodologies for such designs remain unavailable. The purpose of this research is to fill the information gap by offering reliable tools to assist traffic professionals in the design of Superstreets with and without signal control. The entire tool developed in this thesis consists of three models. The first model is used to determine the minimum U-turn offset length for an Un-signalized Superstreet, given the arterial headway distribution of the traffic flows and the distribution of critical gaps among drivers. The second model is designed to estimate the queue size and its variation on each critical link in a signalized Superstreet, based on the given signal plan and the range of observed volumes. Recognizing that the operational performance of a Superstreet cannot be achieved without an effective signal plan, the third model is developed to produce a signal optimization method that can generate progression offsets for heavy arterial flows moving into and out of such an intersection design.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Joint Optimization for Social Content Delivery in Wireless Networks

Over the last decade, success of social networks has significantly reshaped how people consume information. Recommendation of contents based on user profiles is well-received. However, as users become dominantly mobile, little is done to consider the impacts of the wireless environment, especially the capacity constraints and changing channel. In this dissertation, we investigate a centralized wireless content delivery system, aiming to optimize overall user experience given the capacity constraints of the wireless networks, by deciding what contents to deliver, when and how. We propose a scheduling framework that incorporates content-based reward and deliverability. Our approach utilizes the broadcast nature of wireless communication and social nature of content, by multicasting and precaching. Results indicate this novel joint optimization approach outperforms existing layered systems that separate recommendation and delivery, especially when the wireless network is operating at maximum capacity. Utilizing limited number of transmission modes, we significantly reduce the complexity of the optimization. We also introduce the design of a hybrid system to handle transmissions for both system recommended contents ('push') and active user requests ('pull'). Further, we extend the joint optimization framework to the wireless infrastructure with multiple base stations. The problem becomes much harder in that there are many more system configurations, including but not limited to power allocation and how resources are shared among the base stations ('out-of-band' in which base stations transmit with dedicated spectrum resources, thus no interference; and 'in-band' in which they share the spectrum and need to mitigate interference). We propose a scalable two-phase scheduling framework: 1) each base station obtains delivery decisions and resource allocation individually; 2) the system consolidates the decisions and allocations, reducing redundant transmissions. Additionally, if the social network applications could provide the predictions of how the social contents disseminate, the wireless networks could schedule the transmissions accordingly and significantly improve the dissemination performance by reducing the delivery delay. We propose a novel method utilizing: 1) hybrid systems to handle active disseminating requests; and 2) predictions of dissemination dynamics from the social network applications. This method could mitigate the performance degradation for content dissemination due to wireless delivery delay. Results indicate that our proposed system design is both efficient and easy to implement.

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.