19 resultados para dual tableaux and sequent systems

em Digital Commons at Florida International University


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Electrical energy is an essential resource for the modern world. Unfortunately, its price has almost doubled in the last decade. Furthermore, energy production is also currently one of the primary sources of pollution. These concerns are becoming more important in data-centers. As more computational power is required to serve hundreds of millions of users, bigger data-centers are becoming necessary. This results in higher electrical energy consumption. Of all the energy used in data-centers, including power distribution units, lights, and cooling, computer hardware consumes as much as 80%. Consequently, there is opportunity to make data-centers more energy efficient by designing systems with lower energy footprint. Consuming less energy is critical not only in data-centers. It is also important in mobile devices where battery-based energy is a scarce resource. Reducing the energy consumption of these devices will allow them to last longer and re-charge less frequently. Saving energy in computer systems is a challenging problem. Improving a system's energy efficiency usually comes at the cost of compromises in other areas such as performance or reliability. In the case of secondary storage, for example, spinning-down the disks to save energy can incur high latencies if they are accessed while in this state. The challenge is to be able to increase the energy efficiency while keeping the system as reliable and responsive as before. This thesis tackles the problem of improving energy efficiency in existing systems while reducing the impact on performance. First, we propose a new technique to achieve fine grained energy proportionality in multi-disk systems; Second, we design and implement an energy-efficient cache system using flash memory that increases disk idleness to save energy; Finally, we identify and explore solutions for the page fetch-before-update problem in caching systems that can: (a) control better I/O traffic to secondary storage and (b) provide critical performance improvement for energy efficient systems.

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The performance of building envelopes and roofing systems significantly depends on accurate knowledge of wind loads and the response of envelope components under realistic wind conditions. Wind tunnel testing is a well-established practice to determine wind loads on structures. For small structures much larger model scales are needed than for large structures, to maintain modeling accuracy and minimize Reynolds number effects. In these circumstances the ability to obtain a large enough turbulence integral scale is usually compromised by the limited dimensions of the wind tunnel meaning that it is not possible to simulate the low frequency end of the turbulence spectrum. Such flows are called flows with Partial Turbulence Simulation. In this dissertation, the test procedure and scaling requirements for tests in partial turbulence simulation are discussed. A theoretical method is proposed for including the effects of low-frequency turbulences in the post-test analysis. In this theory the turbulence spectrum is divided into two distinct statistical processes, one at high frequencies which can be simulated in the wind tunnel, and one at low frequencies which can be treated in a quasi-steady manner. The joint probability of load resulting from the two processes is derived from which full-scale equivalent peak pressure coefficients can be obtained. The efficacy of the method is proved by comparing predicted data derived from tests on large-scale models of the Silsoe Cube and Texas-Tech University buildings in Wall of Wind facility at Florida International University with the available full-scale data. For multi-layer building envelopes such as rain-screen walls, roof pavers, and vented energy efficient walls not only peak wind loads but also their spatial gradients are important. Wind permeable roof claddings like roof pavers are not well dealt with in many existing building codes and standards. Large-scale experiments were carried out to investigate the wind loading on concrete pavers including wind blow-off tests and pressure measurements. Simplified guidelines were developed for design of loose-laid roof pavers against wind uplift. The guidelines are formatted so that use can be made of the existing information in codes and standards such as ASCE 7-10 on pressure coefficients on components and cladding.

