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Deterministic Object Management in Large Distributed SystemsMikhailov, Mikhail 05 March 2003 (has links)
Caching is a widely used technique to improve the scalability of distributed systems. A central issue with caching is maintaining object replicas consistent with their master copies. Large distributed systems, such as the Web, typically deploy heuristic-based consistency mechanisms, which increase delay and place extra load on the servers, while not providing guarantees that cached copies served to clients are up-to-date. Server-driven invalidation has been proposed as an approach to strong cache consistency, but it requires servers to keep track of which objects are cached by which clients.
We propose an alternative approach to strong cache consistency, called MONARCH, which does not require servers to maintain per-client state. Our approach builds on a few key observations. Large and popular sites, which attract the majority of the traffic, construct their pages from distinct components with various characteristics. Components may have different content types, change characteristics, and semantics. These components are merged together to produce a monolithic page, and the information about their uniqueness is lost. In our view, pages should serve as containers holding distinct objects with heterogeneous type and change characteristics while preserving the boundaries between these objects. Servers compile object characteristics and information about relationships between containers and embedded objects into explicit object management commands. Servers piggyback these commands onto existing request/response traffic so that client caches can use these commands to make object management decisions.
The use of explicit content control commands is a deterministic, rather than heuristic, object management mechanism that gives content providers more control over their content. The deterministic object management with strong cache consistency offered by MONARCH allows content providers to make more of their content cacheable. Furthermore, MONARCH enables content providers to expose internal structure of their pages to clients.
We evaluated MONARCH using simulations with content collected from real Web sites. The results show that MONARCH provides strong cache consistency for all objects, even for unpredictably changing ones, and incurs smaller byte and message overhead than heuristic policies. The results also show that as the request arrival rate or the number of clients increases, the amount of server state maintained by MONARCH remains the same while the amount of server state incurred by server invalidation mechanisms grows.
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Adaptive Prefetching for Visual Data ExplorationDoshi, Punit Rameshchandra 31 January 2003 (has links)
Loading of data from slow persistent memory (disk storage) to main memory represents a bottleneck for current interactive visual data exploration applications, especially when applied to huge volumnes of data. Semantic caching of queries at the client-side is a recently emerging technology that can significantly improve the performance of such systems, though it may not in all cases fully achieve the near real-time responsiveness required by such interactive applications. We hence propose to augment the semantic caching techniques by applying prefetching. That is, the system predicts the user's next requested data and loads the data into the cache as a background process before the next user request is made. Our experimental studies confirm that prefetching indeed achieves performance improvements for interactive visual data exploration. However, a given prefetching technique is not always able to correctly predict changes in a user's navigation pattern. Especially, as different users may have different navigation patterns, implying that the same strategy might fail for a new user. In this research, we tackle this shortcoming by utilizing the adaptation concept of strategy selection to allow the choice of prefetching strategy to change over time both across as well as within one user session. While other adaptive prefetching research has focused on refining a single strategy, we instead have developed a framework that facilitates strategy selection. For this, we explored various metrics to measure performance of prefetching strategies in action and thus guide the adaptive selection process. This work is the first to study caching and prefetching in the context of visual data exploration. In particular, we have implemented and evaluated our proposed approach within XmdvTool, a free-ware visualization system for visually exploring hierarchical multivariate data. We have tested our technique on real user traces gathered by the logging tool of our system as well as on synthetic user traces. Our results confirm that our adaptive approach improves system performance by selecting a good combination of prefetching strategies that adapts to the user's changing navigation patterns.
