La investigación tuvo como objetivo proponer la mejora en el servicio de atención aplicando la teoría de colas para reducir los tiempos de espera del centro médico P&P Anatomy. Se determinó el día con mayor afluencia, los tiempos de espera del paciente, las especialidades más demandadas con Pareto, se calculó la cantidad optima de servidores usando teoría de colas, software QM for Windows y se simuló las mejoras en Promodel. Se tiene mayor afluencia el día sábado, con un tiempo de espera promedio de 32 minutos y las especialidades más demandadas odontología, medicina y terapia física, con un nivel de servicio del 50% y 80 % e insatisfacción 35%. Mediante las propuestas de mejora usando la teoría de colas, y simulación en Promodel, estandarización de tiempos en la atención, se disminuyó a 22 minutos el tiempo de espera, y el porcentaje de utilización en el área de odontología pasó de 86 % a 50 %, en terapia física y medicina de 68 % a de 25,5 %, de igual forma aumentó el nivel de servicio al 95% en odontología y 91% en terapia física y medicina. Finalmente, con la medición del costo /beneficio de la propuesta se obtiene un B/C S/.1,10 con ello se concluye que el proyecto es viable. / The objective of the research was to propose improvement in the care service by applying queuing theory to reduce waiting times at the P&P Anatomy medical center. The busiest day, patient waiting times, the most in-demand specialties were determined with Pareto, the optimal number of servers was calculated using queuing theory, QM for Windows software, and the improvements were simulated in Promodel. There is greater influx on Saturday, with an average waiting time of 32 minutes and the most in-demand specialties: dentistry, medicine and physical therapy, with a service level of 50% and 80% and dissatisfaction 35%. Through improvement proposals using queuing theory, and simulation in Promodel, standardization of care times, the waiting time was reduced to 22 minutes, and the percentage of utilization in the dentistry area went from 86% to 50%. , in physical therapy and medicine from 68% to 25.5%, similarly increased the level of service to 95% in dentistry and 91% in physical therapy and medicine. Finally, with the measurement of the cost/benefit of the proposal, a B/C S/.1,10 is obtained, which concludes that the project is viable.

This research investigates and develops a new approach to the management of service quality with the emphasis on patient and staff satisfaction in the healthcare sector. The challenge of measuring the quality of service in healthcare requires us to view the problem from multiple perspectives. At the philosophical level, the true nature of quality is still debated; at the psychological level, an accurate conceptual representation is problematic; whilst at the physical level, an accurate measurement of the concept still remains elusive to practitioners and academics. This research focuses on the problem of quality measurement in the healthcare sector. The contributions of this research are fourfold: Firstly, it argues that from the technological point of view the research to date into quality of service in healthcare has not considered methods of real-time measurement and monitoring. This research identifies the key elements that are necessary for developing a real-time quality monitoring system for the healthcare environment.Secondly, a unique index is proposed for the monitoring and improvement of healthcare performance using information-theoretic entropy formalism. The index is formulated based on five key performance indicators and was tested as a Healthcare Quality Index (HQI) based on three key quality indicators of dignity, confidence and communication in an Accident and Emergency department. Thirdly, using an M/G/1 queuing model and its underlying Little’s Law, the concept of Effective Satisfaction in healthcare has been proposed. The concept is based on a Staff-Patient Satisfaction Relation Model (S-PSRM) developed using a patient satisfaction model and an empirically tested model developed for measuring staff satisfaction with workload (service time). The argument is presented that a synergy between patient satisfaction and staff satisfaction is the key to sustainable improvement in healthcare quality. The final contribution is the proposal of a Discrete Event Simulation (DES) modelling platform as a descriptive model that captures the random and stochastic nature of healthcare service provision process to prove the applicability of the proposed quality measurement models.

