We present a Markov chain analysis for studying the performance of wireless ad hoc networks. The models presented in this dissertation support an arbitrary backoff strategy. We found that the most important parameter affecting the performance of binary exponential backoff is the initial backoff window size. Our experimental results show that the probability of collision can be reduced when the initial backoff window size equals the number of terminals. Thus, the throughput of the system increases and, at the same time, the delay to transmit the frame is reduced. In our second contribution, we present a new analytical model of a Medium Access Control (MAC) layer for wireless ad hoc networks that takes into account frame retry limits for a four-way handshaking mechanism. This model offers flexibility to address some design issues such as the effects of traffic parameters as well as possible improvements for wireless ad hoc networks. It effectively captures important network performance characteristics such as throughput, channel utilization, delay, and average energy. Under this analytical framework, we evaluate the effect of the Request-to-Send (RTS) state on unsuccessful transmission probability and its effect on performance particularly when the hidden terminal problem is dominant, the traffic is heavy, or the data frame length is very large. By using our proposed model, we show that the probability of collision can be reduced when using a Request-to-Send/Clear- to-Send (RTS/CTS) mechanism. Thus, the throughput increases and, at the same time, the delay and the average energy to transmit the frame decrease. In our third contribution, we present a new analytical model of a MAC layer for wireless ad hoc networks that takes into account channel bit errors and frame retry limits for a two-way handshaking mechanism. This model offers flexibility to address design issues such as the effects of traffic parameters and possible improvements for wireless ad hoc networks. We illustrate that an important parameter affecting the performance of binary exponential backoff is the initial backoff window size. We show that for a low bit error rate (BER) the throughput increases and, at the same time, the delay and the average energy to transmit the frame decrease. Results show also that the negative acknowledgment-based (NAK-based) model proves more useful for a high BER. In our fourth contribution, we present a new analytical model of a MAC layer for wireless ad hoc networks that takes into account Quality of Service (QoS) of the MAC layer for a two-way handshaking mechanism. The model includes a high priority traffic class (class 1) and a low priority traffic class (class 2). Extension of the model to more QoS levels is easily accomplished. We illustrate an important parameter affecting the performance of an Arbitration InterFrame Space (AIFS) and small backoff window size limits. They cause the frame to start contending the channel earlier and to complete the backoff sooner. As a result, the probability of sending the frame increases. Under this analytical framework, we evaluate the effect of QoS on successful transmission probability and its effect on performance, particularly when high priority traffic is dominant. / Graduate

<div>Multi-model inference covers a wide range of modern statistical applications such as variable selection, model confidence set, model averaging and variable importance.</div><div>The performance of multi-model inference depends on the availability of candidate models, whose quality has been rarely studied in literature. In this dissertation, we study genetic algorithm (GA) in order to obtain high-quality candidate models. Inspired by the process of natural selection, GA performs genetic operations such as selection, crossover and mutation iteratively to update a collection of potential solutions (models) until convergence. The convergence properties are studied based on the Markov chain theory and used to design an adaptive termination criterion that vastly reduces the computational cost. In addition, a new schema theory is established to characterize how the current model set is improved through evolutionary process. Extensive numerical experiments are carried out to verify our theory and demonstrate the empirical power of GA, and new findings are obtained for two real data examples. </div>

The objective of the study is to apply Markov chain analysis to analyze student flow through King Abdul Aziz University (KAU) in Saudi Arabia, and to predict important metrics such as graduation and dropout rates. This objective arises from examination of the policies of KAU University. We begin with background information detailing the subject of study, then move into a general outline of stochastic processes. We then use these methods to construct a specific matrix of transition probabilities with data from the university student population. Finally, we discuss the calculation of the possibilities of transition between each level of study and the average time a student takes to complete each stage. The study uses Markov chains with these outcomes to analyze student retention data from the Department of Mathematics at KAU. From this analysis, the study will provide university policy recommendations that can be generalized to examine other universities.

