Browsing by Subject "Stochastic modeling"
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Item Capacity management in health care delivery systems(2012-08) Wang, Wen-YaThis dissertation contains three capacity management problems in health care delivery systems. In particular, Chapter 2 evaluates a panel design problem regarding how clinics may wish to best allocate a pool of heterogeneous patients (i.e. non-acute and acute patients) into physician panels. The analytical results show that neither specialization (i.e. each panel contains patients that are as homogeneous as possible) or equal assignment (i.e. identical panels with same types of patient mix) is a dominant patient allocation strategy. The results also show that equal assignment strategy works better when acute demand is relatively low or high as compared to the capacity, and specialization works better when acute demand is moderate. This chapter serves to highlight the impact of patient composition on the performance of a clinic profile. Chapter 3 investigates how clinics may learn and utilize patients' preference information through an existing web-based interface in appointment booking decisions. Analytical results leading to a partial characterization of an optimal booking policy are presented. Examples show that heuristic decision rules, based on this characterization, perform well and reveal insights about trade-offs among a variety of performance metrics such as expected revenue, patient-PCP match rate, number of patients served, and capacity spoilage rate. Chapter 4 focuses on identifying observable predictors of nurse absenteeism and incorporates these factors into staffing decisions. The analysis highlights the importance of paying attention to unit-level factors and absentee-rate heterogeneity among individual nurses. The data-based investigation confirms that nurses' absence history is a good predictor of their future absences. This result is used as the nurse absenteeism assumption in the model-based investigation that evaluates how to assign nurses to identical nursing units when nurses' absentee rates are heterogeneous. We propose and test several easy-to-use heuristics to identify near optimal staffing strategies for inpatient units.Item Multiscale modeling and analysis of microtubule self-assembly dynamics(2014-08) Castle, Brian ThomasMicrotubules are dynamic biopolymers that self-assemble from individual subunits of αβ-tubulin. Self-assembly dynamics are characterized by stochastic switching between extended phases of growth and shortening, termed dynamic instability. Cellular processes, including the chromosome segregation during mitosis and the proper partitioning of intracellular proteins, are dependent on the dynamic nature of microtubule assembly, which facilitates rapid reorganization and efficient exploration of cellular volume. Microtubule-targeting chemotherapeutic agents, used to treat a wide range of cancer types, bind directly to tubulin subunits and suppress dynamic instability, ultimately impeding the capacity to complete cellular processes. Microscale length changes observed during dynamic instability are the net-effect of the addition and loss of individual subunits, dictated by the interdimer molecular interactions. Therefore, a multiscale approach is necessary to extrapolate submolecular level effects of microtubule-targeting agents to dynamic instability. The work presented in this dissertation integrates multiscale computational modeling and experimental observations with the goal of better understanding the functional mechanisms of microtubule-targeting agents. First, we develop a computational model for the association and dissociation of tubulin subunits, in which the interdimer interaction potentials are specifically simulated. Simulation results indicate that the local polymer end structure sterically inhibits subunit association as much as an order of magnitude. Additionally, the model informs how microtubule-targeting agents could alter assembly dynamics through the properties of the interdimer interactions. Second, the mechanisms of kinetic stabilization by microtubule-targeting agents are tested and constrained by combining predictions from a computational model for microtubule self-assembly and experimental observations in mammalian cells. We find that assembly- and disassembly-promoting agents induce kinetic stabilization via separate mechanisms. One is a true kinetic stabilization, in which the kinetic rates of subunit addition and loss are reduced 10- to 100-fold, while the other is a pseudo-kinetic stabilization, dependent upon mass action of tubulin subunits between polymer and solution. Overall, this work advances our knowledge of the basic physical principles underlying multistranded polymer self-assembly and can inform the future design and development of more effective and tolerable microtubule-targeting drugs.Item A stochastic model of macroscopic traffic flow: theoretical foundations(2012-08) Jabari, Saif EddinIn this thesis, a new stochastic extension of Godunov scheme based traffic flow dynamics is developed using a queuing theoretic approach. In contrast to the common approach of adding noise to deterministic models of traffic flow, the present approach considers probabilistic vehicle inter-crossing times (time headways) at various positions along the road as the source of randomness. Subsequently, time headways are used to describe stochastic vehicle counting processes. These counting processes represent the boundary flows in stochastic conservation equations of traffic flow. The advantage of this approach is that (i) non-negativity of time varying traffic variables (namely, traffic densities) is implicitly ensured, and (ii) the mean dynamic of the stochastic model is the Godunov scheme itself. Neither issue has been addressed in previous stochastic modeling approaches which extend the Godunov scheme and its special case, the cell transmission model. A Gaussian approximation of the queueing model is also proposed for purposes of model tractability. The Gaussian approximation is characterized by deterministic mean and covariance dynamics; the mean dynamics are those of the Godunov scheme. By deriving the Gaussian model, as opposed to assuming Gaussian noise arbitrarily, covariance matrices of traffic variables follow from the physics of traffic flow and can be computed using only few parameters, regardless of system size or how finely the system is discretized. Stationary behavior of the covariance function is analyzed and it is shown that the covariance matrices are bounded. Consequently, estimated covariance matrices are also bounded. As a result, Kalman filters that use the proposed model are stochastically observable, which is a critical issue in real time estimation of traffic dynamics. Model validation was carried out in a real-world signalized arterial setting, where cycle-by-cycle maximum queue sizes were estimated using the Gaussian model as a description of state dynamics in a Kalman filter. The estimated queue sizes were compared to observed maximum queue sizes and the results indicate very good agreement between estimated and observed queue sizes.