Die Dissertationsschrift widmet sich einer systemtheoretischen Untersuchung zur verkehrsabhängigen Steuerung von Lichtsignalanlagen in Straßennetzwerken. Aus einem mathematischen Modell für den Verkehrsablauf auf Knotenzufahrten wird ein Verfahren abgeleitet, mit dem sich Umschaltzeitpunkte und Phasenwechsel flexibel an das tatsächliche Verkehrsgeschehen anpassen lassen. Der Ansatzpunkt ist, die einzelnen Knotenpunkte des Netzwerks lokal zu optimieren. Eine "Grüne Welle" soll sich von selbst einstellen, und zwar genau dann, wenn dadurch lokal Wartezeiten eingespart werden. Indem die lokale Optimierung in ein lokales Stabilisierungsverfahren eingebettet wird, können Instabilitäten aufgrund netzwerkweiter Rückkopplungen ausgeschlossen werden. Das vorgestellte Verfahren setzt sich aus drei Teilen zusammen: (i) einem lokalen Prognoseverfahren zur Bewertung von Schaltzuständen und Phasenübergängen bezüglich zukünftig entstehender Wartezeiten, (ii) einem lokalen Optimierungsverfahren, das jeder Phase einen dynamischen Prioritätsindex zuweist und die Phase mit höchster Priorität zur Bedienung auswählt und (iii) einem lokalen Stabilisierungsverfahren, das zum Einhalten einer mittleren und einer maximalen Bedienperiode korrigierend in die lokale Optimierung eingreift. Indem die Knotenpunkte ausschließlich über die Verkehrsströme gekoppelt sind, ergeben sich die Umschaltzeitpunkte unmittelbar aus den Ankunftszeitpunkten der Fahrzeuge selbst. Die Phasenwechsel stellen sich somit von selbst bedarfsgerecht ein. Simulationsergebnisse machen deutlich, dass sich aufgrund der höheren Flexibilität sowohl die Wartezeiten als auch der Kraftstoffverbrauch senken lassen.

Serverless edge computing is a distributed network and computing system in which the data is processed at the edge of the network based on serverless architecture. It can provide large-scale computing and storage resources with low latency, which are very useful in AI applications such as object detection. However, when analyzing serverless computing architectures, we model them using simple models, such as single server or multi-server queues, and it is important to make sure these models can explain the behaviors of real systems. Therefore, we focus on the performance evaluation of serverless edge computing for AI applications in this project. With that, we aim at proposing more realistic and accurate models for real serverless architectures. In this project, our objective is to evaluate the performance and model mathematically an object-detection application running on a serverless architecture implemented with Kubernetes. This project provides a detailed description of the implementation of the serverless platform and YOLOv5-based object detection application. After implementation, we design experiments and make performance evaluations of the time of object detection results and quality of object detection results. Finally, we conclude that the number of users in the system significantly affects the service time. We observe that there is no queue in the system, so we cannot just use mathematical models with a queue to model the system. Therefore, we consider that the processor sharing model is more appropriate for modeling this serverless architecture. This is very helpful for giving insights on how to make more realistic and accurate mathematical queueing models for serverless architectures. For future work, other researchers can also implement our serverless platform and do further development, such as deploying other serverless applications on it and making performance evaluations. They can also design other use-cases for the experiments and make further analyses on queue modeling of serverless architecture based on this project. / Serverless edge computing är ett distribuerat nätverk och datorsystem där data bearbetas i kanten av nätverket baserat på serverlös arkitektur. Det kan tillhandahålla storskaliga dator- och lagringsresurser med låg latens, vilket är mycket användbart i AI-applikationer som objektdetektering. Men när vi analyserar serverlösa datorarkitekturer modellerar vi dem med hjälp av enkla modeller, till exempel enstaka servrar eller köer med flera servrar, och det är viktigt att se till att dessa modeller kan förklara beteendet hos verkliga system. Därför fokuserar vi på prestandautvärdering av serverlös edge computing för AI-applikationer i detta projekt. Med det siktar vi på att föreslå mer realistiska och exakta modeller för riktiga serverlösa arkitekturer. I detta projekt är vårt mål att utvärdera prestandan och matematiskt modellera en objektdetekteringsapplikation som körs på en serverlös arkitektur implementerad med Kubernetes. Detta projekt ger en detaljerad beskrivning av implementeringen av den serverlösa plattformen och den YOLOv5-baserade objektdetekteringsapplikationen. Efter implementering designar vi experiment och gör prestandautvärderingar av tidpunkten för objektdetekteringsresultat och kvaliteten på objektdetekteringsresultaten. Slutligen drar vi slutsatsen att antalet användare i systemet avsevärt påverkar servicetiden. Vi observerar att det inte finns någon kö i systemet, så vi kan inte bara använda matematiska modeller med en kö för att modellera systemet. Därför anser vi att processordelningsmodellen är mer lämplig för att modellera denna serverlösa arkitektur. Detta är mycket användbart för att ge insikter om hur man gör mer realistiska och exakta matematiska kömodeller för serverlösa arkitekturer. För framtida arbete kan andra forskare också implementera vår serverlösa plattform och göra vidareutveckling, såsom att distribuera andra serverlösa applikationer på den och göra prestandautvärderingar. De kan även designa andra användningsfall för experimenten och göra ytterligare analyser av kömodellering av serverlös arkitektur utifrån detta projekt.

