Developing equations to compute congestion measures for the general G/G/s/c queueing model and networks of such nodes has always been a challenge. One approach to analyzing such systems is to approximate the model-specified general input processes and distributions by processes and distributions from the more computationally friendly family of phase-type processes and distributions. We develop numerical approximation methods for analysis of general time-dependent queueing nodes by introducing new approximations for the time-dependent first two moments of the number-in-system and departure-count processes. / Ph. D.

Enabling more than one function in an entity provides a new cost-effective way to develop a highly reliable system. In this dissertation, we study the reliability of systems containing multi-functional entities. We derive the expressions for reliability of one-shot systems and reliability of each function. A step further, a redundancy allocation problem (RAP) with the objective of maximizing system reliability is formulated. Unlike constructing a system with only single-functional entities, the number of copies of a specific function to be included in each multi-functional entity (i.e., functional redundancy) needs to be determined as part of the design. Moreover, a start-up strategy for turning on specific functions in these components must be decided prior to system operation. We develop a heuristic algorithm and include it in a two-stage Genetic Algorithm (GA) to solve the new RAP. We also apply a modified Tabu search (TS) method for solving such NP-hard problems. Our numerical studies illustrate that the two-stage GA and the TS method are quite effective in searching for high quality solutions. The concept of multi-functional entities can be also applied in probabilistic site selection problem (PSSP). Unlike traditional PSSP with failures either at nodes or on edges, we consider a more general problem, in which both nodes and edges could fail and the edge-level redundancy is included. We formulate the problem as an integer programming optimization problem. To reduce the searching space, two corresponding simplified models formulated as integer linear programming problems are solved for providing a lower bound to the primal problem. Finally, a big challenge in reliability analysis is how to determine the failure distribution of components. This is especially significant for multi-functional entities as more levels of redundancy are considered. We provide an automated model-selection method to construct the best phase-type (PH) distribution for a given data set in terms of the model complexity and the adequacy of statistical fitting. To efficiently utilize the Akaike Information Criterion for balancing the likelihood value and the number of free parameters, the proposed method is carried out in two stages. The detailed subproblems and the related solution procedures are developed and illustrated through numerical studies. The results verify the effectiveness of the proposed model-selection method in constructing PH distributions.

穩定狀態機率是讓我們了解各種排隊網路性能的基礎。在擬生死過程(Quasi-Birth-and-Death) Phase-type 分配中求得穩定狀態機率，通常是依賴排隊網路的結構。在這篇論文中，我們提出了一種計算方法-LU分解，可以求得在排隊網路中有多台服務器的穩定狀態機率。此計算方法提供了一種通用的方法，使得複雜的大矩陣變成小矩陣，並減低計算的複雜性。當需要計算一個複雜的大矩陣，這個成果變得更加重要。文末，我們提到了離開時間間隔，並用兩種方法 (Matlab 和 Promodel) 去計算期望值和變異數，我們發現兩種方法算出的數據相近，接著計算離開顧客的時間間隔相關係數。最後，我們提供數值實驗以計算不同服務器個數產生的離去過程和相關係數，用來說明我們的方法。 / Stationary probabilities are fundamental in response to various measures of performance in queueing networks. Solving stationary probabilities in Quasi-Birth-and-Death(QBD) with phase-type distribution normally are dependent on the structure of the queueing network. In this thesis, a new computing scheme is developed for attaining stationary probabilities in queueing networks with multiple servers. This scheme provides a general approach of consindering the complexity of computing algorithm. The result becomes more significant when a large matrix is involved in computation. After determining the stationary probability, we study the departure process and the moments of inter-departure times. We can obtain the moment of inter-departure times. We compute the moments of inter-departure times and the variance by applying two numerical methods (Matlab and Promodel). The lag-k correlation of inter-departure times is also introduced in the thesis. The proposed approach is proved theoretically and verifieded with illustrative examples.

We propose a situation in which a single employee is responsible for processing incoming claims to an insurance company that can be classified as being one of two possible types. More specifically, we consider a priority-based system having separate buffers to store high priority and low priority incoming claims. We construct a mathematical model and perform queueing analysis to evaluate the performance of this priority-based system, which incorporates the possibility of claims being redistributed, lost, or prematurely processed.

We propose a situation in which a single employee is responsible for processing incoming claims to an insurance company that can be classified as being one of two possible types. More specifically, we consider a priority-based system having separate buffers to store high priority and low priority incoming claims. We construct a mathematical model and perform queueing analysis to evaluate the performance of this priority-based system, which incorporates the possibility of claims being redistributed, lost, or prematurely processed.

