This dissertation addresses the development of integrative modeling strategies capable of combining deterministic and stochastic, discrete and continuous, as well as multi-scale features. The first set of studies combines the purely deterministic modeling methodology of Biochemical Systems Theory (BST) with a hybrid approach, using Functional Petri Nets, which permits the account of discrete features or events, stochasticity, and different types of delays. The efficiency and significance of this combination is demonstrated with several examples, including generic biochemical networks with feedback controls, gene regulatory modules, and dopamine based neuronal signal transduction. A study expanding the use of stochasticity toward systems with small numbers of molecules proposes a rather general strategy for converting a deterministic process model into a corresponding stochastic model. The strategy characterizes the mathematical connection between a stochastic framework and the deterministic analog. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations where internal noise affecting the system needs to be taken into account for a valid conversion from a deterministic to a stochastic model. The conversion procedure is illustrated with several representative examples, including elemental reactions, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. The last study establishes two novel, particle-based methods to simulate biochemical diffusion-reaction systems within crowded environments. These simulation methods effectively simulate and quantify crowding effects, including reduced reaction volumes, reduced diffusion rates, and reduced accessibility between potentially reacting particles. The proposed methods account for fractal-like kinetics, where the reaction rate depends on the local concentrations of the molecules undergoing the reaction. Rooted in an agent based modeling framework, this aspect of the methods offers the capacity to address sophisticated intracellular spatial effects, such as macromolecular crowding, active transport along cytoskeleton structures, and reactions on heterogeneous surfaces, as well as in porous media. Taken together, the work in this dissertation successfully developed theories and simulation methods which extend the deterministic, continuous framework of Biochemical Systems Theory to allow the account of delays, stochasticity, discrete features or events, and spatial effects for the modeling of biological systems, which are hybrid and multiscale by nature.

The design and operation of a high volume conveyor sortation system are important due to its high cost, large footprint and critical role in the system. In this thesis, we study the characteristics of the conveyor sortation system from performance evaluation and design perspectives employing continuous modeling approaches. We present two continuous conveyor models (Delay and Stock Model and Batch on Conveyor Model) with different representation accuracy in a unified mathematical framework. Based on the Batch on Conveyor Model, we develop a fast fluid simulation methodology. We address the feasibility of implementing fluid simulation from modeling capabilities, algorithm design and simulation performance in terms of accuracy and simulation time. From a design perspective, we focus on rates determination and accumulation design in the accumulation and merge subsystem. The optimization problem is to find a minimum cost design that satisfies some predefined performance requirements under stochastic conditions. We first transform this stochastic programming problem into a deterministic nonlinear programming problem through sample path based optimization method. A gradient based method is adopted to solve the deterministic problem. Since there is no closed form for performance metric even for a deterministic input stream, we adopt continuous modeling to develop deterministic performance evaluation models and conduct sensitivity analysis on these models. We explore the prospects of using the two continuous conveyor models we presented.

Zero energy houses and (near) zero energy buildings are among the most ambitious targets of society moving towards an energy efficient built environment. The "zero" energy consumption is most often judged on a yearly basis and should thus be interpreted as yearly net zero energy. The fully self sustainable, i.e. off-grid, home poses a major challenge due to the dynamic nature of building load profiles, ambient weather condition and occupant needs. In current practice, the off-grid status is accomplishable only by relying on backup generators or utilizing a large energy storage system. The research develops a risk based holistic system design method to guarantee a match between onsite sustainable energy generation and energy demand of systems and occupants. Energy self-sufficiency is the essential constraint that drives the design process. It starts with information collection of occupants' need in terms of life style, risk perception, and budget planning. These inputs are stated as probabilistic risk constraints that are applied during design evolution. Risk expressions are developed based on the relationships between power unavailability criteria and "damages" as perceived by occupants. A power reliability assessment algorithm is developed to aggregate the system underperformance causes and estimate all possible power availability outcomes of an off-grid house design. Based on these foundations, the design problem of an off-grid house is formulated as a stochastic programming problem with probabilistic constraints. The results show that inherent risks in weather patterns dominate the risk level of off-grid houses if current power unavailability criteria are used. It is concluded that a realistic and economic design of an off-grid house can only be achieved after an appropriate design weather file is developed for risk conscious design methods. The second stage of the research deals with the potential risk mitigation when an intelligent energy management system is installed. A stochastic model based predictive controller is implemented to manage energy allocation to sub individual functions in the off-grid house during operation. The controller determines in real time the priority of energy consuming activities and functions. The re-evaluation of the risk indices show that the proposed controller helps occupants to reduce damages related to power unavailability, and increase thermal comfort performance of the house. The research provides a risk oriented view on the energy self-sufficiency of off-grid solar houses. Uncertainty analysis is used to verify the match between onsite sustainable energy supply and demand under dynamic ambient conditions in a manner that reveals the risks induced by the fact that new technologies may not perform as well as expected. Furthermore, taking occupants' needs based on their risk perception as constraints in design evolution provides better guarantees for right sized system design.