Virtualisation is one of the underlying technologies that led to the success of cloud computing platforms (CCPs). The technology, along with other features such as multitenancy allows delivering of computing resources in the form of service through efficient sharing of physical resources. As these resources are provided through virtualisation, a robust agreement is outlined for both the quantity and quality-of-service (QoS) in a service level agreement (SLA) documents. QoS is one of the essential components of SLA, where performance is one of its primary aspects. As the technology is progressively maturing and receiving massive acceptance, researchers from industry and academia continue to carry out novel theoretical and practical studies of various essential aspects of CCPs with significant levels of success. This thesis starts with the assessment of the current level of knowledge in the literature of cloud computing in general and CCPs in particular. In this context, a substantive literature review was carried out focusing on performance modelling, testing, analysis and evaluation of Infrastructure as a Service (IaaS), methodologies. To this end, a systematic mapping study (SMSs) of the literature was conducted. SMS guided the choice and direction of this research. The SMS was followed by the development of a novel open queueing network model (QNM) at equilibrium for the performance modelling and analysis of an OpenStack IaaS CCP. Moreover, it was assumed that an external arrival pattern is Poisson while the queueing stations provided exponentially distributed service times. Based on Jackson’s theorem, the model was exactly decomposed into individual M/M/c (c ≥ 1) stations. Each of these queueing stations was analysed in isolation, and closed-form expressions for key performance metrics, such as mean response time, throughput, server (resource) utilisation as well as bottleneck device were determined. Moreover, the research was extended with a proposed open QNM with a bursty external arrival pattern represented by a Compound Poisson Process (CPP) with geometrically distributed batches, or equivalently, variable Generalised Exponential (GE) interarrival and service times. Each queueing station had c (c ≥ 1) GE-type servers. Based on a generic maximum entropy (ME) product form approximation, the proposed open GE-type QNM was decomposed into individual GE/GE/c queueing stations with GE-type interarrival and service times. The evaluation of the performance metrics and bottleneck analysis of the QNM were determined, which provided vital insights for the capacity planning of existing CCP architectures as well as the design and development of new ones. The results also revealed, due to a significant impact on the burstiness of interarrival and service time processes, resulted in worst-case performance bounds scenarios, as appropriate. Finally, an investigation was carried out into modelling and analysis of performance and security trade-offs for a CCP architecture, based on a proposed generalised stochastic Petri net (GSPN) model with security-detection control model (SDCM). In this context, ‘optimal’ combined performance and security metrics were defined with both M-type or GE-type arrival and service times and the impact of security incidents on performance was assessed. Typical numerical experiments on the GSPN model were conducted and implemented using the Möbius package, and an ‘optimal’ trade-offs were determined between performance and security, which are crucial in the SLA of the cloud computing services. / Petroleum technology development fund (PTDF) of the government of Nigeria Usmanu Danfodiyo University, Sokoto

No description available.