Safety analysis is critical when developing new engineering systems. Many systems have to function under randomly occurring events, making stochastic processes useful in a safety modelling context. However, a general stochastic process is very challenging to analyse mathematically. Therefore, model restrictions are necessary to simplify the mathematical analysis. A popular simplified stochastic model is the Semi-Markov process (SMP), which is a generalization of the "memoryless" continuous-time Markov chain. However, only a subclass of Semi-Markov models can be analysed with non-simulation based methods. In these models, the cumulative density function (cdf) of the random variables describing the system is in the form of expolynomials. This thesis investigates the possibility to extend the number of Semi-Markov models that can be analysed with non-simulation based methods by approximating the non-expolynomial random variables with expolynomials. This thesis focus on approximation of models partially described by LogNormal and Weibull distributed random variables. The result shows that it is possible to approximate some Semi-Markov models with non-expolynomial random variables. However, there is an increasing difficulty in approximating a non-expolynomial random variable when the variability in the distribution increases. / Säkerhetsanalys är avgörande när man utvecklar nya tekniska system. Många system måste fungera under slumpmässigt inträffande händelser, vilket gör stokastiska processer användbara i ett säkerhetsmodellerande sammanhang. En allmän stokastisk process är dock mycket utmanande att analysera matematiskt. Därför är begränsningar på modellen nödvändiga för att förenkla den matematiska analysen. En populär förenklad stokastisk modell är Semi-Markov-processen (SMP), vilket är en generalisering av den "minneslösa" tids-kontinuerliga Markov-kedjan. Dock är det endast en underklass av Semi-Markov-modeller som kan analyseras med icke-simuleringsbaserade metoder. I dessa modeller är den kumulativa densitetsfunktionen (cdf) för de slumpmässiga variablerna som beskriver systemet i form av expolynomials. Denna rapport undersöker möjligheten att utöka antalet Semi-Markov-modeller som kan analyseras med icke-simuleringsbaserade metoder genom att approximera de icke-expolynomial slumpvariablerna med expolynomials. Vi fokuserar på approximering av modeller som delvis beskrivs av LogNormal distribuerade och Weibull distribuerade slumpmässiga variabler. Resultatet visar att det är möjligt att approximera vissa stokastiska variabler som är icke-expolynomial i Semi-Markov-modeller. Resultatet visar dock att det är en ökande svårighet att approximera en icke-expolynomial slumpmässiga variabeln när variabiliteten i fördelningen ökar.

En la actualidad, la Internet de las Cosas (Internet of Things, IoT) es una tecnología esencial para la próxima generación de sistemas inalámbricos. La conectividad es la base de IoT, y el tipo de acceso requerido dependerá de la naturaleza de la aplicación. Uno de los principales facilitadores del entorno IoT es la comunicación machine-to-machine (M2M) y, en particular, su enorme potencial para ofrecer conectividad ubicua entre dispositivos inteligentes. Las redes celulares son la elección natural para las aplicaciones emergentes de IoT y M2M. Un desafío importante en las redes celulares es conseguir que la red sea capaz de manejar escenarios de acceso masivo en los que numerosos dispositivos utilizan comunicaciones M2M. Por otro lado, los sistemas celulares han experimentado un tremendo desarrollo en las últimas décadas: incorporan tecnología sofisticada y nuevos algoritmos para ofrecer una amplia gama de servicios. El modelado y análisis del rendimiento de estas redes multiservicio es también una tarea desafiante que podría requerir un gran esfuerzo computacional. Para abordar los desafíos anteriores, nos centramos en primer lugar en el diseño y la evaluación de las prestaciones de nuevos mecanismos de control de acceso para hacer frente a las comunicaciones masivas M2M en redes celulares. Posteriormente nos ocupamos de la evaluación de prestaciones de redes multiservicio y proponemos una nueva técnica analítica que ofrece precisión y eficiencia computacional. Nuestro principal objetivo es proporcionar soluciones para aliviar la congestión en la red de acceso radio cuando un gran número de dispositivos M2M intentan conectarse a la red. Consideramos los siguientes tipos de escenarios: (i) los dispositivos M2M se conectan directamente a las estaciones base celulares, y (ii) forman grupos y los datos se envían a concentradores de tráfico (gateways) que les proporcionan acceso a la infraestructura. En el primer escenario, dado que el número de dispositivos añadidos a la red aumenta continuamente, esta debería ser capaz de manejar el considerable incremento en las solicitudes de acceso. El 3rd Generation Partnership Project (3GPP) ha