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I proposed the study of two distinct aspects of Ten-Eleven Translocation 2 (TET2) protein for understanding specific functions in different body systems. In Part I, I characterized the molecular mechanisms of Tet2 in the hematological system. As the second member of Ten-Eleven Translocation protein family, TET2 is frequently mutated in leukemic patients. Previous studies have shown that the TET2 mutations frequently occur in 20% myelodysplastic syndrome/myeloproliferative neoplasm (MDS/MPN), 10% T-cell lymphoma leukemia and 2% B-cell lymphoma leukemia. Genetic mouse models also display distinct phenotypes of various types of hematological malignancies. I performed 5-hydroxymethylcytosine (5hmC) chromatin immunoprecipitation sequencing (ChIP-Seq) and RNA sequencing (RNA-Seq) of hematopoietic stem/progenitor cells to determine whether the deletion of Tet2 can affect the abundance of 5hmC at myeloid, T-cell and B-cell specific gene transcription start sites, which ultimately result in various hematological malignancies. Subsequent Exome sequencing (Exome-Seq) showed that disease-specific genes are mutated in different types of tumors, which suggests that TET2 may protect the genome from being mutated. The direct interaction between TET2 and Mutator S Homolog 6 (MSH6) protein suggests TET2 is involved in DNA mismatch repair. Finally, in vivo mismatch repair studies show that the loss of Tet2 causes a mutator phenotype. Taken together, my data indicate that TET2 binds to MSH6 to protect genome integrity. In Part II, I intended to better understand the role of Tet2 in the nervous system. 5-hydroxymethylcytosine regulates epigenetic modification during neurodevelopment and aging. Thus, Tet2 may play a critical role in regulating adult neurogenesis. To examine the physiological significance of Tet2 in the nervous system, I first showed that the deletion of Tet2 reduces the 5hmC levels in neural stem cells. Mice lacking Tet2 show abnormal hippocampal neurogenesis along with 5hmC alternations at different gene promoters and corresponding gene expression downregulation. Through the luciferase reporter assay, two neural factors Neurogenic differentiation 1 (NeuroD1) and Glial fibrillary acidic protein (Gfap) were down-regulated in Tet2 knockout cells. My results suggest that Tet2 regulates neural stem/progenitor cell proliferation and differentiation in adult brain.

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The performance of building envelopes and roofing systems significantly depends on accurate knowledge of wind loads and the response of envelope components under realistic wind conditions. Wind tunnel testing is a well-established practice to determine wind loads on structures. For small structures much larger model scales are needed than for large structures, to maintain modeling accuracy and minimize Reynolds number effects. In these circumstances the ability to obtain a large enough turbulence integral scale is usually compromised by the limited dimensions of the wind tunnel meaning that it is not possible to simulate the low frequency end of the turbulence spectrum. Such flows are called flows with Partial Turbulence Simulation.^ In this dissertation, the test procedure and scaling requirements for tests in partial turbulence simulation are discussed. A theoretical method is proposed for including the effects of low-frequency turbulences in the post-test analysis. In this theory the turbulence spectrum is divided into two distinct statistical processes, one at high frequencies which can be simulated in the wind tunnel, and one at low frequencies which can be treated in a quasi-steady manner. The joint probability of load resulting from the two processes is derived from which full-scale equivalent peak pressure coefficients can be obtained. The efficacy of the method is proved by comparing predicted data derived from tests on large-scale models of the Silsoe Cube and Texas-Tech University buildings in Wall of Wind facility at Florida International University with the available full-scale data.^ For multi-layer building envelopes such as rain-screen walls, roof pavers, and vented energy efficient walls not only peak wind loads but also their spatial gradients are important. Wind permeable roof claddings like roof pavers are not well dealt with in many existing building codes and standards. Large-scale experiments were carried out to investigate the wind loading on concrete pavers including wind blow-off tests and pressure measurements. Simplified guidelines were developed for design of loose-laid roof pavers against wind uplift. The guidelines are formatted so that use can be made of the existing information in codes and standards such as ASCE 7-10 on pressure coefficients on components and cladding.^