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On models for performance evaluation and cache resources placement in multi-cache networks / Sur des modèles pour l'évaluation de performance et le placement des ressources de cache dans les réseaux multi-cacheBen Ammar, Hamza 19 March 2019 (has links)
Au cours des dernières années, les fournisseurs de contenu ont connu une forte augmentation des demandes de contenus vidéo et de services riches en média. Compte tenu des limites de la mise à l'échelle du réseau et au-delà des réseaux de diffusion de contenu, les fournisseurs de services Internet développent leurs propres systèmes de mise en cache afin d'améliorer la performance du réseau. Ces facteurs expliquent l'enthousiasme à l'égard du concept de réseau centré sur le contenu et de sa fonction de mise en cache en réseau. La quantification analytique de la performance de la mise en cache n'est toutefois pas suffisamment explorée dans la littérature. De plus, la mise en place d'un système de caching efficace au sein d'une infrastructure réseau est très complexe et demeure une problématique ouverte. Pour traiter ces questions, nous présentons d'abord dans cette thèse un modèle générique et précis de cache nommé MACS (Markov chain-based Approximation of Caching Systems) qui peut être adapté très facilement pour représenter différents schémas de mise en cache et qui peut être utilisé pour calculer différentes mesures de performance des réseaux multi-cache. Nous avons ensuite abordé le problème de l'allocation des ressources de cache dans les réseaux avec capacité de caching. Moyennant notre outil analytique MACS, nous présentons une approche permettant de résoudre le compromis entre différentes mesures de performance en utilisant l'optimisation multi-objectif et nous proposons une adaptation de la métaheuristique GRASP pour résoudre le problème d'optimisation. / In the last few years, Content Providers (CPs) have experienced a high increase in requests for video contents and rich media services. In view of the network scaling limitations and beyond Content Delivery Networks (CDNs), Internet Service Providers (ISPs) are developing their own caching systems in order to improve the network performance. These factors explain the enthusiasm around the Content-Centric Networking (CCN) concept and its in-network caching feature. The analytical quantification of caching performance is, however, not sufficiently explored in the literature. Moreover, setting up an efficient caching system within a network infrastructure is very complex and remains an open problem. To address these issues, we provide first in this thesis a fairly generic and accurate model of caching nodes named MACS (Markov chain-based Approximation of Caching Systems) that can be adapted very easily to represent different caching schemes and which can be used to compute different performance metrics of multi-cache networks. We tackled after that the problem of cache resources allocation in cache-enabled networks. By means of our analytical tool MACS, we present an approach that solves the trade-off between different performance metrics using multi-objective optimization and we propose an adaptation of the metaheuristic GRASP to solve the optimization problem.
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Information-Centric Networking, A natural design for IoT applications? / Le réseau basé sur les informations (ICN), une conception naturelle pour l'Internet des Objets?Meddeb, Maroua 27 September 2017 (has links)
L'Internet des Objets (IdO) est généralement perçu comme l'extension de l'Internet actuel à notre monde physique. Il interconnecte un grand nombre de capteurs / actionneurs, référencés comme des objets, sur Internet. Face aux importants défis imposés par l'hétérogénéité des dispositifs et l'énorme trafic généré, la pile protocolaire actuelle TCP / IP va atteindre ses limites. Le réseau centré sur l'information (ICN) a récemment reçu beaucoup d'attention comme une nouvelle architecture Internet qui a un grand potentiel pour être adoptée dans un système IdO. Le paradigme ICN forme la future architecture Internet qui s’est contrée sur les données elles-mêmes plutôt que sur leurs emplacements dans le réseau. Il s'agit d'un passage d'un modèle de communication centrée sur l'hôte vers un système centré sur le contenu en se basant sur des noms de contenu uniques et indépendants de la localisation, la mise en cache dans le réseau et le routage basé sur les noms. Grâce à ses avantages pertinents, l'ICN peut être un framework viable pour soutenir l’IdO, interconnectant des milliards d'objets contraints hétérogènes. En effet, ICN permet l'accès facile aux données et réduit à la fois le délai de récupération et la charge des requêtes sur les producteurs de données. Parmi plusieurs architectures ICN, le réseau de données nommées (NDN) est considéré comme l'architecture ICN appropriée pour les systèmes IdO. Néanmoins, de nouveaux problèmes ont apparu et s'opposent aux ambitions visées dans l'utilisation de la philosophie ICN dans les environnements IdO. En fait, nous avons identifié trois défis majeurs. Étant donné que les périphériques IdO sont habituellement limités en termes de ressources avec des limitations sévères de l'énergie, de la mémoire et de la puissance de traitement, les techniques de mise en cache en réseau doivent être optimisées. En outre, les données IdO sont transitoires et sont régulièrement mises à jour par les producteurs, ce qui impose des exigences strictes pour maintenir la cohérence des données mises en cache. Enfin, dans un scénario IdO, les objets sont souvent mobiles et nécessitent des stratégies pour maintenir