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This work is subdivided into two main areas: resilient admission control and resilient routing. The work gives an overview of the state of the art of quality of service mechanisms in communication networks and proposes a categorization of admission control (AC) methods. These approaches are investigated regarding performance, more precisely, regarding the potential resource utilization by dimensioning the capacity for a network with a given topology, traffic matrix, and a required flow blocking probability. In case of a failure, the affected traffic is rerouted over backup paths which increases the traffic rate on the respective links. To guarantee the effectiveness of admission control also in failure scenarios, the increased traffic rate must be taken into account for capacity dimensioning and leads to resilient AC. Capacity dimensioning is not feasible for existing networks with already given link capacities. For the application of resilient NAC in this case, the size of distributed AC budgets must be adapted according to the traffic matrix in such a way that the maximum blocking probability for all flows is minimized and that the capacity of all links is not exceeded by the admissible traffic rate in any failure scenario. Several algorithms for the solution of that problem are presented and compared regarding their efficiency and fairness. A prototype for resilient AC was implemented in the laboratories of Siemens AG in Munich within the scope of the project KING. Resilience requires additional capacity on the backup paths for failure scenarios. The amount of this backup capacity depends on the routing and can be minimized by routing optimization. New protection switching mechanisms are presented that deviate the traffic quickly around outage locations. They are simple and can be implemented, e.g, by MPLS technology. The Self-Protecting Multi-Path (SPM) is a multi-path consisting of disjoint partial paths. The traffic is distributed over all faultless partial paths according to an optimized load balancing function both in the working case and in failure scenarios. Performance studies show that the network topology and the traffic matrix also influence the amount of required backup capacity significantly. The example of the COST-239 network illustrates that conventional shortest path routing may need 50% more capacity than the optimized SPM if all single link and node failures are protected.
Die vorliegende Arbeit beschäftigt sich mit der Chaossynchronisation in Netzwerken mit zeitverzögerten Kopplungen. Ein Netzwerk chaotischer Einheiten kann isochron und vollständig synchronisieren, auch wenn der Austausch der Signale einer oder mehreren Verzögerungszeiten unterliegt. In einem Netzwerk identischer Einheiten hat sich als Stabilitätsanalyse die Methode der Master Stability Funktion von Pecora und Carroll etabliert. Diese entspricht für ein Netzwerk gekoppelter iterativer Bernoulli-Abbildungen Polynomen vom Grade der größten Verzögerungszeit. Das Stabilitätsproblem reduziert sich somit auf die Untersuchung der Nullstellen dieser Polynome hinsichtlich ihrer Lage bezüglich des Einheitskreises. Eine solche Untersuchung kann beispielsweise numerisch mit dem Schur-Cohn-Theorem erfolgen, doch auch analytische Ergebnisse lassen sich erzielen. In der vorliegenden Arbeit werden Bernoulli-Netzwerke mit einer oder mehreren zeitverzögerten Kopplungen und/oder Rückkopplungen untersucht. Hierbei werden Aussagen über Teile des Stabilitätsgebietes getroffen, welche unabhängig von den Verzögerungszeiten sind. Des Weiteren werden Aussagen zu Systemen gemacht, welche sehr große Verzögerungszeiten aufweisen. Insbesondere wird gezeigt, dass in einem Bernoulli-Netzwerk keine stabile Chaossynchronisation möglich ist, wenn die vorhandene Verzögerungszeit sehr viel größer ist als die Zeitskala der lokalen Dynamik, bzw. der Lyapunovzeit. Außerdem wird in bestimmten Systemen mit mehreren Verzögerungszeiten anhand von Symmetriebetrachtungen stabile Chaossynchronisation ausgeschlossen, wenn die Verzögerungszeiten in bestimmten Verhältnissen zueinander stehen. So ist in einem doppelt bidirektional gekoppeltem Paar ohne Rückkopplung und mit zwei verschiedenen Verzögerungszeiten stabile Chaossynchronisation nicht möglich, wenn die Verzögerungszeiten in einem Verhältnis von teilerfremden ungeraden ganzen Zahlen zueinander stehen. Es kann zudem Chaossynchronisation ausgeschlossen werden, wenn in einem bipartiten Netzwerk mit zwei großen Verzögerungszeiten zwischen diesen eine kleine Differenz herrscht. Schließlich wird ein selbstkonsistentes Argument vorgestellt, das das Auftreten von Chaossynchronisation durch die Mischung der Signale der einzelnen Einheiten interpretiert und sich unter anderem auf die Teilerfremdheit der Zyklen eines Netzes stützt. Abschließend wird untersucht, ob einige der durch die Bernoulli-Netzwerke gefundenen Ergebnisse sich auf andere chaotische Netzwerke übertragen lassen. Hervorzuheben ist die sehr gute Übereinstimmung der Ergebnisse eines Bernoulli-Netzwerkes mit den Ergebnissen eines gleichartigen Netzwerkes gekoppelter Halbleiterlasergleichungen, sowie die Übereinstimmungen mit experimentellen Ergebnissen eines Systems von Halbleiterlasern.