Numerous studies on Queueing systems, such as Internet traffic flows, have shown to be bursty, self-similar and/or long-range dependent, because of the heavy (long) tails for the various distributions of interest, including intermittent intervals and queue lengths. Other studies have addressed vacation in no-customers’ queueing system or when the server fails. These patterns are important for capacity planning, performance prediction, and optimization of networks and have a negative impact on their effective functioning. Heavy-tailed distributions have been commonly used by telecommunication engineers to create workloads for simulation studies, which, regrettably, may show peculiar queueing characteristics. To cost-effectively examine the impacts of different network patterns on heavy- tailed queues, new and reliable analytical approaches need to be developed. It is decided to establish a brand-new analytical framework based on optimizing entropy functionals, such as those of Shannon, Rényi, Tsallis, and others that have been suggested within statistical physics and information theory, subject to suitable linear and non-linear system constraints. In both discrete and continuous time domains, new heavy tail analytic performance distributions will be developed, with a focus on those exhibiting the power law behaviour seen in many Internet scenarios. The exposition of two major revolutionary approaches, namely the unification of information geometry and classical queueing systems and unifying information length theory with transient queueing systems. After conclusions, open problems arising from this thesis and limitations are introduced as future work.

No / Security mechanisms, such as encryption and authentication protocols, require extra computing resources and therefore, have an adverse effect upon the performance of robotic mobile wireless ad hoc networks (RANETs). Thus, an optimal performance and security trade-off should be one of the main aspects that should be taken into consideration during the design, development, tuning and upgrading of such networks. In this context, an exposition is initially undertaken on the applicability of Petri nets (PNs) and queueing networks (QNs) in conjunction with their generalisations and hybrid integrations as robust quantitative modelling tools for the performance analysis of discrete flow systems, such as computer systems, communication networks and manufacturing systems. To overcome some of the inherent limitations of these models, a novel hybrid modelling framework is explored for the quantitative evaluation of RANETs, where each robotic node is represented by an abstract open hybrid G-GSPN_QN model with head-of-line priorities, subject to combined performance and security metrics (CPSMs). The proposed model focuses on security processing and state-based control and it is based on an open generalised stochastic PN (GSPN) with a gated multi-class 'On-Off' traffic and mobility model. Moreover, it employs a power consumption model and is linked in tandem with an arbitrary QN consisting of finite capacity channel queues with blocking for 'intra' robot component-to-component communication and 'inter' robot-to-robot transmission. Conclusions and future research directions are included.

Um conjunto de modelos compostos de redes de filas em grades finitas servindo como ambientes aleatorios para um ou mais passeios aleatorios, que por sua vez podem afetar o comportamento das filas, e desenvolvido. Duas formas de interacao entre os passeios aleatorios sao consideradas. Para cada modelo, e provado que o processo Markoviano correspondente e recorrente positivo e reversivel. As equacoes de balanceamento detalhado sao analisadas para obter a forma funcional da medida invariante de cada modelo. Em todos os modelos analisados neste trabalho, a medida invariante em uma grade finita tem forma produto. Modelos de redes de filas como ambientes para multiplos passeios aleatorios sao estendidos a grades infinitas. Para cada modelo estendido, sao especificadas as condicoes para a existencia do processo estocastico na grade infinita. Alem disso, e provado que existe uma unica medida invariante na rede infinita cuja projecao em uma subgrade finita e dada pela medida correspondente de uma rede finita. Finalmente, e provado que essa medida invariante na rede infinita e reversivel. / A set of models composed of queueing networks serving as random environments for one or more random walks, which themselves can affect the behavior of the queues, is developed. Two forms of interaction between the random walkers are considered. For each model, it is proved that the corresponding Markov process is positive recurrent and reversible. The detailed balance equa- tions are analyzed to obtain the functional form of the invariant measure of each model. In all the models analyzed in the present work, the invariant measure on a finite lattice has product form. Models of queueing networks as environments for multiple random walks are extended to infinite lattices. For each model extended, the conditions for the existence of the stochastic process on the infinite lattice are specified. In addition, it is proved that there exists a unique invariant measure on the infinite network whose projection on a finite sublattice is given by the corresponding finite- network measure. Finally, it is proved that that invariant measure on the infinite lattice is reversible.

