Cell biology is a branch of science with a seemingly infinite abundance of interesting phenomena which are essential to our understanding of life and which may potentially drive the development of technology that improves our lives. Among the open ended questions within the field, an understanding of how gene networks are affected by limited cellular components is both broad and rich with interest. Common to all cellular systems are enzymes which perform many tasks within cells without which organisms could not remain healthy. Here are presented several explorations of enzymatic processing as well as a tool constructed for this purpose. More specifically, these works consider the effect of coupling of gene networks via competition for enzymes found within the cell. It is shown that a limitation on the number of available enzymes permits the formation of bottlenecks which drastically affect molecular dynamics within cells. These effects potentially afford cell behaviors that in part explain the impressive robustness of life to constantly fluctuating environments. / Ph. D.

This dissertation focuses on reexamining traditional management problems that emerge in service systems where customers or jobs queue for service. In particular, we investigate how a manger should make maintenance and routing decisions in settings where there is a departure from traditional modeling assumptions. In many cases, the performance evaluation of a management problems has, at its heart, a complex, infinite Markov chain which must be solved before any optimization can begin. Unfortunately, most Markov chains are not analytically tractable. In the first essay, we address the solution of infinite state Markov chains. We focus on class M Markov chains, a broad class of chains which is representative of a wide array of problems arising in the management of computer, service, and manufacturing systems where queueing parameters change over time according to a restricted stochastic pattern. We develop a new method, called Clearing Analysis on Phases, for the limiting probability distribution of such chains in exact closed form. In the second essay, we apply the CAP method to answer the question of how a manager should maintain a system in a setting where an online customer-facing service is vulnerable to persistent malware infections. These infections can cause performance degradation and facilitate data theft, both of which have monetary repercussions. Infections can go undetected and can only be removed by a timeconsuming cleanup procedure, which takes the service offline and causes all existing jobs to be discarded without service. In particular, we provide recommendations for when (and in response to what events) a manager should initiate cleanup procedures by solving an infinite state maintenance problem. We quantify the efficiency of various cleanup (maintenance) policies by proposing a revenue model which incorporates both delay-based pricing and data theft costs. In the third essay, we examine queueing systems in call centers and answer the question of a how a manager should route customers to strategic staff who choose their own service rates in response to workload incentives. We address this problem using game theoretic techniques. In particular, we introduce a utility model where the servers choose their service rate in order to maximize a tradeoff between an “effort cost” and a “value of idleness.” We find that relaxing the classical assumption that all servers work at a fixed rate renders traditional routing policies inadequate. Our approach allows us to recommend novel routing policies that are both fair for the staff and efficient for the customers. In the fourth essay we look at web server farms and answer the question of how jobs should be immediately routed to computer servers in a setting where some jobs are more valuable or more important than others. Such settings arise when some jobs are generated by users who are paying for a premium service. We address how a manager should incorporate information about a job’s value when making routing decisions in order to minimize expected value-weighted response times. The heterogeneity in job values greatly the dimensionality of this problem. Via a combination of exact analysis, asymptotic analysis, and simulation, we are able to deduce many unexpected results regarding routing.

Hospitals stand to lose millions of dollars in revenue due to patients who leave without treatment (LWT). Grounded in queueing theory, the purpose of this correlational study was to examine the relationship between daily arrivals, daily staffing, triage time, emergency severity index (ESI), rooming time, door-to-provider time (DTPT), and LWT rates. The target population comprised patients who visited a Connecticut emergency room between October 1, 2017, and May 31, 2018. Archival records (N = 154) were analyzed using multiple linear regression analysis. The results of the multiple linear regression were statistically significant, with F(9,144) = 2902.49, p < .001, and R2 = 0.99, indicating 99% of the variation in LWT was accounted for by the predictor variables. ESI levels were the only variables making a significant contribution to the regression model. The implications for positive social change include the potential for patients to experience increased satisfaction due to the high quality of care and overall improvement in public health outcomes. Hospital leaders might use the information from this study to mitigate LWT rates and modify or manage staffing levels, time that patients must wait for triage, room placement, and DTPT to decrease the rate of LWT in the emergency room.

In this thesis, we study the repair shop scheduling problem(repair-to-stock) and the production/inventory system pricing and production scheduling problem(make-to-stock). For both types of problems, we compare the performance of different scheduling policies. For the make-to-stock type problem, we also study the performance of different pricing strategies. The optimal repair/production scheduling policy of both problems is difficult to characterize, and, therefore, is only formulated as a Markov Decision Process to numerically compute the optimal cost/profit. As an alternative, we propose the dynamic Myopic policy, which is easy to implement. The numerical study we have conducted demonstrates that the performance of Myopic policy is superior compared to the alternative policies and yields costs very close to the optimal for the repair-to-stock type problem. On the other hand, for the make-to-stock type problems, the performance of Myopic policy is not superior compared to the alternative policies when dynamic pricing strategy is implemented.

