The seminal paper by Gerber and Shiu (1998) gave a huge boost to the study of risk theory by not only unifying but also generalizing the treatment and the analysis of various risk-related quantities in one single mathematical function - the Gerber-Shiu expected discounted penalty function, or Gerber-Shiu function in short. The Gerber-Shiu function is known to possess many nice properties, at least in the case of the classical compound Poisson risk model. For example, upon the introduction of a dividend barrier strategy, it was shown by Lin et al. (2003) and Gerber et al. (2006) that the Gerber-Shiu function with a barrier can be expressed in terms of the Gerber-Shiu function without a barrier and the expected value of discounted dividend payments. This result is the so-called dividends-penalty identity, and it holds true when the surplus process belongs to a class of Markov processes which are skip-free upwards. However, one stringent assumption of the model considered by the above authors is that all the interclaim times and the claim sizes are independent, which is in general not true in reality. In this thesis, we propose to analyze the Gerber-Shiu functions under various dependent structures. The main focus of the thesis is the risk model where claims follow a Markovian arrival process (MAP) (see, e.g., Latouche and Ramaswami (1999) and Neuts (1979, 1989)) in which the interclaim times and the claim sizes form a chain of dependent variables. The first part of the thesis puts emphasis on certain dividend strategies. In Chapter 2, it is shown that a matrix form of the dividends-penalty identity holds true in a MAP risk model perturbed by diffusion with the use of integro-differential equations and their solutions. Chapter 3 considers the dual MAP risk model which is a reflection of the ordinary MAP model. A threshold dividend strategy is applied to the model and various risk-related quantities are studied. Our methodology is based on an existing connection between the MAP risk model and a fluid queue (see, e.g., Asmussen et al. (2002), Badescu et al. (2005), Ramaswami (2006) and references therein). The use of fluid flow techniques to analyze risk processes opens the door for further research as to what types of risk model with dependency structure can be studied via probabilistic arguments. In Chapter 4, we propose to analyze the Gerber-Shiu function and some discounted joint densities in a risk model where each pair of the interclaim time and the resulting claim size is assumed to follow a bivariate phase-type distribution, with the pairs assumed to be independent and identically distributed (i.i.d.). To this end, a novel fluid flow process is constructed to ease the analysis. In the classical Gerber-Shiu function introduced by Gerber and Shiu (1998), the random variables incorporated into the analysis include the time of ruin, the surplus prior to ruin and the deficit at ruin. The later part of this thesis focuses on generalizing the classical Gerber-Shiu function by incorporating more random variables into the so-called penalty function. These include the surplus level immediately after the second last claim before ruin, the minimum surplus level before ruin and the maximum surplus level before ruin. In Chapter 5, the focus will be on the study of the generalized Gerber-Shiu function involving the first two new random variables in the context of a semi-Markovian risk model (see, e.g., Albrecher and Boxma (2005) and Janssen and Reinhard (1985)). It is shown that the generalized Gerber-Shiu function satisfies a matrix defective renewal equation, and some discounted joint densities involving the new variables are derived. Chapter 6 revisits the MAP risk model in which the generalized Gerber-Shiu function involving the maximum surplus before ruin is examined. In this case, the Gerber-Shiu function no longer satisfies a defective renewal equation. Instead, the generalized Gerber-Shiu function can be expressed in terms of the classical Gerber-Shiu function and the Laplace transform of a first passage time that are both readily obtainable. In a MAP risk model, the interclaim time distribution must be phase-type distributed. This leads us to propose a generalization of the MAP risk model by allowing for the interclaim time to have an arbitrary distribution. This is the subject matter of Chapter 7. Chapter 8 is concerned with the generalized Sparre Andersen risk model with surplus-dependent premium rate, and some ordering properties of certain ruin-related quantities are studied. Chapter 9 ends the thesis by some concluding remarks and directions for future research.