Um conjunto de modelos compostos de redes de filas em grades finitas servindo como ambientes aleatorios para um ou mais passeios aleatorios, que por sua vez podem afetar o comportamento das filas, e desenvolvido. Duas formas de interacao entre os passeios aleatorios sao consideradas. Para cada modelo, e provado que o processo Markoviano correspondente e recorrente positivo e reversivel. As equacoes de balanceamento detalhado sao analisadas para obter a forma funcional da medida invariante de cada modelo. Em todos os modelos analisados neste trabalho, a medida invariante em uma grade finita tem forma produto. Modelos de redes de filas como ambientes para multiplos passeios aleatorios sao estendidos a grades infinitas. Para cada modelo estendido, sao especificadas as condicoes para a existencia do processo estocastico na grade infinita. Alem disso, e provado que existe uma unica medida invariante na rede infinita cuja projecao em uma subgrade finita e dada pela medida correspondente de uma rede finita. Finalmente, e provado que essa medida invariante na rede infinita e reversivel. / A set of models composed of queueing networks serving as random environments for one or more random walks, which themselves can affect the behavior of the queues, is developed. Two forms of interaction between the random walkers are considered. For each model, it is proved that the corresponding Markov process is positive recurrent and reversible. The detailed balance equa- tions are analyzed to obtain the functional form of the invariant measure of each model. In all the models analyzed in the present work, the invariant measure on a finite lattice has product form. Models of queueing networks as environments for multiple random walks are extended to infinite lattices. For each model extended, the conditions for the existence of the stochastic process on the infinite lattice are specified. In addition, it is proved that there exists a unique invariant measure on the infinite network whose projection on a finite sublattice is given by the corresponding finite- network measure. Finally, it is proved that that invariant measure on the infinite lattice is reversible.