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I proposed the study of two distinct aspects of Ten-Eleven Translocation 2 (TET2) protein for understanding specific functions in different body systems. ^ In Part I, I characterized the molecular mechanisms of Tet2 in the hematological system. As the second member of Ten-Eleven Translocation protein family, TET2 is frequently mutated in leukemic patients. Previous studies have shown that the TET2 mutations frequently occur in 20% myelodysplastic syndrome/myeloproliferative neoplasm (MDS/MPN), 10% T-cell lymphoma leukemia and 2% B-cell lymphoma leukemia. Genetic mouse models also display distinct phenotypes of various types of hematological malignancies. I performed 5-hydroxymethylcytosine (5hmC) chromatin immunoprecipitation sequencing (ChIP-Seq) and RNA sequencing (RNA-Seq) of hematopoietic stem/progenitor cells to determine whether the deletion of Tet2 can affect the abundance of 5hmC at myeloid, T-cell and B-cell specific gene transcription start sites, which ultimately result in various hematological malignancies. Subsequent Exome sequencing (Exome-Seq) showed that disease-specific genes are mutated in different types of tumors, which suggests that TET2 may protect the genome from being mutated. The direct interaction between TET2 and Mutator S Homolog 6 (MSH6) protein suggests TET2 is involved in DNA mismatch repair. Finally, in vivo mismatch repair studies show that the loss of Tet2 causes a mutator phenotype. Taken together, my data indicate that TET2 binds to MSH6 to protect genome integrity. ^ In Part II, I intended to better understand the role of Tet2 in the nervous system. 5-hydroxymethylcytosine regulates epigenetic modification during neurodevelopment and aging. Thus, Tet2 may play a critical role in regulating adult neurogenesis. To examine the physiological significance of Tet2 in the nervous system, I first showed that the deletion of Tet2 reduces the 5hmC levels in neural stem cells. Mice lacking Tet2 show abnormal hippocampal neurogenesis along with 5hmC alternations at different gene promoters and corresponding gene expression downregulation. Through the luciferase reporter assay, two neural factors Neurogenic differentiation 1 (NeuroD1) and Glial fibrillary acidic protein (Gfap) were down-regulated in Tet2 knockout cells. My results suggest that Tet2 regulates neural stem/progenitor cell proliferation and differentiation in adult brain.^

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A methodology for formally modeling and analyzing software architecture of mobile agent systems provides a solid basis to develop high quality mobile agent systems, and the methodology is helpful to study other distributed and concurrent systems as well. However, it is a challenge to provide the methodology because of the agent mobility in mobile agent systems.^ The methodology was defined from two essential parts of software architecture: a formalism to define the architectural models and an analysis method to formally verify system properties. The formalism is two-layer Predicate/Transition (PrT) nets extended with dynamic channels, and the analysis method is a hierarchical approach to verify models on different levels. The two-layer modeling formalism smoothly transforms physical models of mobile agent systems into their architectural models. Dynamic channels facilitate the synchronous communication between nets, and they naturally capture the dynamic architecture configuration and agent mobility of mobile agent systems. Component properties are verified based on transformed individual components, system properties are checked in a simplified system model, and interaction properties are analyzed on models composing from involved nets. Based on the formalism and the analysis method, this researcher formally modeled and analyzed a software architecture of mobile agent systems, and designed an architectural model of a medical information processing system based on mobile agents. The model checking tool SPIN was used to verify system properties such as reachability, concurrency and safety of the medical information processing system. ^ From successful modeling and analyzing the software architecture of mobile agent systems, the conclusion is that PrT nets extended with channels are a powerful tool to model mobile agent systems, and the hierarchical analysis method provides a rigorous foundation for the modeling tool. The hierarchical analysis method not only reduces the complexity of the analysis, but also expands the application scope of model checking techniques. The results of formally modeling and analyzing the software architecture of the medical information processing system show that model checking is an effective and an efficient way to verify software architecture. Moreover, this system shows a high level of flexibility, efficiency and low cost of mobile agent technologies. ^