This thesis is focused on airport departure operations; its objective is to assign a value to surface surveillance information within a collaborative framework. The research develops a cooperative concept that improves the control of departure operations at busy airports and evaluates its merit using a classical and widely accepted airport departure model. The research then assumes departure operations are collaboratively controlled and develops a stochastic model of taxi operations on the airport surface. Finally, this study investigates the effect of feeding back different levels of surface surveillance information to the departure control process. More specifically, it examines the environmental and operational impact of aircraft surface location information on the taxi clearance process. Benefits are evaluated by measuring and comparing engine emissions for given runway utilization rates.

Build-Operate-Transfer (BOT) is a form of Public-Private Partnerships that is commonly used to close the growing gap between the cost of developing and modernizing transportation infrastructure systems and the financial resources available to governments. When assessing the feasibility of a BOT project, private investors consider revenue risk - which is stemmed from the uncertainty about future traffic demand - as a critical factor. A potential approach to mitigating the revenue risk is the offering of revenue risk sharing mechanisms such as Minimum Revenue Guarantee options by the government. In addition to Minimum Revenue Guarantee options, a mechanism known as Traffic Revenue Cap options may also be negotiated, which makes the government entitled to a share of revenue when it grows beyond a specified threshold. Financial valuation of investments in BOT projects should take into account uncertainty about future traffic demand, as well as Minimum Revenue Guarantee and Traffic Revenue Cap options. The conventional valuation methods including Net Present Value (NPV) analysis are not capable of integrating the uncertainty about future traffic demand in the valuation of BOT projects and properly pricing Minimum Revenue Guarantee and Traffic Revenue Cap options. Real options analysis can be used as an alternative approach to valuation of investments in transportation projects under uncertainties. However, the appropriate application of real options analysis to valuation of investments in transportation projects is conditioned upon overcoming specific theoretical challenges. Current real options models do not provide a systematic method for estimating the project volatility, which measures the variability of investment value. Existing models do not provide a method for calculating the market value of Minimum Revenue Guarantee and Traffic Revenue Cap options. Also, current models are not able to characterize the impact of Minimum Revenue Guarantee and Traffic Revenue Cap options on private investors' financial risk profile. The overarching objective of this research is to apply the real options theory in order to price Minimum Revenue Guarantee and Traffic Revenue Cap options under the uncertainty about future traffic demand. To achieve this objective, a real options model is created that characterizes the long-term traffic demand uncertainty in BOT projects and determines investors' financial risk profile under uncertainty about future traffic demand. This model presents a novel method for estimating the project volatility for real options analysis. This model devises a market-based option pricing approach to determine the correct value of Minimum Revenue Guarantee and Traffic Revenue Cap options. An appropriate procedure is created for characterizing the impact of Minimum Revenue Guarantee and Traffic Revenue Cap options on the investors' financial risk profile. The proposed real options model is applied to a BOT project to illustrate the valuation process. The limitations of the proposed real options model, as well as the barriers to its implementation, are identified and recommendations for future research are offered. This research contributes to the state of knowledge by presenting a new method for estimating the project volatility, which is required for the real options analysis of transportation investments. It also introduces a risk-neutral valuation method for pricing the market value of Minimum Revenue Guarantee and Traffic Revenue Cap options in BOT projects. The research also contributes to the state of practice by introducing a novel class of assessment tools for decision makers that characterize the investors' financial risk profile under uncertainty about future traffic demand. Proper methods for pricing of Minimum Revenue Guarantee and Traffic Revenue Cap options are useful to public and private investors, in order to avoid wasting capital in transportation projects.