En raison de l'augmentation des coûts d'énergie et des préoccupations environnementales telles que les empreintes de carbone élevées, les systèmes de la production d'électricité centralisée se restructurent pour profiter des avantages de la production distribuée afin de répondre aux exigences énergétiques toujours croissantes. Les microgrids sont considérés comme une solution possible pour déployer une génération distribuée qui inclut des ressources énergétiques distribuées DERs (Distributed Energy Resources)(e.g, solaire, éolienne, batterie, etc). Dans cette thèse, nous traitons les défis de la gestion d'énergie dans un microgrid industriel où les charges énergétique sont constituées de processus industriels. Notre plan consiste à diviser la gestion de l'énergie du microgrid en deux parties: la production et la demande d’énergie.Du côté de la production d'énergie, les défis incluent la modélisation des générations de puissance et le lissage des fluctuations des DER. Pour modéliser les générations de puissance, nous proposons un modèle basé sur les concepts de service courbé de Network Calculus. En utilisant cet outil mathématique, nous déterminons une quantité minimale de puissance que les DERs peuvent générer; leur agrégation nous donnera une production d'énergie totale dans le microgrid. Après cela, s'il existe un déséquilibre entre la production et la demande d'énergie, nous proposons des stratégies différentes pour minimiser les coûts d'approvisionnement énergétique. Sur la base des données réelles de la consommation d'énergie d'un site industriel situé en France, des économies significatives peuvent être réalisées en adoptant ces stratégies. Dans cette thèse, nous étudions également comment atténuer les effets des fluctuations de puissance des DERs en conjonction avec des systèmes de stockage d'énergie. Pour cela, nous proposons un algorithme de lissage gaussien et nous le comparons avec des algorithmes de lissage trouvés dans l'état de l'art. Nous avons trouvé que l'algorithme proposé utilise de batterie de moins de taille à des fins de lissage par rapport à d'autres algorithmes. À cette fin, nous sommes également intéressés à étudier les effets de la gamme admissible des fluctuations sur les tailles de la batterie.Du côté de la demande, l'objectif est de réduire les coûts de l'énergie grâce aux approches de gestion de la demande DSM (Demand Side Management) telles que Demand Response (DR) et Energy Efficiency. Comme les processus industriels consomment énormément, une petite réduction de la consommation d'énergie en utilisant les approches DSM pourrait se traduire par des économies cruciales. Cette thèse se concentre sur l'approche DR qui peut profiter des prix variables de l'électricité dans le temps pour déplacer les demandes énergétiques des heures de pointe aux heures creuses. Pour atteindre cet objectif, nous comptons sur un modèle basé sur la théorie de file d'attente pour caractériser les comportements temporels (arrivée et départ des tâches) d'un système de fabrication. Après avoir défini les processus d'arrivée et de départ de tâches, une fonction d'utilisation efficace est utilisée pour prédire le comportement de la machine dans un domaine temporel et qui peut afficher son statut (allumé/éteint) à tout moment. En prenant le statut de chaque machine dans une ligne de production comme une entrée, nous proposons également un algorithme de planification DR qui adapte la consommation d'énergie d'une ligne de production aux deux contraintes de puissance disponibles et de taux de production. L'algorithme est codé à l'aide d’une machine d’état fini déterministe (Deterministic Finite State Machine) dans laquelle les transitions d'état se produisent en insérant une tâche à l'entrée du tapis roulant (on peut aussi avoir des transitions sans insertion de taches). Nous définissons des conditions pour l'existence d’un planificateur réalisable et aussi des conditions pour accepter positivement des demandes DRs / Due to increased energy costs and environmental concerns such as elevated carbon footprints, centralized power generation systems are restructuring themselves to reap benefits of distributed generation in order to meet the ever growing energy demands. Microgrids are considered as a possible solution to deploy distributed generation which includes Distributed Energy Resources (DERs) (e.g., solar, wind, battery, etc). In this thesis, we are interested in addressing energy management challenges in an industrial microgrid where energy loads consist of industrial processes. Our plan of attack is to divide the microgrid energy management into supply and demand sides.In supply side, the challenges include modeling of power generations and smoothing out fluctuations of the DERs. To model power generations, we propose amodel based on service curve concepts of Network Calculus (NC). Using this mathematical tool, we determine a minimum amount of power the DERs can generate and aggregating them will give us total power production in the microgrid. After that, if there is an imbalance between energy supply and demand, we put forward different strategies to minimize energy procurement costs. Based on real power consumption data of an industrial site located in France, significant cost savings can be made by adopting the strategies. In this