leurs accessibilités. Dans cette thèse, nous proposons une stratégie de mise en cache optimale qui considère les contraintes des périphériques. Ensuite, nous présentons un nouveau mécanisme de cohérence de cache pour surveiller la validité des contenus mis en cache dans un environnement IdO. En outre, pour améliorer l'efficacité de la mise en cache, nous proposons également une politique de remplacement du cache qui vise à augmenter les performances du système et à maintenir la validité des données. Enfin, nous introduisons un nouveau routage basé sur les noms pour les réseaux NDN / IdO afin de prendre en charge la mobilité des producteurs.Nous simulons et comparons nos propositions à plusieurs propositions pertinentes sous un réseau IdO de trafic réel. Nos contributions présentent de bonnes performances du système en termes de taux de réduction du chemin parcouru par les requêtes, de taux de réduction du nombre des requêtes satisfaites par les serveur, du délai de la réponse et de perte des paquets, de plus, la stratégie de mise en cache offre un faible coût de cache et finalement la validité du contenu est considérablement améliorée grâce au mécanisme de cohérence. / The Internet of Things (IoT) is commonly perceived as the extension of the current Internet to our physical world. It interconnects an unprecedented number of sensors/actuators, referred as things, to the Internet. Facing the important challenges imposed by devices heterogeneity and the tremendous generated traffic, the current Internet protocol suite has reached its limits. The Information-Centric Networking (ICN) has recently received a lot of attention as a potential Internet architecture to be adopted in an IoT ecosystem. The ICN paradigm is shaping the foreseen future Internet architecture by focusing on the data itself rather than its hosting location. It is a shift from a host-centric! communication model to a content-centric one supporting among! others unique and location-independent content names, in-network caching and name-based routing. By leveraging the easy data access, and reducing both the retrieval delay and the load on the data producer, the ICN can be a viable framework to support the IoT, interconnecting billions of heterogeneous constrained objects. Among several ICN architectures, the Named Data Networking (NDN) is considered as a suitable ICN architecture for IoT systems. Nevertheless, new issues have emerged slowing down the ambitions besides using the ICN paradigm in IoT environments. In fact, we have identified three major challenges. Since IoT devices are usually resource-constrained with harsh limitations on energy, memory and processing power, the adopted in-network caching techniques should be optimized. Furthermore, IoT data are transient and frequently updated by the producer which imposes stringent requirements to maintain cached data freshness. Finally, in IoT scenario, devices are ! frequently mobile and IoT applications require keeping data continuity. In this thesis, we propose a caching strategy that considers devices constraints. Then, we introduce a novel cache freshness mechanism to monitor the validity of cached contents in an IoT environment. Furthermore, to improve caching efficiency, we also propose a cache replacement policy that targets to raise the system performances and maintain data freshness. Finally, we introduce a novel name-based routing for NDN/IoT networks to support the producer mobility. We simulate and compare our proposals to several relevant schemes under a real traffic IoT network. Our schemes exhibit good system performances in terms of hop reduction ratio, server hit reduction ratio, response latency and packet loss, yet it provides a low cache cost and significantly improves the content validity.
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Optimizing Main Memory Usage in Modern Computing Systems to Improve Overall System PerformanceCampello, Daniel Jose 20 June 2016 (has links)
Operating Systems use fast, CPU-addressable main memory to maintain an application’s temporary data as anonymous data and to cache copies of persistent data stored in slower block-based storage devices. However, the use of this faster memory comes at a high cost. Therefore, several techniques have been implemented to use main memory more efficiently in the literature. In this dissertation we introduce three distinct approaches to improve overall system performance by optimizing main memory usage.
First, DRAM and host-side caching of file system data are used for speeding up virtual machine performance in today’s virtualized data centers. The clustering of VM images that share identical pages, coupled with data deduplication, has the potential to optimize main memory usage, since it provides more opportunity for sharing resources across processes and across different VMs. In our first approach, we study the use of content and semantic similarity metrics and a new algorithm to cluster VM images and place them in hosts where through deduplication we improve main memory usage.
Second, while careful VM placement can improve memory usage by eliminating duplicate data, caches in current systems employ complex machinery to manage the cached data. Writing data to a page not present in the file system page cache causes the operating system to synchronously fetch the page into memory, blocking the writing process. In this thesis, we address this limitation with a new approach to managing page writes involving buffering the written data elsewhere in memory and unblocking the writing process immediately. This buffering allows the system to service file writes faster and with less memory resources.