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Choosing between Light Rail Transit (LRT) and Bus Rapid Transit (BRT) systems is often controversial and not an easy task for transportation planners who are contemplating the upgrade of their public transportation services. These two transit systems provide comparable services for medium-sized cities from the suburban neighborhood to the Central Business District (CBD) and utilize similar right-of-way (ROW) categories. The research is aimed at developing a method to assist transportation planners and decision makers in determining the most feasible system between LRT and BRT. ^ Cost estimation is a major factor when evaluating a transit system. Typically, LRT is more expensive to build and implement than BRT, but has significantly lower Operating and Maintenance (OM) costs than BRT. This dissertation examines the factors impacting capacity and costs, and develops cost models, which are a capacity-based cost estimate for the LRT and BRT systems. Various ROW categories and alignment configurations of the systems are also considered in the developed cost models. Kikuchi's fleet size model (1985) and cost allocation method are used to develop the cost models to estimate the capacity and costs. ^ The comparison between LRT and BRT are complicated due to many possible transportation planning and operation scenarios. In the end, a user-friendly computer interface integrated with the established capacity-based cost models, the LRT and BRT Cost Estimator (LBCostor), was developed by using Microsoft Visual Basic language to facilitate the process and will guide the users throughout the comparison operations. The cost models and the LBCostor can be used to analyze transit volumes, alignments, ROW configurations, number of stops and stations, headway, size of vehicle, and traffic signal timing at the intersections. The planners can make the necessary changes and adjustments depending on their operating practices. ^

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The purpose of this investigation was to develop and implement a general purpose VLSI (Very Large Scale Integration) Test Module based on a FPGA (Field Programmable Gate Array) system to verify the mechanical behavior and performance of MEM sensors, with associated corrective capabilities; and to make use of the evolving System-C, a new open-source HDL (Hardware Description Language), for the design of the FPGA functional units. System-C is becoming widely accepted as a platform for modeling, simulating and implementing systems consisting of both hardware and software components. In this investigation, a Dual-Axis Accelerometer (ADXL202E) and a Temperature Sensor (TMP03) were used for the test module verification. Results of the test module measurement were analyzed for repeatability and reliability, and then compared to the sensor datasheet. Further study ideas were identified based on the study and results analysis. ASIC (Application Specific Integrated Circuit) design concepts were also being pursued.

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With advances in science and technology, computing and business intelligence (BI) systems are steadily becoming more complex with an increasing variety of heterogeneous software and hardware components. They are thus becoming progressively more difficult to monitor, manage and maintain. Traditional approaches to system management have largely relied on domain experts through a knowledge acquisition process that translates domain knowledge into operating rules and policies. It is widely acknowledged as a cumbersome, labor intensive, and error prone process, besides being difficult to keep up with the rapidly changing environments. In addition, many traditional business systems deliver primarily pre-defined historic metrics for a long-term strategic or mid-term tactical analysis, and lack the necessary flexibility to support evolving metrics or data collection for real-time operational analysis. There is thus a pressing need for automatic and efficient approaches to monitor and manage complex computing and BI systems. To realize the goal of autonomic management and enable self-management capabilities, we propose to mine system historical log data generated by computing and BI systems, and automatically extract actionable patterns from this data. This dissertation focuses on the development of different data mining techniques to extract actionable patterns from various types of log data in computing and BI systems. Four key problems—Log data categorization and event summarization, Leading indicator identification , Pattern prioritization by exploring the link structures , and Tensor model for three-way log data are studied. Case studies and comprehensive experiments on real application scenarios and datasets are conducted to show the effectiveness of our proposed approaches.