thesis, we also study how to mitigate the effects of power fluctuations of DERs in conjunction with Energy Storage Systems (ESSs). For this purpose, we propose a Gaussian-based smoothing algorithm and compare it with state-of-the-art smoothing algorithms. We found out that the proposed algorithm uses less battery size for smoothing purposes when compared to other algorithms. To this end, we are also interested in investigating effects of allowable range of fluctuations on battery sizes.In demand side, the aim is to reduce energy costs through Demand Side Management (DSM) approaches such as Demand Response (DR) and Energy Efficiency (EE). As industrial processes are power-hungry consumers, a small power consumption reduction using the DSM approaches could translate into crucial savings. This thesis focuses on DR approach that can leverage time varying electricity prices to move energy demands from peak to off-peak hours. To attain this goal, we rely on a queuing theory-based model to characterize temporal behaviors (arrival and departure of jobs) of a manufacturing system. After defining job arrival and departure processes, an effective utilization function is used to predict workstation’s (or machine’s) behavior in temporal domain that can show its status (working or idle) at any time. Taking the status of every machine in a production line as an input, we also propose a DR scheduling algorithm that adapts power consumption of a production line to available power and production rate constraints. The algorithm is coded using Deterministic Finite State Machine (DFSM) in which state transitions happen by inserting a job (or not inserting) at conveyor input. We provide conditions for existence of feasible schedules and conditions to accept DR requests positively.To verify analytical computations on the queuing part, we have enhanced Objective Modular Network Testbed in C++ (OMNET++) discrete event simulator for fitting it to our needs. We modified various libraries in OMNET++ to add machine and conveyor modules. In this thesis, we also setup a testbed to experiment with a smart DR protocol called Open Automated Demand Response (OpenADR) that enables energy providers (e.g., utility grid) to ask consumers to reduce their power consumption for a given time. The objective is to explore how to implement our DR scheduling algorithm on top of OpenADR

The number of Web traffic flows dominates Internet traffic today and most Web interactions are short-lived HTTP connections handled by TCP. Most core Internet routers use Drop Tail queuing which produces bursts of packet drops that contribute to unfair service. This thesis introduces two new active queue management (AQM) algorithms, PISA (PI with Short-lived flows Adjustment) and PIMC (PI with Minimum Cwnd). These AQMs are built on top of the PI (Proportional Integrator). To evaluate the performance of PISA and PIMC, a new simple model of HTTP traffic was developed for the NS-2 simulation. TCP sources inform PISA and PIMC routers of their congestion window by embedding a source hint in the packet header. Using the congestion window, PISA drops packets from short-lived Web flows less than packets from long-lived flows. Using a congestion window, PIMC does not drop a packet when congestion window is below a fixed threshold. This study provides a series of NS-2 experiments to investigate the behavior of PISA and PIMC. The results show fewer drops for both PISA and PIMC that avoids timeouts and increases the rate at which Web objects are sent. PISA and PIMC improve the performance of HTTP flows significantly over PI. PISA performs slightly better than PIMC.

在服務經濟的時代，人們為了提升生活品質越來越重視心靈需求而非過往所重視的物質需求。文化創意產業提供的原創性以及內容扮演越來越重要的角色，文化創意產業近年來在世界各國之經濟地位也漸趨重要；本篇論文提出一個透過網際網路提供台灣國立故宮博物院動態展覽的嶄新影音廣播服務--「故宮影音頻道」。故宮影音頻道意圖透過影音多媒體展示，更全方位且完整地呈現中華文物的精緻特質和內涵，以帶給瀏覽者更清晰具體的文物觀賞體驗，以及激發瀏覽者之創意靈感。 故宮影音頻道為了符合高標準的服務品質以及處理來自世界各地使用者的潛在高峰需求而特別設計負載平衡的機制。本篇論文更進一步地探討故宮影音頻道平台後端作業流程的技術挑戰以及展示提供線上影音廣播服務的具備彈性、靈活、分散特性的雲端平台。首先，我們在雲端平台上建立具有處理大量使用者的負載平衡機制的故宮影音頻道。接著我們讓故宮影音頻道上線進行實驗、收集資料及分析。根據實驗的結果，我們為了維持高標準的服務品質應用排隊理論設計了兩階段的服務系統，最後探討在不同電腦及網路環境下，如何利用該服務系統計算出符合服務品質的設定。 / The iPalace Video Channel is a video-based website and provide people around the world a brand new video-broadcasting service on the Internet which introduces relics in National Palace Museum in Taiwan. The iPalace Video Channel is designed to meet the high standard of service quality which users can watch videos without delay and be capable of coping with potential high peak demands from worldwide. In this paper, first, we establish the iPalace Video Channel and an elastic and reliable mechanism via load balancing that is capable of handling potential huge peak-demand of video services. Second, we conduct an experiment by sampling the video-based service in practice and evaluating the presented approach online. Third, from the finding of evaluation, we establish the two phase service system for delivering video services with high standard of service quality. Finally, we discuss the formal queuing model of video services from which the settings of the queuing system that satisfy acceptable service quality could be calculated under various computer and network environments

University of Macau / Faculty of Business Administration / Department of Accounting and Information Management