In this thesis, we study the repair shop scheduling problem(repair-to-stock) and the production/inventory system pricing and production scheduling problem(make-to-stock). For both types of problems, we compare the performance of different scheduling policies. For the make-to-stock type problem, we also study the performance of different pricing strategies. The optimal repair/production scheduling policy of both problems is difficult to characterize, and, therefore, is only formulated as a Markov Decision Process to numerically compute the optimal cost/profit. As an alternative, we propose the dynamic Myopic policy, which is easy to implement. The numerical study we have conducted demonstrates that the performance of Myopic policy is superior compared to the alternative policies and yields costs very close to the optimal for the repair-to-stock type problem. On the other hand, for the make-to-stock type problems, the performance of Myopic policy is not superior compared to the alternative policies when dynamic pricing strategy is implemented.

Although healthcare operations management has been an active and popular research direction over the past few years, there is a lack of formal quantitative models to analyze the ambulance o oad delay problem. O oad delays occur when an ambulance arriving at a hospital Emergency Department (ED) is forced to remain in front of the ED until a bed is available for the patient. Thus, the ambulance and the paramedic team are responsible to care for the patient until a bed becomes available inside the ED. But it is not as simple as waiting for a bed, as EDs also admit patients based on acuity levels. While the main cause of this problem is the lack of capacity to treat patients inside the EDs, Emergency Medical Services (EMS) coverage and availability are signi cantly a ected. In this thesis, we develop three network queueing models to analyze the o oad delay problem. In order to capture the main cause of those delays, we construct queueing network models that include both EMS and EDs. In addition, we consider patients arriving to the EDs by themselves (walk-in patients) since they consume ED capacity as well. In the rst model, ED capacity is modeled as the combination of bed, nurse, and doctor. If a patient with higher acuity level arrives to the ED, the current patient's service is interrupted. Thus, the service discipline at the EDs is preemptive resume. We also assume that the time the ambulance needs to reach the patient, upload him into the ambulance, and transfer him to the ED (transit time) is negligible. We develop e cient algorithms to construct the model Markov chain and solve for its steady state probability distribution using Matrix Analytic Methods. Moreover, we derive di erent performance measures to evaluate the system performance under di erent settings in terms of the number of beds at each ED, Length Of Stay (LOS) of patients at an ED, and the number of ambulances available to serve a region. Although capacity limitations and increasing demand are the main drivers for this problem, our computational analysis show that ambulance dispatching decisions have a substantial impact on the total o oad delays incurred. In the second model, the number of beds at each ED is used to model the service capacity. As a result of this modeling approach, the service discipline of patients is assumed to be nonpreemptive priority. We also assume that transit times of ambulances are negligible. To analyze the queueing network, we develop a novel algorithm to construct the system Markov chain by de ning a layer for each ED in a region. We combine the Markov chain layers based on the fact that regional EDs are only connected by the number of available ambulances to serve the region. Using Matrix Analytic Methods, we nd the limiting probabilities and use the results to derive di erent system performance measures. Since each ED's patients are included in the model simultaneously, we solve only for small instances with our current computational resources. In the third model, we decompose the regional network into multiple single EDs. We also assume that patients arriving by ambulances have higher nonpreemptive priority discipline over walk-in patients. Unlike the rst two models, we assume that transit times of ambulances are exponentially distributed. To analyze the decomposed queueing network performance, we construct a Markov chain and solve for its limiting probabilities using Matrix Analytic Methods. While the main objective for the rst two models is performance evaluation, in this model we optimize the steady state dispatching decisions for ambulance patients. To achieve this goal, we develop an approximation scheme for the expected o oad delays and expected waiting times of patients. Computational analysis conducted suggest that larger EDs should be loaded more heavily in order to keep the total o oad delays at minimal levels.

In the first half of this thesis, we extend the results of Halfin and Whitt to generally distributed service times. This is accomplished by first writing the system equations for the G/GI/N queue in a manner similar to the system equations for G/GI/Infinity queue. We next identify a key relationship between these two queues. This relationship allows us to leverage several existing results for the G/GI/Infinity queue in order to prove our main result. Our main result in the first part of this thesis is to show that the diffusion scaled queue length process for the G/GI/N queue in the Halfin-Whitt regime converges to a limiting stochastic process which is driven by a Gaussian process and satisfies a stochastic convolution equation. We also show that a similar result holds true for the fluid scaled queue length process under general initial conditions. Customer abandonment is also a common feature of many call centers. Some researchers have even gone so far as to suggest that the level of customer abandonment is the single most important metric with regards to a call center's performance. In the second half of this thesis, we improve upon a result of Ward and Glynn's concerning the GI/GI/1+GI queue in heavy traffic. Whereas Ward and Glynn obtain a diffusion limit result for the GI/GI/1+GI queue in heavy traffic which incorporates only the density the abandonment distribution at the origin, our result incorporate the entire abandonment distribution. This is accomplished by a scaling the hazard rate function of the abandonment distribution as the system moves into heavy traffic. Our main results are to obtain diffusion limits for the properly scaled workload and queue length processes in the GI/GI/1+GI queue. The limiting diffusions we obtain are reflected at the origin with a negative drift which is dependent upon the hazard rate of the abandonment distribution. Because these diffusions have an analytically tractable steady-state distribution, they can be used to provide a closed-form approximation for the steady-state distribution of the queue length and workload processes in a GI/GI/1+GI queue. We demonstrate the accuracy of these approximations through simulation.