In our last approach, we investigate the use of emerging byte-addressable persistent memory technology to extend main memory as a less costly alternative to exclusively using expensive DRAM. We motivate and build a tiered memory system wherein persistent memory and DRAM co-exist and provide improved application performance at lower cost and power consumption with the goal of placing the right data in the right memory tier at the right time. The proposed approach seamlessly performs page migration across memory tiers as access patterns change and/or to handle tier memory pressure.
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Caching and prefetching for efficient video services in mobile networks / Caching et prefetching pour une livraison plus efficace des contenus vidéo dans les réseaux mobilesGouta, Ali 15 January 2015 (has links)
Les réseaux cellulaires ont connu une croissance phénoménale du trafic alimentée par les nouvelles technologies d'accès cellulaire. Cette croissance est en grande partie tirée par l'émergence du trafic HTTP adaptatif streaming (HAS) comme une nouvelle technologie de diffusion des contenus vidéo. Le principe du HAS est de rendre disponible plusieurs qualités de la même vidéo en ligne et que les clients choisissent la meilleure qualité qui correspond à leur bande passante. Chaque niveau d'encodage est segmenté en des chunks, qui dont la durée varie de 2 à 10 secondes. L'émergence du HAS a introduit des nouvelles contraintes sur les systèmes de livraison des contenus vidéo en particulier sur les systèmes de caches. Dans ce contexte, nous menons une analyse détaillée des données du trafic HAS collecté en France et fournie par le plus grand opérateur de téléphonie mobile du pays. Tout d'abord, nous analysons et modélisons le comportement des clients qui demandent des contenus VoD et live. Ces analyses nous ont permis d'identifier les facteurs qui impactent la performance des systèmes de cache et de proposer un nouveau algorithme de remplacement de contenus qu'on appelle WA-LRU. WA-LRU exploite la localité temporelle des chunks dans le contenu et la connaissance de la charge du trafic dans le réseau afin d'améliorer la performance du cache. Ensuite, nous analysons et modélisons la logique d'adaptation entre les qualités vidéo basés sur des observations empiriques. Nous montrons que le changement fréquent entre les encodages réduit considérablement la performance des systèmes de cache. Dans ce contexte, nous présentons CF-DASH une implémentation libre d'un player DASH qui vise à réduire les changements fréquents entre qualités, assure une bonne QoE des clients et améliore la performance des systèmes de caches. La deuxième partie de la thèse est dédié à la conception, simulation et implémentation d'une solution de préchargement des contenus vidéo sur terminaux mobiles. Nous concevons un système que nous appelons «Central Predictor System (CPsys)" qui prédit le comportement des clients mobiles et leurs consommations des vidéos. Nous évaluons CPSys avec des traces de trafic réel. Enfin, nous développons une preuve de concept de notre solution de préchargement. / Recently, cellular networks have witnessed a phenomenal growth of traffic fueled by new high speed broadband cellular access technologies. This growth is in large part driven by the emergence of the HTTP Adaptive Streaming (HAS) as a new video delivery method. In HAS, several qualities of the same videos are made available in the network so that clients can choose the quality that best fits their bandwidth capacity. This strongly impacts the viewing pattern of the clients, their switching behavior between video qualities, and thus beyond on content delivery systems. In this context, we provide an analysis of a real HAS dataset collected in France and provided by the largest French mobile operator. Firstly, we analyze and model the viewing patterns of VoD and live streaming HAS sessions and we propose a new cache replacement strategy, named WA-LRU. WA-LRU leverages the time locality of video segments within the HAS content. We show that WA-LRU improves the performance of the cache. Second, we analyze and model the adaptation logic between the video qualities based on empirical observations. We show that high switching behaviors lead to sub optimal caching performance, since several versions of the same content compete to be cached. In this context we investigate the benefits of a Cache Friendly HAS system (CF-DASH) which aims at improving the caching efficiency in mobile networks and to sustain the quality of experience of mobile clients. Third, we investigate the mobile video prefetching opportunities. We show that CPSys can achieve high performance as regards prediction correctness and network utilization efficiency. We further show that CPSys outperforms other prefetching schemes from the state of the art. At the end, we provide a proof-of-concept implementation of our prefetching system.