This dissertation deals with three problems in health care. In the first, we consider the incentives to change prices and capital levels at hospitals, using optimal control under the assumption that private payers charge higher prices if patients consume more hospital services. The main results are that even with fixed technology, investment and prices exhibit explosive growth, and that prices and capital stock grow in proportion to one another. In the second chapter, we study the flow of nosocomial infections in an intensive care unit. We use data from Cook County Hospital, along with numerous results from the literature, to construct a discrete event simulation. This model highlights emergent properties from treating the flow of patients and pathogens in one interconnected system, and sheds light on how nosocomial infections relate to hospital costs. We find that the system is not decomposable to individual systems, exhibiting behavior that would be difficult to explain in isolation. In the third chapter, we analyze a proposed change in diversion policies at hospitals, in order to increase the number of patients served, without an increase in resources. Overcrowding in hospital emergency departments is caused in part by the inability to send patients to main hospital wards, due to limited capacity. When a hospital is completely full, the hospital often goes on ambulance diversion, until some spare capacity has opened up. Diversion is costly, and often leads to waves of diversions in systems of hospitals, a situation that is regarded as highly problematic in public health. We construct and analyze a continuous-time Markov chain model for one hospital. The intuition behind the model is that load-balancing between various hospitals in a metro area may hinder full congestion. We find that a more flexible contract may benefit all parties, through the partial diversion of federally insured patients, when a hospital is very close to full. Discrete event simulation models are run to assess the effect, using data from DeKalb Medical Center, and also to show that in a two-hospital system, more federally insured patients are served using this mechanism.

The modeling and evaluation calculus FMC-QE, the Fundamental Modeling Concepts for Quanti-tative Evaluation [1], extends the Fundamental Modeling Concepts (FMC) for performance modeling and prediction. In this new methodology, the hierarchical service requests are in the main focus, because they are the origin of every service provisioning process. Similar to physics, these service requests are a tuple of value and unit, which enables hierarchical service request transformations at the hierarchical borders and therefore the hierarchical modeling. Through reducing the model complexity of the models by decomposing the system in different hierarchical views, the distinction between operational and control states and the calculation of the performance values on the assumption of the steady state, FMC-QE has a scalable applica-bility on complex systems. According to FMC, the system is modeled in a 3-dimensional hierarchical representation space, where system performance parameters are described in three arbitrarily fine-grained hierarchi-cal bipartite diagrams. The hierarchical service request structures are modeled in Entity Relationship Diagrams. The static server structures, divided into logical and real servers, are de-scribed as Block Diagrams. The dynamic behavior and the control structures are specified as Petri Nets, more precisely Colored Time Augmented Petri Nets. From the structures and pa-rameters of the performance model, a hierarchical set of equations is derived. The calculation of the performance values is done on the assumption of stationary processes and is based on fundamental laws of the performance analysis: Little's Law and the Forced Traffic Flow Law. Little's Law is used within the different hierarchical levels (horizontal) and the Forced Traffic Flow Law is the key to the dependencies among the hierarchical levels (vertical). This calculation is suitable for complex models and allows a fast (re-)calculation of different performance scenarios in order to support development and configuration decisions. Within the Research Group Zorn at the Hasso Plattner Institute, the work is embedded in a broader research in the development of FMC-QE. While this work is concentrated on the theoretical background, description and definition of the methodology as well as the extension and validation of the applicability, other topics are in the development of an FMC-QE modeling and evaluation tool and the usage of FMC-QE in the design of an adaptive transport layer in order to fulfill Quality of Service and Service Level Agreements in volatile service based environments. This thesis contains a state-of-the-art, the description of FMC-QE as well as extensions of FMC-QE in representative general models and case studies. In the state-of-the-art part of the thesis in chapter 2, an overview on existing Queueing Theory and Time Augmented Petri Net models and other quantitative modeling and evaluation languages and methodologies is given. Also other hierarchical quantitative modeling frameworks will be considered. The description of FMC-QE in chapter 3 consists of a summary of the foundations of FMC-QE, basic