Ground level ozone is one of the most ubiquitous air pollutants in urban areas, and is generated by photochemical reactions of oxides of nitrogen (NOx) and volatile organic compounds (VOCs). The effectiveness of emission reduction strategies for ozone precursors is typically evaluated using gridded, photochemical air quality models. One of the underlying assumptions in these models is that industrial emissions are nearly constant, since many industrial facilities operate continuously at a constant rate of output. However, recent studies performed in the Houston-Galveston-Brazoria area indicate that some industrial emission sources exhibit high temporal emission variability that can lead to very rapid ozone formation, especially when emissions are composed of highly reactive volatile organic compounds. This work evaluates the impact of variable emissions from industrial sources on ground-level ozone formation in Houston area, utilizing a unique hourly emission inventory, known as the 2006 Special Inventory, created as a part of the second Texas Air Quality Study. Comparison of the hourly emissions inventory data with ambient measurements indicated that the impact of the variability of industrial source emissions on ozone can be significant. Photochemical modeling predictions showed that the variability in industrial emissions can lead to differences in local ozone concentrations of as much as 27 ppb at individual ozone monitor locations. The hourly emissions inventory revealed that industrial source emissions are highly variable in nature with diverse temporal patterns and stochastic behavior. Petrochemical and chemical manufacturing flares, which represent the majority of emissions in the 2006 Special Inventory, were grouped into categories based on industrial process, chemical composition of the flared gas, and the temporal patterns of their emissions. Stochastic models were developed for each categorization of flare emissions with the goal of simulating the characterized temporal emission variability. The stochastic models provide representative temporal profiles for flares in the petrochemical manufacturing and chemical manufacturing sectors, and as such serve as more comprehensive input for photochemical air quality modeling. / text

Delivering health care services in an efficient and effective way has become a great challenge for many countries due to the aging population worldwide, rising health expenses, and increasingly complex healthcare delivery systems. It is widely recognized that models and analytical tools can aid decision-making at various levels of the healthcare delivery process, especially when decisions have to be made under uncertainty. This thesis employs stochastic models to improve decision-making under uncertainty in two specific healthcare settings: inpatient flow management and infectious disease modeling. In Part I of this thesis, we study patient flow from the emergency department (ED) to hospital inpatient wards. This line of research aims to develop insights into effective inpatient flow management to reduce the waiting time for admission to inpatient wards from the ED. Delayed admission to inpatient wards, also known as ED boarding, has been identified as a key contributor to ED overcrowding and is a big challenge for many hospitals. Part I consists of three main chapters. In Chapter 2 we present an extensive empirical study of the inpatient department at our collaborating hospital. Motivated by this empirical study, in Chapter 3 we develop a high fidelity stochastic processing network model to capture inpatient flow with a focus on the transfer process from the ED to the wards. In Chapter 4 we devise a new analytical framework, two-time-scale analysis, to predict time-dependent performance measures for some simplified versions of our proposed model. We explore both exact Markov chain analysis and diffusion approximations. Part I of the thesis makes contributions in three dimensions. First, we identify several novel features that need to be built into our proposed stochastic network model. With these features, our model is able to capture inpatient flow dynamics at hourly resolution and reproduce the empirical time-dependent performance measures, whereas traditional time-varying queueing models fail to do so. These features include unconventional non-i.i.d. (independently and identically distributed) service times, an overflow mechanism, and allocation delays. Second, our two-time-scale framework overcomes a number of challenges faced by existing analytical methods in analyzing models with these novel features. These challenges include time-varying arrivals and extremely long service times. Third, analyzing the developed stochastic network model generates a set of useful managerial insights, which allow hospital managers to (i) identify strategies to reduce the waiting time and (ii) evaluate the trade-off between the benefit of reducing ED congestion and the cost from implementing certain policies. In particular, we identify early discharge policies that can eliminate the excessively long waiting times for patients requesting beds in the morning. In Part II of the thesis, we model the spread of influenza pandemics with a focus on identifying factors that may lead to multiple waves of outbreak. This line of research aims to provide insights and guidelines to public health officials in pandemic preparedness and response. In Chapter 6 we evaluate the impact of seasonality and viral mutation on the course of an influenza pandemic. In Chapter 7 we evaluate the impact of changes in social mixing patterns, particularly mass gatherings and holiday traveling, on the disease spread. In Chapters 6 and 7 we develop agent-based simulation models to capture disease spread across both time and space, where each agent represents an individual with certain socio-demographic characteristics and mixing patterns. The important contribution of our models is that the viral transmission characteristics and social contact patterns, which determine the scale and velocity of the disease spread, are no longer static. Simulating the developed models, we study the effect of the starting season of a pandemic, timing and degree of viral mutation, and duration and scale of mass gatherings and holiday traveling on the disease spread. We identify possible scenarios under which multiple outbreaks can occur during an influenza pandemic. Our study can help public health officials and other decision-makers predict the entire course of an influenza pandemic based on emerging viral characteristics at the initial stage, determine what data to collect, foresee potential multiple waves of attack, and better prepare response plans and intervention strategies, such as postponing or cancelling public gathering events.