This thesis deals with the chaotic dynamics of nonlinear networks consisting of semiconductor lasers which have time-delayed self-feedbacks or mutual couplings. These semiconductor lasers are simulated numerically by the Lang-Kobayashi equations. The central issue is how the chaoticity of the lasers, measured by the maximal Lyapunov exponent, changes when the delay time is changed. It is analysed how this change of chaoticity with increasing delay time depends on the reflectivity of the mirror for the self-feedback or the strength of the mutal coupling, respectively. The consequences of the different types of chaos for the effect of chaos synchronization of mutually coupled semiconductor lasers are deduced and discussed. At the beginning of this thesis, the master stability formalism for the stability analysis of nonlinear networks with delay is explained. After the description of the Lang-Kobayashi equations and their linearizations as a model for the numerical simulation of semiconductor lasers with time-delayed couplings, the artificial sub-Lyapunov exponent $\lambda_{0}$ is introduced. It is explained how the sign of the sub-Lyapunov exponent can be determined by experiments. The notions of "strong chaos" and "weak chaos" are introduced and distinguished by their different scaling properties of the maximal Lyapunov exponent with the delay time. The sign of the sub-Lyapunov exponent $\lambda_{0}$ is shown to determine the occurence of strong or weak chaos. The transition sequence "weak to strong chaos and back to weak chaos" upon monotonically increasing the coupling strength $\sigma$ of a single laser's self-feedback is shown for numerical calculations of the Lang-Kobayashi equations. At the transition between strong and weak chaos, the sub-Lyapunov exponent vanishes, $\lambda_{0}=0$, resulting in a special scaling behaviour of the maximal Lyapunov exponent with the delay time. Transitions between strong and weak chaos by changing $\sigma$ can also be found for the Rössler and Lorenz dynamics. The connection between the sub-Lyapunov exponent and the time-dependent eigenvalues of the Jacobian for the internal laser dynamics is analysed. Counterintuitively, the difference between strong and weak chaos is not directly visible from the trajectory although the difference of the trajectories induces the transitions between the two types of chaos. In addition, it is shown that a linear measure like the auto-correlation function cannot unambiguously reveal the difference between strong and weak chaos either. Although the auto-correlations after one delay time are significantly higher for weak chaos than for strong chaos, it is not possible to detect a qualitative difference. If two time-scale separated self-feedbacks are present, the shorter feedback has to be taken into account for the definition of a new sub-Lyapunov exponent $\lambda_{0,s}$, which in this case determines the occurence of strong or weak chaos. If the two self-feedbacks have comparable delay times, the sub-Lyapunov exponent $\lambda_{0}$ remains the criterion for strong or weak chaos. It is shown that the sub-Lyapunov exponent scales with the square root of the effective pump current $\sqrt{p-1}$, both in its magnitude and in the position of the critical coupling strengths. For networks with several distinct sub-Lyapunov exponents, it is shown that the maximal sub-Lyapunov exponent of the network determines whether the network's maximal Lyapunov exponent scales strongly or weakly with increasing delay time. As a consequence, complete synchronization of a network is excluded for arbitrary networks which contain at least one strongly chaotic laser. Furthermore, it is demonstrated that the sub-Lyapunov exponent of a driven laser depends on the number of the incoherently superimposed inputs from unsynchronized input lasers. For networks of delay-coupled lasers operating in weak chaos, the condition $|\gamma_{2}|<\mathrm{e}^{-\lambda_{\mathrm{m}}\,\tau}$ for stable chaos synchronization is deduced using the master stability formalism. Hence, synchronization of any network depends only on the properties of a single laser with self-feedback and the eigenvalue gap of the coupling matrix. The characteristics of the master stability function for the Lang-Kobayashi dynamics is described, and consequently, the master stability function is refined to allow for precise practical prediction of synchronization. The prediction of synchronization with the master stability function is demonstrated for bidirectional and unidirectional networks. Furthermore, the master stability function is extended for two distinct delay times. Finally, symmetries and resonances for certain values of the ratio of the delay times are shown for the master stability function of the Lang-Kobyashi equations.