propuesto el access class barring (ACB) como una solución práctica para el control de congestión en la red de acceso radio y la red troncal. El ajuste correcto de los parámetros de ACB de acuerdo con la intensidad del tráfico es crítico, pero cómo hacerlo de forma dinámica y autónoma es un problema complejo cuya solución no está recogida en las especificaciones del 3GPP. Esta tesis doctoral contribuye al análisis del rendimiento y al diseño de nuevos algoritmos que implementen efectivamente este mecanismo, y así superar los desafíos introducidos por las comunicaciones masivas M2M. En el segundo escenario, dado que la heterogeneidad de los dispositivos IoT y las arquitecturas celulares basadas en hardware imponen desafíos aún mayores para permitir una comunicación flexible y eficiente en los sistemas inalámbricos 5G, esta tesis doctoral también contribuye al diseño de software-defined gateways (SD-GWs) en una nueva arquitectura propuesta para redes inalámbricas definidas por software que se denomina SoftAir. Esto permite manejar tanto un gran número de dispositivos como el volumen de datos que estarán vertiendo en la red. Otra contribución de esta tesis doctoral es la propuesta de una técnica novedosa para el análisis de prestaciones de redes multiservicio de alta capacidad que se basa en un nuevo enfoque del modelizado analítico de sistemas que operan a diferentes escalas temporales. Este enfoque utiliza el análisis del transitorio de una serie de subcadenas absorbentes y lo denominamos absorbing Markov chain approximation (AMCA). Nuestros resultados muestran que para un coste computacional dado, AMCA calcula los parámetros de prestaciones habituales de un sistema con mayor precisión, en comparación con los resultados obtenidos por otr / Nowadays, Internet of Things (IoT) is an essential technology for the upcoming generation of wireless systems. Connectivity is the foundation for IoT, and the type of access required will depend on the nature of the application. One of the leading facilitators of the IoT environment is machine-to-machine (M2M) communication, and particularly, its tremendous potential to offer ubiquitous connectivity among intelligent devices. Cellular networks are the natural choice for emerging IoT and M2M applications. A major challenge in cellular networks is to make the network capable of handling massive access scenarios in which myriad devices deploy M2M communications. On the other hand, cellular systems have seen a tremendous development in recent decades; they incorporate sophisticated technology and algorithms to offer a broad range of services. The modeling and performance analysis of these large multi-service networks is also a challenging task that might require high computational effort. To address the above challenges, we first concentrate on the design and performance evaluation of novel access control schemes to deal with massive M2M communications. Then, we focus on the performance evaluation of large multi-service networks and propose a novel analytical technique that features accuracy and computational efficiency. Our main objective is to provide solutions to ease the congestion in the radio access or core network when massive M2M devices try to connect to the network. We consider the following two types of scenarios: (i) massive M2M devices connect directly to cellular base stations, and (ii) they form clusters and the data is forwarded to gateways that provide them with access to the infrastructure. In the first scenario, as the number of devices added to the network is constantly increasing, the network should handle the considerable increment in access requests. Access class barring (ACB) is proposed by the 3rd Generation Partnership Project (3GPP) as a practical congestion control solution in the radio access and core network. The proper tuning of the ACB parameters according to the traffic intensity is critical, but how to do so dynamically and autonomously is a challenging task that has not been specified. Thus, this dissertation contributes to the performance analysis and optimal design of novel algorithms to implement effectively this barring scheme and overcome the challenges introduced by massive M2M communications. In the second scenario, since the heterogeneity of IoT devices and the hardware-based cellular architectures impose even greater challenges to enable flexible and efficient communication in 5G wireless systems, this dissertation also contributes to the design of software-defined gateways (SD-GWs) in a new architecture proposed for wireless software-defined networks called SoftAir. The deployment of these SD-GWs represents an alternative solution aiming at handling both a vast number of devices and the volume of data they will be pouring into the network. Another contribution of this dissertation is to propose a novel technique for the performance analysis of large multi-service networks. The underlying