## 004 Datenverarbeitung; Informatik

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This thesis is devoted to the study of computational complexity theory, a branch of theoretical computer science. Computational complexity theory investigates the inherent difficulty in designing efficient algorithms for computational problems. By doing so, it analyses the scalability of computational problems and algorithms and places practical limits on what computers can actually accomplish. Computational problems are categorised into complexity classes. Among the most important complexity classes are the class NP and the subclass of NP-complete problems, which comprises many important optimisation problems in the field of operations research. Moreover, with the P-NP-problem, the class NP represents the most important unsolved question in computer science. The first part of this thesis is devoted to the study of NP-complete-, and more generally, NP-hard problems. It aims at improving our understanding of this important complexity class by systematically studying how altering NP-hard sets affects their NP-hardness. This research is related to longstanding open questions concerning the complexity of unions of disjoint NP-complete sets, and the existence of sparse NP-hard sets. The second part of the thesis is also dedicated to complexity classes but takes a different perspective: In a sense, after investigating the interior of complexity classes in the first part, the focus shifts to the description of complexity classes and thereby to the exterior in the second part. It deals with the description of complexity classes through leaf languages, a uniform framework which allows us to characterise a great variety of important complexity classes. The known concepts are complemented by a new leaf-language model. To a certain extent, this new approach combines the advantages of the known models. The presented results give evidence that the connection between the theory of formal languages and computational complexity theory might be closer than formerly known.

Overlay networks establish logical connections between users on top of the physical network. While randomly connected overlay networks provide only a best effort service, a new generation of structured overlay systems based on Distributed Hash Tables (DHTs) was proposed by the research community. However, there is still a lack of understanding the performance of such DHTs. Additionally, those architectures are highly distributed and therefore appear as a black box to the operator. Yet an operator does not want to lose control over his system and needs to be able to continuously observe and examine its current state at runtime. This work addresses both problems and shows how the solutions can be combined into a more self-organizing overlay concept. At first, we evaluate the performance of structured overlay networks under different aspects and thereby illuminate in how far such architectures are able to support carrier-grade applications. Secondly, to enable operators to monitor and understand their deployed system in more detail, we introduce both active as well as passive methods to gather information about the current state of the overlay network.

Verteilte dynamische Systeme unter lokalen und globalen Gesichtspunkten zu optimieren ist eine schwierige Aufgabe. Zwar sind grundsätzliche Auswirkungen einzelner Maßnahmen häufig bekannt, durch widerstrebende Ziele, Wechselwirkungen zwischen Prozessen und Nebenwirkungen von Maßnahmen ist ein analytisches Vorgehen bei der Optimierung nicht möglich. Besonders schwierig wird es, wenn lokale Einheiten einerseits ihre Ziele und Autonomie behalten sollen, aber durch zentrale Vorgaben bzw. Anreize so gesteuert werden sollen, dass ein übergeordnetes Ziel erreicht wird. Ein praktisches Beispiel dieses allgemeinen Optimierungsproblems findet sich im Gesundheitswesen. Das Management von modernen Kliniken ist stets mit dem Problem konfrontiert, die Qualität der Pflege zu gewährleisten und gleichzeitig kosteneffizient zu arbeiten. Hier gilt es unter gegeben Rahmenbedingungen und bei Respektierung der Autonomie der Funktionseinheiten, Optimierungsmaßnahmen zu finden und durchzuführen. Vorhandene Werkzeuge zur Simulation und Modellierung bieten für diese Aufgabe keine ausreichend guten Vorgehensmodelle und Modellierungsmechanismen. Die agentenbasierte Simulation ermöglicht die Abbildung solcher Systeme und die Durchführung von Simulationsexperimenten zur Bewertung einzelner Maßnahmen. Es werden Lösungswege und Werkzeuge vorgestellt und evaluiert, die den Benutzer bei der Formalisierung des Wissens und der Modellierung solch komplexer Szenarien unterstützen und ein systematisches Vorgehen zur Optimierung ermöglichen.

Performance Evaluation of Efficient Resource Management Concepts for Next Generation IP Networks
(2007)

Next generation networks (NGNs) must integrate the services of current circuit-switched telephone networks and packet-switched data networks. This convergence towards a unified communication infrastructure necessitates from the high capital expenditures (CAPEX) and operational expenditures (OPEX) due to the coexistence of separate networks for voice and data. In the end, NGNs must offer the same services as these legacy networks and, therefore, they must provide a low-cost packet-switched solution with real-time transport capabilities for telephony and multimedia applications. In addition, NGNs must be fault-tolerant to guarantee user satisfaction and to support business-critical processes also in case of network failures. A key technology for the operation of NGNs is the Internet Protocol (IP) which evolved to a common and well accepted standard for networking in the Internet during the last 25 years. There are two basically different approaches to achieve QoS in IP networks. With capacity overprovisioning (CO), an IP network is equipped with sufficient bandwidth such that network congestion becomes very unlikely and QoS is maintained most of the time. The second option to achieve QoS in IP networks is admission control (AC). AC represents a network-inherent intelligence that admits real-time traffic flows to a single link or an entire network only if enough resources are available such that the requirements on packet loss and delay can be met. Otherwise, the request of a new flow is blocked. This work focuses on resource management and control mechanisms for NGNs, in particular on AC and associated bandwidth allocation methods. The first contribution consists of a new link-oriented AC method called experience-based admission control (EBAC) which is a hybrid approach dealing with the problems inherent to conventional AC mechanisms like parameter-based or measurement-based AC (PBAC/MBAC). PBAC provides good QoS but suffers from poor resource utilization and, vice versa, MBAC uses resources efficiently but is susceptible to QoS violations. Hence, EBAC aims at increasing the resource efficiency while maintaining the QoS which increases the revenues of ISPs and postpones their CAPEX for infrastructure upgrades. To show the advantages of EBAC, we first review today’s AC approaches and then develop the concept of EBAC. EBAC is a simple mechanism that safely overbooks the capacity of a single link to increase its resource utilization. We evaluate the performance of EBAC by its simulation under various traffic conditions. The second contribution concerns dynamic resource allocation in transport networks which implement a specific network admission control (NAC) architecture. In general, the performance of different NAC systems may be evaluated by conventional methods such as call blocking analysis which has often been applied in the context of multi-service asynchronous transfer mode (ATM) networks. However, to yield more practical results than abstract blocking probabilities, we propose a new method to compare different AC approaches by their respective bandwidth requirements. To present our new method for comparing different AC systems, we first give an overview of network resource management (NRM) in general. Then we present the concept of adaptive bandwidth allocation (ABA) in capacity tunnels and illustrate the analytical performance evaluation framework to compare different AC systems by their capacity requirements. Different network characteristics influence the performance of ABA. Therefore, the impact of various traffic demand models and tunnel implementations, and the influence of resilience requirements is investigated. In conclusion, the resources in NGNs must be exclusively dedicated to admitted traffic to guarantee QoS. For that purpose, robust and efficient concepts for NRM are required to control the requested bandwidth with regard to the available transmission capacity. Sophisticated AC will be a key function for NRM in NGNs and, therefore, efficient resource management concepts like experience-based admission control and adaptive bandwidth allocation for admission-controlled capacity tunnels, as presented in this work are appealing for NGN solutions.