Ziele: Evaluierung der Versorgungslage von Patienten mit akutem ST-Hebungsinfarkt im 2007 neu gegründeten Herzinfarktnetz Mainfranken und Vergleich von Ist-Zustand und Leitlinienempfehlungen. Analyse der Behandlungszeiten und Identifizierung von Verbesserungsmöglichkeiten im Netzwerk. Darüber hinaus sollte untersucht werden, ob Feedbackveranstaltungen als Qualitätsmanagement-Intervention die Behandlungszeiten im Laufe des Untersuchungszeitraumes verbessern. Methoden: Von Oktober 2007 bis Dezember 2008 wurden verschiedene Basisdaten sowie die Daten der Rettungs- und Therapiekette von Patienten mit akutem ST-Hebungsinfarkt (Symptomdauer <12h), die in der Medizinischen Klinik und Poliklinik I des Universitätsklinikums Würzburg mit dem Ziel einer PCI akut-koronarangiographiert wurden, im Rahmen der multizentrischen FiTT-STEMI-Studie prospektiv erfasst. Im Untersuchungszeitraum wurden die analysierten Daten alle drei Monate im Rahmen einer Feedbackveranstaltung allen Beteiligten der Rettungs- und Therapiekette demonstriert. Ergebnisse: Im genannten Zeitraum konnten 188 Patienten in die Studie eingeschlossen werden (19% weiblich, 81% männlich), wovon 85% eine PCI im Anschluss an die Koronarangiographie erhielten. Das mittlere Alter betrug 62±12 Jahre, 15% der Patienten waren über 75 Jahre. Der mittlere TIMI-Risk-Score lag bei 3,7 Punkten. Die intrahospitale Letalität lag bei 6,9%. Die Prähospitalzeit betrug im Median 120min; es ergab sich keine signifikante Veränderung über die Quartale. Ein Sekundärtransport bzw. ein prähospitaler Kontakt zum Hausarzt verlängerten die Prähospitalzeit im Median um 173 bzw. 57min. Die Door-to-balloon(D2B)-Zeit betrug im Gesamtuntersuchungszeitraum im Median 76min, nur 33% der Patienten erreichten eine leitliniengerechte D2B-Zeit von <60min. Die meiste Zeit innerhalb der D2B-Zeit entfiel auf die Zeit vom Erreichen der PCI-Klinik bis zum Herzkatheterlabor (Door-to-cath-Zeit). Die Verkürzung der D2B-Zeit von 80min im ersten auf 70min im fünften Quartal war statistisch nicht signifikant. Die Contact-to-balloon(C2B)-Zeit betrug im Gesamtuntersuchungszeitraum im Median 139min und konnte innerhalb des Untersuchungszeitraums statistisch signifikant von 164min im ersten auf 112min im fünften Quartal gesenkt werden. Dadurch konnte die Anzahl der leitliniengerecht behandelten Patienten (C2B-Zeit<120min) von 15 auf 58% im Gesamtkollektiv bzw. 24 auf 63% bei Patienten mit Primärtransport erhöht werden. Schlussfolgerung: Das Patientenkollektiv des Herzinfarktnetzes Mainfranken entsprach bezüglich der Basischarakteristika dem anderer nationaler und internationaler Register. Da eine PCI innerhalb von 120min nach medizinischem Erstkontakt als bestmögliche Therapie beim ST-Hebungsinfarkt angesehen wird und trotz der Verbesserung im Untersuchungszeitraum im fünften Quartal nur 58% der Patienten eine PCI in diesem Zeitintervall erhielten, sollten alle Anstrengungen unternommen werden die D2B- und C2B-Zeiten im Herzinfarktnetz weiter zu verkürzen. Hierfür sollte eine Direktübergabe im Herzkatheterlabor ermöglicht werden, da die Door-to-cath-Zeit in Würzburg im Median 36 bis 48min in Anspruch nahm. Darüber hinaus sollte durch Aufklärungs- und Informationsarbeit sowie Schulungen für Rettungspersonal und Patienten versucht werden einen Sekundärtransport oder Hausarztkontakt sowie ein verzögertes Alarmieren des Rettungsdienstes zu vermeiden, da sich hierdurch die Prähospitalzeit massiv verlängerte. Inwieweit die im Untersuchungszeitraum gezeigte Verkürzung der Zeiten mit den durchgeführten Feedbackveranstaltungen zusammenhängt bleibt ungewiss, da die Veränderung auch durch die Etablierung des neu gegründeten Netzwerks an sich bedingt sein kann.