Since World War I, the area of acoustic undersea warfare has witnessed several research activities targeting the development of advanced systems to accurately detect and localize underwater moving targets. One of the main categories of these systems is the passive sound navigation and ranging (SONAR) that searches for the location of the ships and submarines by listening to the radiated noise produced by their propellers, machinery, and flow dynamics. The performance of the passive sonar highly depends on the particular array signal processing algorithms used in practice. Presently, one of the main challenges is to accurately estimate the target direction of arrival (DOA) in severe underwater environments. This thesis is proposed to enhance the DOA estimation in two distinct applications. This first application is to improve the spatial resolution of the uniform linear towed arrays. This is done by applying new spatial extrapolation techniques called 2D- and 3D- fast orthogonal search (FOS) for both uniform linear and rectangular arrays, respectively. The presented methods show better performance than the conventional methods with respect to signal to noise ratio (SNR), number of snapshots and angular separation. Moreover it reduces the computational complexity required by the spatial extrapolation methods based on linear prediction approach. The other application concerns with developing a new DOA estimation that provides better spatial spectrum than the one provided by conventional beamforming (CBF) when a nonuniform linear array of directional frequency analysis and recording (DIFAR) sonobuoys is employed. The introduced technique or the so called fourth order cumulant beamforming (FOCBF) and shows an outstanding performance compared to CBF especially in low SNR. Furthermore, a warping FOC-BF (WFOC-BF) method obtained by augmenting a warping beamforming technique with FOC-BF is proposed to reduce the required computational complexity by FOC-BF while preserving the same performance. / Thesis (Ph.D, Electrical & Computer Engineering) -- Queen's University, 2012-06-27 14:59:33.941

In this thesis, a system to locate an electrostatic discharge (ESD) event within an electronic device has been developed. ESD can cause a device to fail legally required radiated emissions limits as well as disrupt intended operation. The system used a fast oscilloscope with four channels, each channel attached to a high frequency near-field antenna. These antennas were placed at known locations in three dimensional space to measure the fields radiated from the ESD event. A Time-Difference-of-Arrival technique was used to calculate the location of the ESD event. Quick determination of the ESD event location provides developers with a tool that saves them time and money by eliminating the time-consuming and tedious method of general ESD mitigation within a product.

In this study, a single machine batch-scheduling problem with incompatible jobs and dynamic arrivals is examined. The objective function is the minimization of the total flow time of the jobs. For solving problems a case specific branch and bound algorithm with a heuristic upper bound scheme and two alternative lower bound procedures is used. An extensive computational experiment is conducted to investigate the effects of certain parameters on the computation time. For the most difficult parameter combination branch and bound algorithm can solve the problems about 25 jobs with 4 different job types in a 10 minutes time on average. For the problem types with higher number of jobs and the most difficult parameter combination proposed upper bound heuristic can be used to obtain near optimal solutions.

This study investigates the manifestation of geometric features of turbine blades in signatures of non-optical time of arrival (ToA) probes. The approach enables an evaluation of the various signal characteristics used for defining ToA for a range of airfoil geometries and provides knowledge about additional waveform characteristics. The objective of this research is to increase the accuracy of microwave ToA probes by gaining a better understanding of the microwave signals in five steps. Firstly, ToA definitions used in the past are compared. Considering accuracy, computational effort, and versatility, the constant fraction crossing definition is found to be the most accurate. Secondly, an experimental apparatus capable of measuring airfoil ToA with microwave probes and optical probes as a reference is designed and built. As a third step, a catalog of 16 turbine blade geometries is developed. Fourthly, the signatures of these turbine blades are acquired using both the optical and the microwave probes. Finally, the impact of the geometric effects on the signatures is evaluated. The quality of the microwave results is found to be highly dependent on the polarization of the microwaves. Analysis of the time domain signal shows that decreasing the blade width, increasing the chord angle, or incorporating a blade tip pocket or a varying cross-section leads to a decrease in the amplitude of the peak caused by the blade. Increasing the blade width and incorporating a chord angle leads to an increase in peak width. A frequency domain analysis is conducted on the microwave signals and verified using a synthetic signal. This analysis confirms the findings from the time domain analysis. The time domain analysis of the laser measurements shows that the spatial resolution of the laser is much higher than that of the microwave sensor. Consequently, the signal acquired with the optical setup provides a good means of defining the blade ToA. The knowledge gained in this study about the sensor and its interaction with passing blade tips of varying geometry can be used to enhance the understanding of microwave ToA measurements. This knowledge provides further insight into airfoil and engine health.