The Software Life Cycle (SLC) often comprises a complex sequence of processes, each with many subparts where various execution decisions throughout the pipeline can greatly affect the success or failure of a given project. Some of the most important decisions involve the allocation of scarce resources throughout the SLC, which are often based on estimations about future market demand and various extraneous factors of high stochasticity. Despite numerous efforts in standardization, many projects are still highly dependent on the subjective aptitude of individual managers, who may in turn rely on ad hoc techniques rather than standardized and repeatable ones. The results can be unpredictability and undue reliance on specific individuals. This paper considers imposing a mathematical framework on two of the key aspects of SLC: Deciding how to dynamically allocate available resources throughout the development pipeline, and when to stop further work on a given task in light of the associated Return On Investment (ROI) metrics. In so doing, the software development process is modeled as a problem in New Product Development (NPD) Management, which can be approached using control theory and stochastic combinatorial optimization techniques. The paper begins by summarizing some of the previous developments in these fields, and proposes some future research directions for solving complex resource allocation problems under stochastic settings. The outcome is a formal framework that when combined with competent Configuration Management techniques, can rapidly achieve near-optimal solutions at each stage of the SLC in a standardized manner. / text

This dissertation is concerned with travel time uncertainty in transportation networks due to ephemeral phenomena such as incidents or poor weather. Such events play a major role in nonrecurring congestion, which is estimated to comprise between one-third and one-half of all delay on freeways. Although past research has considered many individual aspects of this problem, this dissertation is unique in bringing a comprehensive approach, beginning with study of its causes, moving to discussion of its effects on traveler behavior, and then demonstrating how these models can be applied to mitigate the effects of this uncertainty. In particular, two distinctive effects of uncertainty are incorporated into all aspects of these models: nonlinear traveler behavior, encompassing risk aversion, schedule delay, on-time arrival, and other user objectives that explicitly recognize travel time uncertainty; and information and adaptive routing, where travelers can adjust their routes through the network as they acquire information on its condition. In order to accurately represent uncertain events in a mathematical model, some quantitative description of these events and their impacts must be available. On freeways, a large amount of travel data is collected through intelligent transportation systems (ITS), although coverage is far from universal, and very little data is collected on arterial streets. This dissertation develops a statistical procedure for estimating probability distributions on speed, capacity, and other operational metrics by applying regression to locations where such data is available. On arterials, queueing theory is used to develop novel expressions for expected delay conditional on the signal indication. The effects of this uncertainty are considered next, both at the individual (route choice) and collective (equilibrium) levels. For individuals, the optimal strategy is no longer a path, but an adaptive policy which allows for flexible re-routing as information is acquired. Dynamic programming provides an efficient solution to this problem. Issues related to cycling in optimal policies are examined in some depth. While primarily a technical concern, the presence of cycling can be discomforting and needs to be addressed. When considering collective behavior, the simultaneous choices of many self-optimizing users (who need not share the same behavioral objective) can be expressed as the solution to a variational inequality problem, leading to existence and uniqueness results under certain regularity conditions. An improved policy loading algorithm is also provided for the case of linear traveler behavior. Finally, three network improvement strategies are considered: locating information-providing devices; adaptive congestion pricing; and network design. Each of these demonstrates how the routing and equilibrium models can be applied, using small networks as testbed locations. In particular, the information provision and adaptive congestion pricing strategies are extremely difficult to represent without an adaptive equilibrium model such as the one provided in this dissertation. / text

ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / The University of Arizona's Aerial Robotics Club (ARC) sponsors the development of an unmanned aerial vehicle (UAV) able to compete in the annual Association for Unmanned Vehicle Systems International (AUVSI) Seafarer Chapter Student Unmanned Aerial Systems competition. Modern programming frameworks are utilized to develop a robust distributed imagery and telemetry pipeline as a backend for a mission operator user interface. This paper discusses the design changes made for the 2013 AUVSI competition including integrating low-latency first-person view, updates to the distributed task backend, and incremental and asynchronous updates the operator's user interface for real-time data analysis.