In this thesis we study various aspects of chaos synchronization of time-delayed coupled chaotic maps. A network of identical nonlinear units interacting by time-delayed couplings can synchronize to a common chaotic trajectory. Even for large delay times the system can completely synchronize without any time shift. In the first part we study chaotic systems with multiple time delays that range over several orders of magnitude. We show that these time scales emerge in the Lyapunov spectrum: Different parts of the spectrum scale with the different delays. We define various types of chaos depending on the scaling of the maximum exponent. The type of chaos determines the synchronization ability of coupled networks. This is, in particular, relevant for the synchronization properties of networks of networks where time delays within a subnetwork are shorter than the corresponding time delays between the different subnetworks. If the maximum Lyapunov exponent scales with the short intra-network delay, only the elements within a subnetwork can synchronize. If, however, the maximum Lyapunov exponent scales with the long inter-network connection, complete synchronization of all elements is possible. The results are illustrated analytically for Bernoulli maps and numerically for tent maps. In the second part the attractor dimension at the transition to complete chaos synchronization is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks of Bernoulli units as a function of the network size. Furthermore the scaling of the Kaplan-Yorke dimension as well as of the Kolmogorov entropy with system size and time delay is investigated. Finally, we study the change in the attractor dimension for systems with parameter mismatch. In the third and last part the linear response of synchronized chaotic systems to small external perturbations is studied. The distribution of the distances from the synchronization manifold, i.e., the deviations between two synchronized chaotic units due to external perturbations on the transmitted signal, is used as a measure of the linear response. It is calculated numerically and, for some special cases, analytically. Depending on the model parameters this distribution has power law tails in the region of synchronization leading to diverging moments. The linear response is also quantified by means of the bit error rate of a transmitted binary message which perturbs the synchronized system. The bit error rate is given by an integral over the distribution of distances and is studied numerically for Bernoulli, tent and logistic maps. It displays a complex nonmonotonic behavior in the region of synchronization. For special cases the distribution of distances has a fractal structure leading to a devil's staircase for the bit error rate as a function of coupling strength. The response to small harmonic perturbations shows resonances related to coupling and feedback delay times. A bi-directionally coupled chain of three units can completely filter out the perturbation. Thus the second moment and the bit error rate become zero.
The subject of this thesis is the controllability of interconnected linear systems, where the interconnection parameter are the control variables. The study of accessibility and controllability of bilinear systems is closely related to their system Lie algebra. In 1976, Brockett classified all possible system Lie algebras of linear single-input, single-output (SISO) systems under time-varying output feedback. Here, Brockett's results are generalized to networks of linear systems, where time-varying output feedback is applied according to the interconnection structure of the network. First, networks of linear SISO systems are studied and it is assumed that all interconnections are independently controllable. By calculating the system Lie algebra it is shown that accessibility of the controlled network is equivalent to the strong connectedness of the underlying interconnection graph in case the network has at least three subsystems. Networks with two subsystems are not captured by these proofs. Thus, we give results for this particular case under additional assumption either on the graph structure or on the dynamics of the node systems, which are both not necessary. Additionally, the system Lie algebra is studied in case the interconnection graph is not strongly connected. Then, we show how to adapt the ideas of proof to networks of multi-input, multi-output (MIMO) systems. We generalize results for the system Lie algebra on networks of MIMO systems both under output feedback and under restricted output feedback. Moreover, the case with generalized interconnections is studied, i.e. parallel edges and linear dependencies in the interconnection controls are allowed. The new setting demands to distinguish between homogeneous and heterogeneous networks. With this new setting only sufficient conditions can be found to guarantee accessibility of the controlled network. As an example, networks with Toeplitz interconnection structure are studied.
With the introduction of OpenFlow by the Stanford University in 2008, a process began in the area of network research, which questions the predominant approach of fully distributed network control. OpenFlow is a communication protocol that allows the externalization of the network control plane from the network devices, such as a router, and to realize it as a logically-centralized entity in software. For this concept, the term "Software Defined Networking" (SDN) was coined during scientific discourse.