Clinical supervision is integral to promoting the professional development of counselors-in-training and gatekeeping the counseling services provided by counselor trainees (Bernard & Goodyear, 2014). Despite the value of studying participants’ retrospective perceptions about or reflections upon supervision, the supervisory process in which supervision transpires is infrequently quantified and measured (Holloway, 1982; Holloway, 1987). As described by most developmental supervision models, clinical supervision is “a process with sequential and qualitatively distinct stages through which supervisors and trainees progress” (Littrell, Lee-Borden, & Lorenz, 1976, p. 134). In order to capture these stages and phenomena with observable and measurable units, the author used six states of interest to measure the supervision process, which exhibit the progressively complex nature of clinical supervision. The six states include: (a) social interfacing (non-skills phase), (b) reflecting on foundational competencies, (c) deepening case conceptualization, (d) processing the relational management, (e) overcoming personal and multicultural barriers, and (f) furthering professional development. These states underpin the codebook of this study and are used to conceptualize the supervision process. Although the interactions between the supervisor and supervisee are transient and difficult to grasp, supervisory interactions move from one state to another. Indeed, state-transitional dynamics of clinical supervision are subject to a constellation of factors that supervisors and supervisees initially bring in and constantly reinforce, such as supervisory styles, supervisee developmental levels, supervisory working alliance, and supervisee satisfaction with clinical supervision. By using Markov chain analysis, this study detects the overall transitional dynamics of supervisory dyads and investigates how transitional dynamics vary based on the aforementioned variables that manifest themselves as supervision dynamics unfold and closely interface with other supervision variables. Results of this study provide implications for clinical supervisors, counselor educators, and counselors-in-training.

Transforming the aging electric grid to a smart grid is an active area of research in industry and the government. One of the main objectives of the smart grid is to improve the efficiency of power generation, transmission and distribution and also to improve the stability and the reliability of the grid. In order to achieve this, various processes involved in power generation, transmission, and distribution should be armed with advanced sensor technologies, computing, communication and networking capabilities to an unprecedented level. These high speed data transfer and computational abilities aid power system engineers to obtain wide area measurements, achieve better control of power system operations and improve the reliability of power supply and the efficiency of different power grid operations. In the process of making the grid smarter, problems existing in traditional grid applications can be identified and solutions have to be developed to fix the identified issues. In this dissertation, two problems that aid power system engineers to meet the above mentioned smart grid's objective are researched. One problem is related to the distribution-side smart grid and the other one is a part of the transmission-side smart grid. Advanced Metering Infrastructure (AMI) is one of the important distribution-side smart grid applications. AMI is a technology where smart meters are installed at customer site which gives the utilities the ability to monitor and collect information related to the amount of electricity, water, and gas consumed by the user. Many recent research studies suggested the use of 3G cellular CDMA2000 for AMI network as it provides an advanced and cost effective solution for smart grid communications. Taking into account both technical and non-technical factors such as extended lifetime, security, availability and control of the solution, Alliander, an electric utility in Netherlands deployed a private 3G CDMA2000 network for smart metering. Although 3G CDMA2000 satisfies the requirements of smart grid applications, an analysis on the use of the current state of the art 3G CDMA2000 for smart grid applications indicates that its usage results in high percentage of control overhead, high latency and high power consumption for data transfer. As a part of this dissertation, we proposed FLEX-MAC - a new Medium Access Control (MAC) protocol that reduces the latency and overhead in smart meter data collection when compared to 3G CDMA2000 MAC. As mentioned above the second problem studied in this dissertation is related to the transmission-side grid. Power grid transmission and sub-transmission lines are generally protected by distance relays. After a thorough analysis of U.S. historical blackouts, North American Electric Reliability Council (NERC) has concluded that the hidden failure induced tripping of distance relays is responsible for 70% of the U.S. blackouts. As a part of this dissertation, agent based distance relaying protection scheme is proposed to improve the robustness of distance relays to hidden failures and thus reduce the probability of blackouts. This dissertation has two major contributions. First, a hierarchically distributed non-intrusive Agent Aided Distance Relaying Protection Scheme (AADRPS) is proposed to improve the robustness of distance relays to hidden failures. The problem of adapting the proposed AADRPS to a larger power system network consisting of thousands of buses is modeled as an integer linear programming multiple facility location optimization problem. Distance relaying protection scheme is a real time system and has stringent timing requirements. Therefore, in order to verify if the proposed AADRPS meets the timing requirements or not and also to check for deadlocks, verification models based on UPPAAL real time model checker are provided in this dissertation. So, the entire framework consisting of AADRPS that aids in increasing the robustness of distance relays and reducing the possibility of blackouts, the multiple facility location optimization models and the UPPAAL real time model checker verification models form one of the major contributions of this dissertation. The second contribution is related to the MAC layer of AMI networks. In this dissertation, FLEX-MAC - a novel and flexible MAC protocol is proposed to reduce the overhead and latency in smart meter data collection. The novelty of the FLEX-MAC lies in its ability to change the mode of operation based on the type of the data being collected in a smart meter network. FLEX-MAC employs Frame and Channel Reserved (FCR) MAC or Frame Reserved and Random Channel (FRRC) MAC for scheduled data collection. Power outage data in an AMI network is considered as a random data . In a densely populated area, during an outage, a large number of smart meters attempt to report the outage, which significantly increases the Random Access CHannel (RACH) load. In order to reduce the RACH traffic during an outage, this dissertation proposes a Time Hierarchical Scheme (THS). Also, in order to minimize the total time to collect the power outage data, a Backward Recursive Dynamic Programming (BRDP) approach is proposed to adapt the transmission rate of smart meters reporting an outage. Both the Optimal Transmission Rate Adaption and Time Hierarchical Scheme form the basis of OTRA-THS MAC which is employed by FLEX-MAC for random data collection. Additionally, in this work, Markov chain models are presented for evaluating the performance of FCR and FRRC MACs in terms of average throughput and delay. Also, another Markov model is presented to find the mean time to absorption or mean time to collect power outage data of OTRA-TH MAC during an outage. / Ph. D.