本論文針對隨機數位網路提出一套可行的計算機制，以提供網路管理者進行資源分配與壅塞管理的分析工具。我們研究兩種利潤最佳化模型，探討在預算控制下的頻寬分配方式。因為資源有限，網路管理者無法隨時提供足夠頻寬以滿足隨機的網路需求，而量測網路連結成功與否的阻塞機率(Blocking Probability)為評估此風險之一種指標。我們利用頻寬分配、網路需求量和虛擬端對端路徑的數量等變數，推導阻塞機率函數，並證明阻塞機率的單調性(Monotonicity)和凸性(Convexity)等數學性質。在不失一般性之假設下，我們驗證阻塞機率是(1)隨頻寬增加而變小；(2)在特定的頻寬分配區間內呈凸性；(3)隨網路需求量增加而變大；(4)隨虛擬路徑的數量增加而變小。 本研究探討頻寬分配與阻塞機率之關係，藉由推導單調性和凸性等性質，提供此兩種利潤模型解的最適條件與求解演算法。同時，我們引用經濟學的彈性概念，提出三種模型參數對阻塞機率變化量的彈性定義，並分別進行頻寬分配、網路需求量和虛擬路徑數量對邊際利潤函數的敏感度分析。當網路上的虛擬路徑數量非常大時，阻塞機率的計算將變得複雜難解，因此我們利用高負荷極限理論(Heavy-Traffic Limit Theorem)提供阻塞機率的估計式，並分析其漸近行為(Asymptotic Behavior)。本論文的主要貢獻是分析頻寬分配與阻塞機率之間的關係及其數學性質。網路管理者可應用本研究提出的分析工具，在總預算限制下規劃寬頻網路的資源分配，並根據阻塞機率進行網路參數的調控。 / This thesis considers the problem of bandwidth allocation on communication networks with multiple traffic classes, where bandwidth is determined under the budget constraint. Due to the limited budget, there exists a risk that the network service providers can not assert a 100% guaranteed availability for the stochastic traffic demand at all times. We derive the blocking probabilities of connections as a function of bandwidth, traffic demand and the available number of virtual end-to-end paths for all service classes. Under general assumptions, we prove that the blocking probability is directionally (i) decreasing in bandwidth, (ii) convex in bandwidth for specific regions, (iii) increasing in traffic demand, and (iv) decreasing in the number of virtual paths. We also demonstrate the monotone and convex relations among those model parameters and the expected path occupancy. As the number of virtual paths is huge, we derive a heavy-traffic queueing model, and provide a diffusion approximation and its asymptotic analysis for the blocking probability, where the traffic intensity increases to one from below. Taking the blocking probability into account, two revenue management schemes are introduced to allocate bandwidth under budget control. The revenue/profit functions are studied in this thesis through the monotonicity and convexity of the blocking probability and expected path occupancy. Optimality conditions are derived to obtain an optimal bandwidth allocation for two revenue management schemes, and a solution algorithm is developed to allocate limited budget among competing traffic classes. In addition, we present three elasticities of the blocking probability to study the effect of changing model parameters on the average revenue in analysis of economic models. The sensitivity analysis and economic elasticity notions are proposed to investigate the marginal revenue for a given traffic class by changing bandwidth, traffic demand and the number of virtual paths, respectively. The main contribution of the present work is to prove the relationship between the blocking probability and allocated bandwidth under the budget constraint. Those results are also verified with numerical examples interpreting the blocking probability, utilization level, average revenue, etc. The relationship between blocking probability and bandwidth allocation can be applied in the design and provision of broadband communication networks by optimally choosing model parameters under budget control for sharing bandwidth in terms of blocking/congestion costs.

This thesis presents a cross-layer design and optimization for emerging wideband wireless networks supporting multimedia applications, considering the interactions of the wireless channel characteristics, the physical and link layer protocols, and the user-perceived Quality-of-Service (QoS). As wireless channels are error-prone and broadcast in nature, both the error control mechanisms and the Media Access Control (MAC) protocols are critical for resource utilization and QoS provisioning. How to analyze, design and optimize the high-rate wireless networks by considering the characteristics of the propagation channels and wideband communication technologies is an open, challenging issue. In this thesis, we consider two important wideband wireless systems, the Ultra-Wideband (UWB) and the Orthogonal Frequency-Division Multiplexing (OFDM) systems. First, we propose the packet-level channel models based on Finite State Markov Chains (FSMCs) for the two systems, which present the statistical properties of the propagation channels and the transmission systems. Second, by incorporating the proposed packet-level channel models, we develop analytical frameworks for quantifying the performance of the high-rate wireless networks, combining the channel fading, physical- and link-layer error-control mechanisms and MAC protocols. Third, to mitigate the impact of channel fading and impairments, a cross-layer joint error-control mechanism is proposed. In addition, we also investigate the impact of channel fading on the video streaming applications, and propose a simple admission control algorithm to ensure QoS. As considering the physical-layer characteristics is critical for ensuring QoS and efficiency of resource utilization, the packet-level channel models, cross-layer analytical frameworks, networking protocols and simulation methodologies proposed in this dissertation are essential for future proliferation of high-rate wireless networks.