Continuous Descent Arrival (CDA) procedures have been shown to minimize the thrust required during landing, thereby reducing noise, emissions, and fuel usage for commercial aircraft. Thus, implementation of CDA at Atlanta's Hartsfield-Jackson International Airport, the world's busiest airport, would result in significant reductions in environmental impact and airline operating costs. The Air Transportation Laboratory at Georgia Tech, Delta Air Lines, and the local FAA facilities (Atlanta Center and Atlanta TRACON) collaborated to design CDA procedures for early morning arrivals from the west coast. Using the Tool for Analysis of Separation and Throughput (TASAT), we analyzed the performance of various aircraft types over a wide range of weights and wind conditions to determine the optimum descent profile parameters and to find the required spacing between aircraft types at a fixed metering point to implement the procedure. However, to see the full benefits of CDA, these spacing targets must be adhered, lest there will be a loss in capacity or negation of the noise, emissions, and fuel savings benefits. Thus a method was developed to determine adjustments to cruise speeds while aircraft are still en route, to achieve these spacing targets and to optimize fleet wide fuel burn increase. The tool in development, En route Speed Change Optimization Relay Tool (ESCORT), has been shown to solve the speed change problem quickly, incorporating aircraft fuel burn information and dividing the speed changes fairly across multiple airlines. The details of this tool will be explained in this thesis defense. Flight tests were conducted in April-May of 2007, where it was observed that the spacing targets developed by TASAT were accurate but that delivery of these aircraft to the metering point with the desired spacing targets was very challenging without automation. Thus, further flight tests will be conducted in 2008 using the en route spacing tool described above to validate the improvement it provides in terms of accurately delivering aircraft to the metering point.

A MAP/PH/1 queue is a queue having a Markov arrival process (MAP), and a single server with phase-type (PH -type) distributed service time. This thesis considers the departure process from these type of queues. We use matrix analytic methods, the Jordan canonical form of matrices, non-linear filtering and approximation techniques. The departure process of a queue is important in the analysis of networks of queues, as it may be the arrival process to another queue in the network. If a simple description were to exist for a departure process, the analysis of at least feed-forward networks of these queues would then be analytically tractable. Chapter 1 is an introduction to some of the literature and ideas surrounding the departure process from MAP/PH/1 queues. Chapter 2 sets up the basic notation and establishes some results which are used throughout the thesis. It contains a preliminary consideration of PH -type distributions, PH -renewal processes, MAP s, MAP/PH/1 queues, non-linear filtering and the Jordan canonical form. Chapter 3 is an expansion of "The Output process of an MMPP/M/1 queue", where the question of whether a MAP description can exist for the departure process of a non-trivial MAP/M/1 queue is considered. In a 1994 paper, Olivier and Walrand conjectured that the departure process of a MAP/PH/1 queue is not a MAP unless the queue is a stationary M/M/1 queue. This conjecture was prompted by their claim that the departure process of an MMPP/M/1 queue is not MAP unless the queue is a stationary M/M/1 queue. We show that their proof has an algebraic error, which leaves open the above question of whether the departure process of an MMPP/PH/1 queue is a MAP or not. In Chapter 4, the more fundamental problem of identifying stationary M/M/1 queues in the class of MAP/PH/1 queues is considered. It is essential to be able to determine from its generator when a stationary MAP is a Poisson process. This does not appear to have been discussed in the literature prior to the author's paper, where this deficiency was remedied using ideas from non-linear filtering theory, to give a characterisation as to when a stationary MAP is a Poisson process. Chapter 4 expands upon "When is a MAP Poisson". This investigation of higher order representations of the Poisson process is motivated by first considering when a higher order PH -type distribution is just negative exponential. In Chapter 5, we consider the related question of minimal order representations for PH -type distributions, an issue which has attracted much interest in the literature. A discussion of other authors' ideas is given and these ideas are then inter-related to the work presented in Chapter 4 on the PH -type distributions. The MAP/M/1 queue is then considered in Chapter 6 from the perspective of whether having an exact level and phase independent stationary distribution of the geometric form [Formula - Not available: see pdf version of the abstract] implies that the MAP is Poisson. The answer is in the affirmative for this question, but the converse is not strictly true. Apart from showing the ubiquitous asymptotic form of level and phase independence exhibited by all stable MAP/M/1 queues, we prove that a very large class of stable queues, exhibits what we have termed shift-one level and phase independence. Stable MAP/M/1 queues exhibiting shift-one level and phase independence, are characterised by a stationary distribution of the following form: [Formula - Not Available: see pdf version of the abstract] In Chapter 7, a family of approximations is proposed for the output process of a stationary MAP/PH/1 queue. To check the viability of these approximations, they are used as input to another single server queue. Performance measures for the second server are obtained analytically in both the tandem and approximation cases, thus eliminating the need for simulation to compare results. Comparison of these approximations is also made against other approximation methods in the literature. In Chapter 8, we show that our approximations from Chapter 7 have the property of exactly matching the inter-departure time distribution. Our kth approximation also accurately captures the first k-1 lag-correlation coefficients of the stationary departure process. The proofs of this direct association between lag-correlation coefficients and the level of complexity k are given. / Thesis (Ph.D.)--School of Applied Mathematics, 1999.