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A Targeted Denial of Service Attack on Data Caching NetworksGouge, Jeffrey B 01 January 2015 (has links)
With the rise of data exchange over the Internet, information-centric networks have become a popular research topic in computing. One major research topic on Information Centric Networks (ICN) is the use of data caching to increase network performance. However, research in the security concerns of data caching networks is lacking. One example of a data caching network can be seen using a Mobile Ad Hoc Network (MANET).
Recently, a study has shown that it is possible to infer military activity through cache behavior which is used as a basis for a formulated denial of service attack (DoS) that can be used to attack networks using data caching. Current security issues with data caching networks are discussed, including possible prevention techniques and methods. A targeted data cache DoS attack is developed and tested using an ICN as a simulator. The goal of the attacker would be to fill node caches with unpopular content, thus making the cache useless. The attack would consist of a malicious node that requests unpopular content in intervals of time where the content would have been just purged from the existing cache. The goal of the attack would be to corrupt as many nodes as possible without increasing the chance of detection. The decreased network throughput and increased delay would also lead to higher power consumption on the mobile nodes, thus increasing the effects of the DoS attack.
Various caching polices are evaluated in an ICN simulator program designed to show network performance using three common caching policies and various cache sizes. The ICN simulator is developed using Java and tested on a simulated network. Baseline data are collected and then compared to data collected after the attack. Other possible security concerns with data caching networks are also discussed, including possible smarter attack techniques and methods.
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A QUANTITATIVE FRAMEWORK FOR CDN-BASED OVER-THE-TOP VIDEO STREAMING SYSTEMSAbubakr O Alabbasi (8187867) 06 January 2020 (has links)
<div>The demand for global video has been burgeoning across industries. With the expansion and improvement of video-streaming services, cloud-based video is evolving into a necessary feature of any successful business for reaching internal and external audiences. Over-the-top (OTT) video streaming, e.g., Netfix and YouTube, has been dominating the global IP traffic in recent years. More than 50% of OTT video traffic are now delivered through content distribution networks (CDNs). Even though multiple solutions have been proposed for improving congestion in the CDN system, managing the ever-increasing traffic requires a fundamental understanding of the system and the different design fexibilities (control knobs) to make the best use of the hardware limitations. In Addition, there is no analytical understanding for the key quality of experience (QoE) attributes (stall duration, average quality, etc.) for video streaming when transmitted using CDN-based multi-tier infrastructure, which is the focus of this thesis. The key contribution of this thesis is to provide a white-box analytical understanding of the key QoE attributes of the enduser in cloud storage systems, which can be used to systematically address the choppy user experience and have optimized system designs. The rst key design involves the scheduling strategy, that chooses the subset of CDN servers to obtain the content. The second key design involves the quality of each video chunk. The third key design involves deciding which contents to cache at the edge routers and which content needs to be stored at the CDN. Towards solving these challenges, this dissertation is divided into three parts. Part 1 considers video streaming over distributed systems where the video segments are encoded using an erasure code for better reliability. Part 2 looks at the problem of optimizing the tradeoff between quality and stall of the streamed videos. In Part 3, we consider caching partial contents of the videos at the CDN as well as at the edge-routers to further optimize video streaming services. We present a model for describing a today's representative multi-tier system architecture</div><div>for video streaming applications, typically composed of a centralized origin server, several CDN sites and edge-caches. Our model comprehensively considers the following factors: limited caching spaces at the CDN sites and edge-routers, allocation of CDN for a video request, choice of different ports from the CDN, and the central storage and bandwidth allocation. With this model, we optimize different quality of experience (QoE) measures and present novel, yet efficient, algorithms to solve the formulated optimization problems. Our extensive simulation results demonstrate that the proposed algorithms signicantly outperform the state-of-the-art strategies. We take one step further and implement a small-scale video streaming system in a real cloud environment, managed by Openstack, and validate our results</div>