For the network operators, this concept has several advantages. The two most important can be summarized under the points cost savings and flexibility. Firstly, it is possible through the uniform interface for network hardware ("Southbound API"), as implemented by OpenFlow, to combine devices and software from different manufacturers, which increases the innovation and price pressure on them. Secondly, the realization of the network control plane as a freely programmable software with open interfaces ("Northbound API") provides the opportunity to adapt it to the individual circumstances of the operator's network and to exchange information with the applications it serves. This allows the network to be more flexible and to react more quickly to changing circumstances as well as transport the traffic more effectively and tailored to the user’s "Quality of Experience" (QoE).
The approach of a separate network control layer for packet-based networks is not new and has already been proposed several times in the past. Therefore, the SDN approach has raised many questions about its feasibility in terms of efficiency and applicability. These questions are caused to some extent by the fact that there is no generally accepted definition of the SDN concept to date. It is therefore a part of this thesis to derive such a definition. In addition, several of the open issues are investigated. This Investigations follow the three aspects: Performance Evaluation of Software Defined Networking, applications on the SDN control layer, and the usability of SDN Northbound-API for creation application-awareness in network operation.
Performance Evaluation of Software Defined Networking: The question of the efficiency of an SDN-based system was from the beginning one of the most important. In this thesis, experimental measurements of the performance of OpenFlow-enabled switch hardware and control software were conducted for the purpose of answering this question. The results of these measurements were used as input parameters for establishing an analytical model of the reactive SDN approach. Through the model it could be determined that the performance of the software control layer, often called "Controller", is crucial for the overall performance of the system, but that the approach is generally viable. Based on this finding a software for analyzing the performance of SDN controllers was developed. This software allows the emulation of the forwarding layer of an SDN network towards the control software and can thus determine its performance in different situations and configurations. The measurements with this software showed that there are quite significant differences in the behavior of different control software implementations. Among other things it has been shown that some show different characteristics for various switches, in particular in terms of message processing speed. Under certain circumstances this can lead to network failures.
Applications on the SDN control layer: The core piece of software defined networking are the intelligent network applications that operate on the control layer. However, their development is still in its infancy and little is known about the technical possibilities and their limitations. Therefore, the relationship between an SDN-based and classical implementation of a network function is investigated in this thesis. This function is the monitoring of network links and the traffic they carry. A typical approach for this task has been built based on Wiretapping and specialized measurement hardware and compared with an implementation based on OpenFlow switches and a special SDN control application. The results of the comparison show that the SDN version can compete in terms of measurement accuracy for bandwidth and delay estimation with the traditional measurement set-up. However, a compromise has to be found for measurements below the millisecond range.
Another question regarding the SDN control applications is whether and how well they can solve existing problems in networks. Two programs have been developed based on SDN in this thesis to solve two typical network issues. Firstly, the tool "IPOM", which enables considerably more flexibility in the study of effects of network structures for a researcher, who is confined to a fixed physical test network topology.
The second software provides an interface between the Cloud Orchestration Software "OpenNebula" and an OpenFlow controller. The purpose of this software was to investigate experimentally whether a pre-notification of the network of an impending relocation of a virtual service in a data center is sufficient to ensure the continuous operation of that service. This was demonstrated on the example of a video service.
Usability of the SDN Northbound API for creating application-awareness in network operation: Currently, the fact that the network and the applications that run on it are developed and operated separately leads to problems in network operation. SDN offers with the Northbound-API an open interface that enables the exchange between information of both worlds during operation. One aim of this thesis was to investigate whether this interface can be exploited so that the QoE experienced by the user can be maintained on high level. For this purpose, the QoE influence factors were determined on a challenging application by means of a subjective survey study. The application is cloud gaming, in which the calculation of video game environments takes place in the cloud and is transported via video over the network to the user. It was shown that apart from the most important factor influencing QoS, i.e., packet loss on the downlink, also the type of game type and its speed play a role. This demonstrates that in addition to QoS the application state is important and should be communicated to the network. Since an implementation of such a state conscious SDN for the example of Cloud Gaming was not possible due to its proprietary implementation, in this thesis the application “YouTube video streaming” was chosen as an alternative. For this application, status information is retrievable via the "Yomo" tool and can be used for network control. It was shown that an SDN-based implementation of an application-aware network has distinct advantages over traditional network management methods and the user quality can be obtained in spite of disturbances.