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Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

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A wireless mesh network is a mesh network implemented over a wireless network system such as wireless LANs. Wireless Mesh Networks(WMNs) are promising for numerous applications such as broadband home networking, enterprise networking, transportation systems, health and medical systems, security surveillance systems, etc. Therefore, it has received considerable attention from both industrial and academic researchers. This dissertation explores schemes for resource management and optimization in WMNs by means of network routing and network coding.^ In this dissertation, we propose three optimization schemes. (1) First, a triple-tier optimization scheme is proposed for load balancing objective. The first tier mechanism achieves long-term routing optimization, and the second tier mechanism, using the optimization results obtained from the first tier mechanism, performs the short-term adaptation to deal with the impact of dynamic channel conditions. A greedy sub-channel allocation algorithm is developed as the third tier optimization scheme to further reduce the congestion level in the network. We conduct thorough theoretical analysis to show the correctness of our design and give the properties of our scheme. (2) Then, a Relay-Aided Network Coding scheme called RANC is proposed to improve the performance gain of network coding by exploiting the physical layer multi-rate capability in WMNs. We conduct rigorous analysis to find the design principles and study the tradeoff in the performance gain of RANC. Based on the analytical results, we provide a practical solution by decomposing the original design problem into two sub-problems, flow partition problem and scheduling problem. (3) Lastly, a joint optimization scheme of the routing in the network layer and network coding-aware scheduling in the MAC layer is introduced. We formulate the network optimization problem and exploit the structure of the problem via dual decomposition. We find that the original problem is composed of two problems, routing problem in the network layer and scheduling problem in the MAC layer. These two sub-problems are coupled through the link capacities. We solve the routing problem by two different adaptive routing algorithms. We then provide a distributed coding-aware scheduling algorithm. According to corresponding experiment results, the proposed schemes can significantly improve network performance.^

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Modern power networks incorporate communications and information technology infrastructure into the electrical power system to create a smart grid in terms of control and operation. The smart grid enables real-time communication and control between consumers and utility companies allowing suppliers to optimize energy usage based on price preference and system technical issues. The smart grid design aims to provide overall power system monitoring, create protection and control strategies to maintain system performance, stability and security. This dissertation contributed to the development of a unique and novel smart grid test-bed laboratory with integrated monitoring, protection and control systems. This test-bed was used as a platform to test the smart grid operational ideas developed here. The implementation of this system in the real-time software creates an environment for studying, implementing and verifying novel control and protection schemes developed in this dissertation. Phasor measurement techniques were developed using the available Data Acquisition (DAQ) devices in order to monitor all points in the power system in real time. This provides a practical view of system parameter changes, system abnormal conditions and its stability and security information system. These developments provide valuable measurements for technical power system operators in the energy control centers. Phasor Measurement technology is an excellent solution for improving system planning, operation and energy trading in addition to enabling advanced applications in Wide Area Monitoring, Protection and Control (WAMPAC). Moreover, a virtual protection system was developed and implemented in the smart grid laboratory with integrated functionality for wide area applications. Experiments and procedures were developed in the system in order to detect the system abnormal conditions and apply proper remedies to heal the system. A design for DC microgrid was developed to integrate it to the AC system with appropriate control capability. This system represents realistic hybrid AC/DC microgrids connectivity to the AC side to study the use of such architecture in system operation to help remedy system abnormal conditions. In addition, this dissertation explored the challenges and feasibility of the implementation of real-time system analysis features in order to monitor the system security and stability measures. These indices are measured experimentally during the operation of the developed hybrid AC/DC microgrids. Furthermore, a real-time optimal power flow system was implemented to optimally manage the power sharing between AC generators and DC side resources. A study relating to real-time energy management algorithm in hybrid microgrids was performed to evaluate the effects of using energy storage resources and their use in mitigating heavy load impacts on system stability and operational security.