definitions, the graphical notations, the FMC-QE Calculus and the modeling of open queueing networks as an introductory example. The extensions of FMC-QE in chapter 4 consist of the integration of the summation method in order to support the handling of closed networks and the modeling of multiclass and semaphore scenarios. Furthermore, FMC-QE is compared to other performance modeling and evaluation approaches. In the case study part in chapter 5, proof-of-concept examples, like the modeling of a service based search portal, a service based SAP NetWeaver application and the Axis2 Web service framework will be provided. Finally, conclusions are given by a summary of contributions and an outlook on future work in chapter 6. [1] Werner Zorn. FMC-QE - A New Approach in Quantitative Modeling. In Hamid R. Arabnia, editor, Procee-dings of the International Conference on Modeling, Simulation and Visualization Methods (MSV 2007) within WorldComp ’07, pages 280 – 287, Las Vegas, NV, USA, June 2007. CSREA Press. ISBN 1-60132-029-9. / FMC-QE (Fundamental Modeling Concepts for Quantitative Evaluation [1]) ist eine auf FMC, den Fundamental Modeling Concepts, basierende Methodik zur Modellierung des Leistungsverhaltens von Systemen mit einem dazugehörenden Kalkül zur Erstellung von Leistungsvorhersagen wie Antwortzeiten und Durchsatz. In dieser neuen Methodik steht die Modellierung der hierarchischen Bedienanforderungen im Mittelpunkt, da sie der Ursprung aller dienstbasierenden Systeme sind. Wie in der Physik sind in FMC-QE die Bedienanforderungen Tupel aus Wert und Einheit, um Auftragstransformationen an Hierarchiegrenzen zu ermöglichen. Da die Komplexität durch eine Dekomposition in mehreren Sichten und in verschiedene hierarchische Schichten, die Unterscheidung von Operations- und Kontrollzuständen, sowie dazugehörige Berechungen unter Annahme der Stationarität reduziert wird, skaliert die Anwendbarkeit von FMC-QE auf komplexe Systeme. Gemäß FMC wird das zu modellierende System in einem 3-dimensionalen hierarchischen Beschreibungsraum dargestellt. Die quantitativen Kenngrößen der Systeme werden in drei beliebig frei-granularen hierarchischen bi-partiten Graphen beschrieben. Die hierarchische Struktur der Bedienanforderungen wird in Entity Relationship Diagrammen beschrieben. Die statischen Bedienerstrukturen, unterteilt in logische und reale Bediener, sind in Aufbaudiagrammen erläutert. Außerdem werden Petri Netze, genauer Farbige Zeit-behaftete Petri Netze, dazu verwendet, die dynamischen Abläufe, sowie die Kontrollflüsse im System zu beschreiben. Anschließend wird eine Menge von hierarchischen Gleichungen von der Struktur und den Parametern des Modells abgeleitet. Diese Gleichungen, die auf dem stationären Zustand des Systems beruhen, basieren auf den beiden Fundamental Gesetzen der Leistungsanalyse, dem Gesetz von Little und dem Verkehrsflussgesetz. Das Gesetz von Little definiert hierbei Beziehungen innerhalb einer hierarchischen Schicht (horizontal) und das Verkehrsflussgesetz wiederum Beziehungen zwischen hierarchischen Schichten (vertikal). Die Berechungen erlauben Leistungsvorhersagen für komplexe Systeme durch eine effiziente Berechnung von Leistungsgrößen für eine große Auswahl von System- und Lastkonfigurationen. Innerhalb der Forschungsgruppe von Prof. Dr.-Ing Werner Zorn am Hasso Plattner Institut an der Universität Potsdam ist die vorliegende Arbeit in einen größeren Forschungskontext im Bereich FMC-QE eingebettet. Während hier ein Fokus auf dem theoretischen Hintergrund, der Beschreibung und der Definition der Methodik als auch der Anwendbarkeit und Erweiterung gelegt wurde, sind andere Arbeiten auf dem Gebiet der Entwicklung einer Anwendung zur Modellierung und Evaluierung von Systemen mit FMC-QE bzw. der Verwendung von FMC-QE zur Entwicklung einer adaptiven Transportschicht zur Einhaltung von Dienstgüten (Quality of Service) und Dienstvereinbarungen (Service Level Agreements) in volatilen dienstbasierten Systemen beheimatet. Diese Arbeit umfasst einen Einblick in den Stand der Technik, die Beschreibung von FMC-QE sowie die Weiterentwicklung von FMC-QE in repräsentativen allgemeinen Modellen und Fallstudien. Das Kapitel 2: Stand der Technik gibt einen Überblick über die Warteschlangentheorie, Zeit-behaftete Petri Netze, weitere Leistungsbeschreibungs- und Leistungsvorhersagungstechniken sowie die Verwendung von Hierarchien in Leistungsbeschreibungstechniken. Die Beschreibung von FMC-QE in Kapitel 3 enthält die Erläuterung der Grundlagen von FMC-QE, die Beschreibung einiger Grundannahmen, der graphischen Notation, dem mathematischen Modell und einem erläuternden Beispiel. In Kapitel 4: Erweiterungen von FMC-QE wird die Behandlung weiterer allgemeiner Modelle, wie die Modellklasse von geschlossenen Netzen, Synchronisierung und Mehrklassen-Modelle beschrieben. Außerdem wird FMC-QE mit dem Stand der Technik verglichen. In Kapitel 5 werden Machbarkeitsstudien beschrieben. Schließlich werden in Kapitel 6 eine Zusammenfassung und ein Ausblick gegeben. [1] Werner Zorn. FMC-QE - A New Approach in Quantitative Modeling. In Hamid R. Arabnia, editor, Proceedings of the International Conference on Modeling, Simulation and Visualization Methods (MSV 2007) within WorldComp ’07, 280 – 287, Las Vegas, NV, USA, Juni 2007. CSREA Press. ISBN 1-60132-029-9.