Urban areas are currently facing challenges in terms of traffic congestion due to city expansion and population increase. In some cases, physical solutions are limited. For example, in certain areas it is not possible to expand roads or build a new bridge. Therefore, making public transpiration (PT) affordable, more attractive and intelligent could be a potential solution for these challenges. Accuracy in bus running time and bus arrival time is a key component of making PT attractive to ridership. In this thesis, a dynamic model based on Kalman filter (KF) has been developed to predict bus running time and dwell time while taking into account real-time road incidents. The model uses historical data collected by Automatic Vehicle Location system (AVL) and Automatic Passenger Counters (APC) system. To predict the bus travel time, the model has two components of running time prediction (long and short distance prediction) and dwell time prediction. When the bus closes its doors before leaving a bus stop, the model predicts the travel time to all downstream bus stops. This is long distance prediction. The model will then update the prediction between the bus’s current position and the upcoming bus stop based on real-time data from AVL. This is short distance prediction. Also, the model predicts the dwell time at each coming bus stop. As a result, the model reduces the difference between the predicted arrival time and the actual arrival time and provides a better understanding for the transit network which allows lead to have a good traffic management.

O presente estudo teve por objetivo examinar alguns indicadores de regressão e de crescimento do primogênito, longitudinalmente, da gestação aos dois anos de vida do irmão. Foi realizado estudo de caso coletivo, do qual participaram três primogênitos e seus respectivos genitores, em três momentos de análise dos dados (no terceiro trimestre de gestação, aos doze e aos vinte e quatro meses do bebê). Os participantes pertenciam à amostra de um projeto longitudinal maior. Com as crianças, foi aplicado um teste projetivo e as mães e os pais responderam, separadamente, a entrevistas semi-dirigidas. Análise de conteúdo revelou um predomínio de indicadores de regressão do primogênito no período gestacional, tanto a partir do ponto de vista da criança quanto da mãe e do pai. Aos vinte e quatro meses, o teste projetivo revelou indicadores tanto de regressão quanto de crescimento, enquanto para os genitores continuou predominando a regressão. No que tange aos sentimentos maternos e paternos, percebeu-se culpa, preocupação e receio provocados pela regressão do primogênito, durante a gestação e aos vinte e quatro meses. Os genitores parecem ter acolhido mais facilmente a regressão durante a gestação. Ainda que tenham acolhido a regressão aos doze e aos vinte e quatro meses, também estimularam comportamento “de adulto” no primogênito. Aos vinte e quatro meses, predominaram estresse, cansaço, incômodo, impaciência frente à regressão, e orgulho, contentamento e surpresa diante do crescimento. Os resultados revelaram que a regressão foi um meio que o primogênito encontrou para enfrentar o contexto de chegada de um irmão, enquanto que o crescimento revelou a capacidade para novas conquistas ou ainda os custos de assumir novas responsabilidades e o papel de filho mais velho. Assim, tanto as manifestações regressivas quanto as de crescimento oportunizaram um ir e vir saudável e a possibilidade de amadurecimento ou de desenvolvimento rumo à independência. As implicações desses achados que envolvem o processo de tornar-se irmão são destacadas no âmbito da pesquisa e clínico. / The present study aimed to examine longitudinally, from pregnancy to the second child’s second year, some indicators of regression and growth in the firstborn. A collective-case study was carried out, in which three firstborn and their parents took part. The data were collected in three different moments: third trimester of pregnancy, at the baby’s twelfth and twenty-first month. The participants were sellected from a larger longitudinal project. A projective test was used in order to acess the children’s point of view whilst the parents’ point of view was examined through an individual semi-structured interview with each parent. Content analysis revealed a predominance of indicators of regression in the firstborn during pregnancy, both from the children’s and the parents’ point of view. When the firstborn was 24 months old, the projective test revealed indicators of both regression and growth, while from the parents’ perspective, there was still predominance of regression. As far as maternal and paternal feelings are concerned, parents reported guilt, concern and fear, provoked by the firstborn’s regression, during pregnancy and when the second child was 24 months old. The parents seem to have accepted these feelings more easily during pregnancy. Even though they seem to have accepted regression when the second child was 24 months old, they also stimulated “adult-like” behaviour in the firstborn. When the firstborn was twenty-four months, parents reported stress, tiredness, uneasiness, impatience in response to regression in the firstborn, and pride, hapiness and surprise in response to growth. The results revealed that regression was used as a means to cope with the context of a sibling’s arrival whereas growth revealed the firstborn’s capacity for new achievements or the costs involved in assuming new responsibilities and the role of an older child. Therefore, both regressive and growth manifestations enabled a healthy to and fro and the possibility of maturation or development towards independence. The research and clinical implications of these findings that involve the process of becoming a sibling are highlighted.