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Modern electric machine drives, particularly three phase permanent magnet machine drive systems represent an indispensable part of high power density products. Such products include; hybrid electric vehicles, large propulsion systems, and automation products. Reliability and cost of these products are directly related to the reliability and cost of these systems. The compatibility of the electric machine and its drive system for optimal cost and operation has been a large challenge in industrial applications. The main objective of this dissertation is to find a design and control scheme for the best compromise between the reliability and optimality of the electric machine-drive system. The effort presented here is motivated by the need to find new techniques to connect the design and control of electric machines and drive systems. ^ A highly accurate and computationally efficient modeling process was developed to monitor the magnetic, thermal, and electrical aspects of the electric machine in its operational environments. The modeling process was also utilized in the design process in form finite element based optimization process. It was also used in hardware in the loop finite element based optimization process. The modeling process was later employed in the design of a very accurate and highly efficient physics-based customized observers that are required for the fault diagnosis as well the sensorless rotor position estimation. Two test setups with different ratings and topologies were numerically and experimentally tested to verify the effectiveness of the proposed techniques. ^ The modeling process was also employed in the real-time demagnetization control of the machine. Various real-time scenarios were successfully verified. It was shown that this process gives the potential to optimally redefine the assumptions in sizing the permanent magnets of the machine and DC bus voltage of the drive for the worst operating conditions. ^ The mathematical development and stability criteria of the physics-based modeling of the machine, design optimization, and the physics-based fault diagnosis and the physics-based sensorless technique are described in detail. ^ To investigate the performance of the developed design test-bed, software and hardware setups were constructed first. Several topologies of the permanent magnet machine were optimized inside the optimization test-bed. To investigate the performance of the developed sensorless control, a test-bed including a 0.25 (kW) surface mounted permanent magnet synchronous machine example was created. The verification of the proposed technique in a range from medium to very low speed, effectively show the intelligent design capability of the proposed system. Additionally, to investigate the performance of the developed fault diagnosis system, a test-bed including a 0.8 (kW) surface mounted permanent magnet synchronous machine example with trapezoidal back electromotive force was created. The results verify the use of the proposed technique under dynamic eccentricity, DC bus voltage variations, and harmonic loading condition make the system an ideal case for propulsion systems.^

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In the discussion - Ethics, Value Systems And The Professionalization Of Hoteliers by K. Michael Haywood, Associate Professor, School of Hotel and Food Administration, University of Guelph, Haywood initially presents: “Hoteliers and executives in other service industries should realize that the foundation of success in their businesses is based upon personal and corporate value systems and steady commitment to excellence. The author illustrates how ethical issues and manager morality are linked to, and shaped by the values of executives and the organization, and how improved professionalism can only be achieved through the adoption of a value system that rewards contributions rather than the mere attainment of results.” The bottom line of this discussion is, how does the hotel industry reconcile its behavior with that of public perception? “The time has come for hoteliers to examine their own standards of ethics, value systems, and professionalism,” Haywood says. And it is ethics that are at the center of this issue; Haywood holds that component in an estimable position. “Hoteliers must become value-driven,” advises Haywood. “They must be committed to excellence both in actualizing their best potentialities and in excelling in all they do. In other words, the professionalization of the hotelier can be achieved through a high degree of self-control, internalized values, codes of ethics, and related socialization processes,” he expands. “Serious ethical issues exist for hoteliers as well as for many business people and professionals in positions of responsibility,” Haywood alludes in defining some inter-industry problems. “The acceptance of kickbacks and gifts from suppliers, the hiding of income from taxation authorities, the lack of interest in installing and maintaining proper safety and security systems, and the raiding of competitors' staffs are common practices,” he offers, with the reasoning that if these problems can occur within ranks, then there is going to be a negative backlash in the public/client arena as well. Haywood divides the key principles of his thesis statement - ethics, value systems, and professionalism – into specific elements, and then continues to broaden the scope of each element. Promotion, product/service, and pricing are additional key components in Haywood’s discussion, and he addresses each with verve and vitality. Haywood references the four character types - craftsmen, jungle fighters, company men, and gamesmen – via a citation to Michael Maccoby, in the portion of the discussion dedicated to morality and success. Haywood closes with a series of questions derived from Lawrence Miller's American Spirit, Visions of a New Corporate Culture, each question designed to focus, shape, and organize management's attention to the values that Miller sets forth in his piece.

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Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.