On s'intéresse à l'étude d'algorithmes stochastiques pour l'optimisation numérique boîte-noire. Dans la première partie de cette thèse, on présente une méthodologie pour évaluer efficacement des stratégies d'adaptation du step-size dans le cas de l'optimisation boîte-noire sans contraintes. Le step-size est un paramètre important dans les algorithmes évolutionnaires tels que les stratégies d'évolution; il contrôle la diversité de la population et, de ce fait, joue un rôle déterminant dans la convergence de l'algorithme. On présente aussi les résultats empiriques de la comparaison de trois méthodes d'adaptation du step-size. Ces algorithmes sont testés sur le testbed BBOB (black-box optimization benchmarking) de la plateforme COCO (comparing continuous optimisers). Dans la deuxième partie de cette thèse, sont présentées nos contributions dans le domaine de l'optimisation boîte-noire avec contraintes. On analyse la convergence linéaire d'algorithmes stochastiques adaptatifs pour l'optimisation sous contraintes dans le cas de contraintes linéaires, gérées avec une approche Lagrangien augmenté adaptative. Pour ce faire, on étend l'analyse par chaines de Markov faite dans le cas d'optimisation sans contraintes au cas avec contraintes: pour chaque algorithme étudié, on exhibe une classe de fonctions pour laquelle il existe une chaine de Markov homogène telle que la stabilité de cette dernière implique la convergence linéaire de l'algorithme. La convergence linéaire est déduite en appliquant une loi des grands nombres pour les chaines de Markov, sous l'hypothèse de la stabilité. Dans notre cas, la stabilité est validée empiriquement. / We investigate various aspects of adaptive randomized (or stochastic) algorithms for both constrained and unconstrained black-box continuous optimization. The first part of this thesis focuses on step-size adaptation in unconstrained optimization. We first present a methodology for assessing efficiently a step-size adaptation mechanism that consists in testing a given algorithm on a minimal set of functions, each reflecting a particular difficulty that an efficient step-size adaptation algorithm should overcome. We then benchmark two step-size adaptation mechanisms on the well-known BBOB noiseless testbed and compare their performance to the one of the state-of-the-art evolution strategy (ES), CMA-ES, with cumulative step-size adaptation. In the second part of this thesis, we investigate linear convergence of a (1 + 1)-ES and a general step-size adaptive randomized algorithm on a linearly constrained optimization problem, where an adaptive augmented Lagrangian approach is used to handle the constraints. To that end, we extend the Markov chain approach used to analyze randomized algorithms for unconstrained optimization to the constrained case. We prove that when the augmented Lagrangian associated to the problem, centered at the optimum and the corresponding Lagrange multipliers, is positive homogeneous of degree 2, then for algorithms enjoying some invariance properties, there exists an underlying homogeneous Markov chain whose stability (typically positivity and Harris-recurrence) leads to linear convergence to both the optimum and the corresponding Lagrange multipliers. We deduce linear convergence under the aforementioned stability assumptions by applying a law of large numbers for Markov chains. We also present a general framework to design an augmented-Lagrangian-based adaptive randomized algorithm for constrained optimization, from an adaptive randomized algorithm for unconstrained optimization.