O presente estudo teve por objetivo examinar alguns indicadores de regressão e de crescimento do primogênito, longitudinalmente, da gestação aos dois anos de vida do irmão. Foi realizado estudo de caso coletivo, do qual participaram três primogênitos e seus respectivos genitores, em três momentos de análise dos dados (no terceiro trimestre de gestação, aos doze e aos vinte e quatro meses do bebê). Os participantes pertenciam à amostra de um projeto longitudinal maior. Com as crianças, foi aplicado um teste projetivo e as mães e os pais responderam, separadamente, a entrevistas semi-dirigidas. Análise de conteúdo revelou um predomínio de indicadores de regressão do primogênito no período gestacional, tanto a partir do ponto de vista da criança quanto da mãe e do pai. Aos vinte e quatro meses, o teste projetivo revelou indicadores tanto de regressão quanto de crescimento, enquanto para os genitores continuou predominando a regressão. No que tange aos sentimentos maternos e paternos, percebeu-se culpa, preocupação e receio provocados pela regressão do primogênito, durante a gestação e aos vinte e quatro meses. Os genitores parecem ter acolhido mais facilmente a regressão durante a gestação. Ainda que tenham acolhido a regressão aos doze e aos vinte e quatro meses, também estimularam comportamento “de adulto” no primogênito. Aos vinte e quatro meses, predominaram estresse, cansaço, incômodo, impaciência frente à regressão, e orgulho, contentamento e surpresa diante do crescimento. Os resultados revelaram que a regressão foi um meio que o primogênito encontrou para enfrentar o contexto de chegada de um irmão, enquanto que o crescimento revelou a capacidade para novas conquistas ou ainda os custos de assumir novas responsabilidades e o papel de filho mais velho. Assim, tanto as manifestações regressivas quanto as de crescimento oportunizaram um ir e vir saudável e a possibilidade de amadurecimento ou de desenvolvimento rumo à independência. As implicações desses achados que envolvem o processo de tornar-se irmão são destacadas no âmbito da pesquisa e clínico. / The present study aimed to examine longitudinally, from pregnancy to the second child’s second year, some indicators of regression and growth in the firstborn. A collective-case study was carried out, in which three firstborn and their parents took part. The data were collected in three different moments: third trimester of pregnancy, at the baby’s twelfth and twenty-first month. The participants were sellected from a larger longitudinal project. A projective test was used in order to acess the children’s point of view whilst the parents’ point of view was examined through an individual semi-structured interview with each parent. Content analysis revealed a predominance of indicators of regression in the firstborn during pregnancy, both from the children’s and the parents’ point of view. When the firstborn was 24 months old, the projective test revealed indicators of both regression and growth, while from the parents’ perspective, there was still predominance of regression. As far as maternal and paternal feelings are concerned, parents reported guilt, concern and fear, provoked by the firstborn’s regression, during pregnancy and when the second child was 24 months old. The parents seem to have accepted these feelings more easily during pregnancy. Even though they seem to have accepted regression when the second child was 24 months old, they also stimulated “adult-like” behaviour in the firstborn. When the firstborn was twenty-four months, parents reported stress, tiredness, uneasiness, impatience in response to regression in the firstborn, and pride, hapiness and surprise in response to growth. The results revealed that regression was used as a means to cope with the context of a sibling’s arrival whereas growth revealed the firstborn’s capacity for new achievements or the costs involved in assuming new responsibilities and the role of an older child. Therefore, both regressive and growth manifestations enabled a healthy to and fro and the possibility of maturation or development towards independence. The research and clinical implications of these findings that involve the process of becoming a sibling are highlighted.