This dissertation consists of two self-contained studies. The first study, in the domain of stochastic inventory theory, addresses the structure of optimal ordering policies in a periodic review setting. We take multiple sources of a single product to imply an ordering cost function that is nondecreasing, piecewise linear, and convex. Our main contribution is a proof of the optimality of a finite generalized base stock policy under an average cost criterion. Our inventory model is formulated as a Markov decision process with complete observations. Orders are delivered immediately. Excess demand is fully backlogged, and the function describing holding and backlogging costs is convex. All parameters are stationary, and the random demands are independent and identically distributed across periods. The (known) distribution function is subject to mild assumptions along with the holding and backlogging cost function. Our proof uses a vanishing discount approach. We extend our results from a continuous environment to the case where demands and order quantities are integral. The second study is in the area of capacity planning. Our overarching contribution is a relatively simple and fast solution approach for the fleet composition problem faced by a retail distribution firm, focusing on the context of a major beverage distributor. Vehicles to be included in the fleet may be of multiple sizes; we assume that spot transportation capacity will be available to supplement the fleet as needed. We aim to balance the fixed costs of the fleet against exposure to high variable costs due to reliance on spot capacity. We propose a two-stage stochastic linear programming model with fixed recourse. The demand on a particular day in the planning horizon is described by the total quantity to be delivered and the total number of customers to visit. Thus, daily demand throughout the entire planning period is captured by a bivariate probability distribution. We present an algorithm that efficiently generates a "definitive" collection of bases of the recourse program, facilitating rapid computation of the expected cost of a prospective fleet and its gradient. The equivalent convex program may then be solved by a standard gradient projection algorithm.

Thesis (Ph.D.) -- Mississippi State University. Department of Computer Science and Engineering. / Title from title screen. Includes bibliographical references.

Understanding the complex dynamics that underpin the response of structures in the occurrence of earthquakes is of paramount importance in ensuring community resilience. The operational continuity of structures is influenced by the performance of nonstructural components, also known as secondary structures. Inherent vulnerability characteristics, nonlinearities and uncertainties in their properties or in the excitation pose challenges that render their response determination as a non-straightforward task. This dissertation settles in the context of mathematical modelling and response quantification of seismically driven secondary systems. The case of bilinear hysteretic, rigid-plastic and free-standing rocking oscillators is first considered, as a representative class of secondary systems of distinct behaviour excited at a single point in the primary structure. The equations governing their full dynamic interaction with linear primary oscillators are derived with the purpose of assessing the appropriateness of simplified analysis methods where the secondary-primary feedback action is not accounted for. Analyses carried out in presence of pulse-type excitation have shown that the cascade approximation can be considered satisfactory for bilinear systems provided the secondary-primary mass ratio is adequately low and the system does not approach resonance. For the case of sliding and rocking systems, much lighter secondary systems need to be considered if the cascade analysis is to be adopted, with the validity of the approximation dictated by the selection of the input parameters. Based on the premise that decoupling is permitted, new analytical solutions are derived for the pulse driven nonlinear oscillators considered, conveniently expressing the seismic response as a function of the input parameters and the relative effects are quantified. An efficient numerical scheme for a general-type of excitation is also presented and is used in conjunction with an existing nonstationary stochastic far-field ground motion model to determine the seismic response spectra for the secondary oscillators at given site and earthquake characteristics. Prompted by the presence of uncertainty in the primary structure, and in line with the classical modal analysis, a novel approach for directly characterising uncertainty in the modal shapes, frequencies and damping ratios of the primary structure is proposed. A procedure is then presented for the identification of the model parameters and demonstrated with an application to linear steel frames with uncertain semi-rigid connections. It is shown that the proposed approach reduces the number of the uncertain input parameters and the size of the dynamic problem, and is thus particularly appealing for the stochastic assessment of existing structural systems, where partial modal information is available e.g. through operational modal analysis testing. Through a numerical example, the relative effect of stochasticity in a bi-directional seismic input is found to have a more prominent role on the nonlinear response of secondary oscillators when compared to the uncertainty in the primary structure. Further extending the analyses to the case of multi-attached linear secondary systems driven by deterministic seismic excitation, a convenient variant of the component-mode synthesis method is presented, whereby the primary-secondary dynamic interaction is accounted for through the modes of vibration of the two components. The problem of selecting the vibrational modes to be retained in analysis is then addressed for the case of secondary structures, which may possess numerous low frequency modes with negligible mass, and a modal correction method is adopted in view of the application for seismic analysis. The influence of various approaches to build the viscous damping matrix of the primary-secondary assembly is also investigated, and a novel technique based on modal damping superposition is proposed. Numerical applications are demonstrated through a piping secondary system multi-connected on a primary frame exhibiting various irregularities in plan and elevation, as well as a multi-connected flexible secondary system. Overall, this PhD thesis delivers new insights into the determination and understanding of the response of seismically driven secondary structures. The research is deemed to be of academic and professional engineering interest spanning several areas including seismic engineering, extreme events, structural health monitoring, risk mitigation and reliability analysis.