This work focuses on the performance characterization of distributed collaborative ad-hoc networks, focusing on such metrics as the lifetime, latency, and throughput capacity of two such classes of networks. The first part concerns modeling and optimization of static Wireless Sensor Networks, specifically dealing with the issues of energy efficiency, lifetime, and latency. We analyze and characterize these performance measures and discuss various fundamental design tradeoffs. For example, energy efficiency in wireless sensor networks can only be improved at the cost of the latency (the delay incurred during communication). It has been clearly shown that improvement in energy efficiency through data aggregation increases the latency in the network. In addition, sleep-active duty cycling of nodes (devices constituting the network), a commonly employed mechanism to conserve battery lifetime in such networks, has adverse effects on their functionality and capacity. Hence these issues deserve a detailed study. The second part of this work concerns performance modeling of Delay Tolerant Networks (DTNs) and Sparse Mobile Ad-Hoc Networks (SPMANETs) in general. We first investigate the effect of modern coding, such as the application of packet-level rateless codes, on the latency, reliability, and energy efficiency of the network. These codes provide us the means to break large messages into smaller packets thereby enabling efficient communication. The work then focuses on developing and formalizing an information-theoretic framework for Delay Tolerant- and other Sparse Mobile Networks. This is enabled by the use of an embedded-Markov-chain approach used for complex queuing-theoretic problems. An important goal of this work is to incorporate a wide range of mobility models into the analysis framework. Yet another important question will be the effect of changing the mobility on the comparative performance of networking protocols. Lastly, the framework will be extended to various communication paradigms such as two-hop vs multi-hop routing, unicast, and multicast.

Customer call centers with hundreds of agents working in parallel are ubiquitous in many industries. These systems have a large amount of daily traffic that is stochastic in nature. It becomes more and more difficult to manage a call center because of its increasingly large scale and the stochastic variability in arrival and service processes. In call center operations, customer abandonment is a key factor and may significantly impact the system performance. It must be modeled explicitly in order for an operational model to be relevant for decision making. In this thesis, a large-scale call center is modeled as a queue with many parallel servers. To model the customer abandonment, each customer is assigned a patience time. When his waiting time for service exceeds his patience time, a customer abandons the system without service. We develop analytical and numerical tools for analyzing such a queue. We first study a sequence of G/G/n+GI queues, where the customer patience times are independent and identically distributed (iid) following a general distribution. The focus is the abandonment and the queue length processes. We prove that under certain conditions, a deterministic relationship holds asymptotically in diffusion scaling between these two stochastic processes, as the number of servers goes to infinity. Next, we restrict the service time distribution to be a phase-type distribution with d phases. Using the aforementioned asymptotic relationship, we prove limit theorems for G/Ph/n+GI queues in the quality- and efficiency-driven (QED) regime. In particular, the limit process for the customer number in each phase is a d-dimensional piecewise Ornstein-Uhlenbeck (OU) process. Motivated by the diffusion limit process, we propose two approximate models for a GI/Ph/n+GI queue. In each model, a d-dimensional diffusion process is used to approximate the dynamics of the queue. These two models differ in how the patience time distribution is built into them. The first diffusion model uses the patience time density at zero and the second one uses the entire patience time distribution. We also develop a numerical algorithm to analyze these diffusion models. The algorithm solves the stationary distribution of each model. The computed stationary distribution is used to estimate the queue's performance. A crucial part of this algorithm is to choose an appropriate reference density that controls the convergence of the algorithm. We develop a systematic approach to constructing a reference density. With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments. These experiments also show that the diffusion models are good approximations of queues with a moderate to large number of servers.