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Workload Driven Designs for Cost-Effective Non-Volatile Memory HierarchiesTimothy A Pritchett (9179468) 28 July 2020 (has links)
Compared to traditional hard-disk drives (HDDs), non-volatile (NV) memory technologies offer significant performance advantages on one hand, but also incur significant cost and asymmetric write-performance on the other. A common strategy to manage such cost- and performance-differentials is to use hierarchies such that a small, but intensely accessed, working set is staged in the NV storage (selective caching). However, when this working set includes write-heavy data, the low write-lifetime of NV storage necessitates significant over-provisioning to maintain required lifespans (e.g., storage lifespan must match or exceed 3 year server lifespan). One may think that employing DRAM-based write-buffers can filter writes that trickle through to the NV storage and thus alleviate the write-pressure felt at the NV storage. Unfortunately, selective caches, when used with common recency-based or frequency-based replacement, have access patterns that require large write buffers (e.g., 100MB+ relative to a 12GB cache) to filter writes adequately. Further, these large DRAM write-buffers also require backup-power to ensure the durability of disk writes. More sophisticated replacement policies that combine recency and frequency can reduce the size of the DRAM buffer (while preserving write-filtering), but are so computationally-expensive that they can limit the I/O rate, especially for simple controllers (e.g., RAID controller). <br>My first contribution is the design and implementation of WriteGuard– a self-tuning sieving write-buffer algorithm that filters writes as well as the highly-effective (but computationally-expensive) algorithms while requiring lightweight computation comparable to a simple LRU-based write-buffer. While WriteGuard reduces the capacity needed for DRAM buffering (to approx. 64 MB), it does not eliminate the need for DRAM buffers (and corresponding power backup).<br>For my second thrust, I identify two specific application characteristics – (1) the vast majority of the write-buffer’s contents is composed of write-dominant blocks, and (2) the vast majority of blocks in the write-buffer are overwritten within a period of 28 hours. I show that these characteristics help enable a high-density, optimized STT-MRAM as a replacement for DRAM, which enables durable write-buffers (thus eliminating the cost of power backup for the write-buffer). My optimized STT-MRAM-based write buffer achieves higher density by (a) trading off superfluous durability by exploiting characteristic (2), and (b) deoptimizing the read-performance of STT-MRAM by leveraging characteristic (1). Together, the techniques increase the density of STT-MRAM by 20% with low or no impact on write-buffer performance.<br>
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Optimierte Visualisierung auf segmentierten AnzeigenLorenz, Mario 07 July 2005 (has links)
Diese Arbeit beschreibt den Entwurf und die Funktionsweise einer parallelen OpenGL-Renderingschnittstelle, die den effizienten Betrieb unmodifizierter graphischer Anwendungen auf segmentierten Anzeigen ermöglicht. Diese Schnittstelle integriert sich vollständig in eine verteilte graphische Benutzeroberfläche. Die herausragende Eigenschaft der entwickelten parallelen OpenGL-Schnittstelle ist ihre gleich bleibende Bildrate bei wachsender Anzahl von Segmenten. Als Erweiterung des frei verfügbaren Chromium-Systems stellt die Implementation eine virtuelle Graphikpipeline mit der Gesamtauflösung der segmentierten Anzeige bereit, die den eingehenden Datenstrom über ein Kommunikationsnetzwerk an die Knoten eines Visualisierungsclusters überträgt. Jeder Knoten des Clusters rendert einen Ausschnitt des Gesamtbildes und bringt diesen auf dem zugehörigen Segment synchronisiert zur Anzeige. Die interne Verarbeitung der von der Applikation generierten OpenGL-Datenströme unterscheidet sich jedoch grundlegend von der existierenden Lösung. Während die Tilesort-SPU von Chromium die Daten entsprechend der Segmentierung der Anzeige sortiert und sequenziell an die relevanten Knoten versendet, überträgt die in der Arbeit vorgestellte Schnittstelle die Graphikbefehle simultan. Die dadurch erreichte Vermeidung redundanter Übertragungen bewirkt bereits einen besseren Durchsatz der Kommunikationskanäle und zusätzlich eine signifikante Verringerung der Prozessorbelastung des Applikationsrechners. Die freie gewordene Kapazität schafft wiederum die Voraussetzung für die Anwendung verschiedener Optimierungsverfahren zur weiteren Steigerung der graphischen Gesamtleistung der parallelen Schnittstelle. Dazu zählt neben der Zwischenspeicherung von Datensequenzen in einem Stream Cache die Filterung der OpenGL-Kommandoströme mit graphischen Culling-Verfahren. Speziell zum aktiv-stereoskopischen Rendern auf dem an der Professur vorhandenen zylindrischen Projektionssystem enthält die Schnittstelle Anpassungen für die Synchronisationshardware und die bildbasierte Korrektur der Parallaxe.
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