complexity of the network, particularly concerning its size and the ample range of configuration options, makes the solution of the analytical models computationally costly. However, a typical characteristic of these networks is that they support multiple types of traffic flows operating at different time-scales. This time-scale separation can be exploited to reduce considerably the computational cost associated to determine the key performance indicators. Thus, we propose a novel analytical modeling approach based on the transient regime analysis, that we name absorbing Markov chain approximation (AMCA). For a given computational cost, AMCA finds common performance indicators with greater accuracy, when compared to the results obtained by other approximate methods proposed in the literature. / En l'actualitat, la Internet de les Coses (Internet of Things, IoT) és una tecnologia essencial per a la propera generació de sistemes sense fil. La connectivitat és la base d'IoT, i el tipus d'accés requerit dependrà de la naturalesa de l'aplicació. Un dels principals facilitadors de l'entorn IoT és la comunicació machine-to-machine (M2M) i, en particular, el seu enorme potencial per oferir connectivitat ubiqua entre dispositius intel · ligents. Les xarxes mòbils són l'elecció natural per a les aplicacions emergents de IoT i M2M. Un desafiament important en les xarxes mòbils que actualment está rebent molta atenció és aconseguir que la xarxa siga capaç de gestionar escenaris d'accés massiu en què una gran quantitat de dispositius utilitzen comunicacions M2M. D'altra banda, els sistemes mòbils han experimentat un gran desenvolupament en les últimes dècades: incorporen tecnologia sofisticada i nous algoritmes per oferir una àmplia gamma de serveis. El modelatge i análisi del rendiment d'aquestes xarxes multiservei és també un desafiament important que podria requerir un gran esforç computacional. Per abordar els desafiaments anteriors, en aquesta tesi doctoral ens centrem en primer lloc en el disseny i l'avaluació de les prestacions de nous mecanismes de control d'accés per fer front a les comunicacions massives M2M en xarxes cel · lulars. Posteriorment ens ocupem de l'avaluació de prestacions de xarxes multiservei i proposem una nova tècnica analítica que ofereix precisió i eficiència computacional. El nostre principal objectiu és proporcionar solucions per a alleujar la congestió a la xarxa d'accés ràdio quan un gran nombre de dispositius M2M intenten connectar-se a la xarxa. Considerem els dos tipus d'escenaris següents: (i) els dispositius M2M es connecten directament a les estacions base cel · lulars, i (ii) formen grups i les dades s'envien a concentradors de trànsit (gateways) que els proporcionen accés a la infraestructura. En el primer escenari, atès que el nombre de dispositius afegits a la xarxa augmenta contínuament, aquesta hauria de ser capaç de gestionar el considerable increment en les sol · licituds d'accés. El 3rd Generation Partnership Project (3GPP) ha proposat l'access class barring (ACB) com una solució pràctica per al control de congestió a la xarxa d'accès ràdio i la xarxa troncal. L'ajust correcte dels paràmetres d'ACB d'acord amb la intensitat del trànsit és crític, però com fer-ho de forma dinàmica i autònoma és un problema complex, la solució del qual no està recollida en les especificacions del 3GPP. Aquesta tesi doctoral contribueix a l'anàlisi del rendiment i al disseny de nous algoritmes que implementen efectivament aquest mecanisme, i així superar els desafiaments introduïts per les comunicacions massives M2M en les xarxes mòbils actuals i futures. En el segon escenari, atès que l'heterogeneïtat dels dispositius IoT i les arquitectures cel · lulars basades en hardware imposen desafiaments encara més grans per permetre una comunicació flexible i eficient en els sistemes sense fil 5G, aquesta tesi doctoral també contribueix al disseny de software-defined gateways (SD-GWS) en una nova arquitectura proposada per a xarxes sense fils definides per programari que s'anomena SoftAir. Això permet gestionar tant un gran nombre de dispositius com el volum de dades que estaran abocant a la xarxa. Una altra contribució d'aquesta tesi doctoral és la proposta d'una tècnica innovadora per a l'anàlisi de prestacions de xarxes multiservei d'alta capacitat que es basa en un nou enfocament del modelitzat analític de sistemes que operen a diferents escales temporals. Aquest enfocament utilitza l'anàlisi del transitori d'una sèrie de subcadenes absorbents i l'anomenem absorbing Markov chain Approximation (AMCA). Els nostres resultats mostren que per a un cost computacional donat, AMCA calcula els paràmetres de prestacions habituals d / Tello Oquendo, LP. (2018). Design and Performance Analysis of Access Control Mechanisms for Massive Machine-to-Machine Communications in Wireless Cellular Networks [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/107946