Routing is one of the most important issues in any communication network. It defines on which path packets are transmitted from the source of a connection to the destination. It allows to control the distribution of flows between different locations in the network and thereby is a means to influence the load distribution or to reach certain constraints imposed by particular applications. As failures in communication networks appear regularly and cannot be completely avoided, routing is required to be resilient against such outages, i.e., routing still has to be able to forward packets on backup paths even if primary paths are not working any more.
Throughout the years, various routing technologies have been introduced that are very different in their control structure, in their way of working, and in their ability to handle certain failure cases. Each of the different routing approaches opens up their own specific questions regarding configuration, optimization, and inclusion of resilience issues. This monograph investigates, with the example of three particular routing technologies, some concrete issues regarding the analysis and optimization of resilience. It thereby contributes to a better general, technology-independent understanding of these approaches and of their diverse potential for the use in future network architectures.
The first considered routing type, is decentralized intra-domain routing based on administrative IP link costs and the shortest path principle. Typical examples are common today's intra-domain routing protocols OSPF and IS-IS. This type of routing includes automatic restoration abilities in case of failures what makes it in general very robust even in the case of severe network outages including several failed components. Furthermore, special IP-Fast Reroute mechanisms allow for a faster reaction on outages. For routing based on link costs, traffic engineering, e.g. the optimization of the maximum relative link load in the network, can be done indirectly by changing the administrative link costs to adequate values.
The second considered routing type, MPLS-based routing, is based on the a priori configuration of primary and backup paths, so-called Label Switched Paths. The routing layout of MPLS paths offers more freedom compared to IP-based routing as it is not restricted by any shortest path constraints but any paths can be setup. However, this in general involves a higher configuration effort.
Finally, in the third considered routing type, typically centralized routing using a Software Defined Networking (SDN) architecture, simple switches only forward packets according to routing decisions made by centralized controller units. SDN-based routing layouts offer the same freedom as for explicit paths configured using MPLS. In case of a failure, new rules can be setup by the controllers to continue the routing in the reduced topology. However, new resilience issues arise caused by the centralized architecture. If controllers are not reachable anymore, the forwarding rules in the single nodes cannot be adapted anymore. This might render a rerouting in case of connection problems in severe failure scenarios infeasible.
In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer science, mathematics, and physics working on datasets from biology, economics, sociology, political sciences, and many others, network science serves as a paradigm for interdisciplinary research.
One of the major goals in network science is to unravel the relationship between topological graph structure and a network’s function. As evidence suggests, systems from the same fields, i.e. with similar function, tend to exhibit similar structure. However, it is still vague whether a similar graph structure automatically implies likewise function. This dissertation aims at helping to bridge this gap, while particularly focusing on the role of triadic structures.
After a general introduction to the main concepts of network science, existing work devoted to the relevance of triadic substructures is reviewed. A major challenge in modeling triadic structure is the fact that not all three-node subgraphs can be specified independently
of each other, as pairs of nodes may participate in multiple of those triadic subgraphs.
In order to overcome this obstacle, we suggest a novel class of generative network models based on so called Steiner triple systems. The latter are partitions of a graph’s vertices into pair-disjoint triples (Steiner triples). Thus, the configurations on Steiner triples can be specified independently of each other without overdetermining the network’s link
structure.
Subsequently, we investigate the most basic realization of this new class of models. We call it the triadic random graph model (TRGM). The TRGM is parametrized by a probability distribution over all possible triadic subgraph patterns. In order to generate a network instantiation of the model, for all Steiner triples in the system, a pattern is drawn from the distribution and adjusted randomly on the Steiner triple. We calculate the degree distribution of the TRGM analytically and find it to be similar to a Poissonian distribution. Furthermore, it is shown that TRGMs possess non-trivial triadic structure. We discover inevitable correlations in the abundance of certain triadic subgraph
patterns which should be taken into account when attributing functional relevance to particular motifs – patterns which occur significantly more frequently than expected at random. Beyond, the strong impact of the probability distributions on the Steiner triples on the occurrence of triadic subgraphs over the whole network is demonstrated. This interdependence allows us to design ensembles of networks with predefined triadic substructure. Hence, TRGMs help to overcome the lack of generative models needed for assessing the relevance of triadic structure.
We further investigate whether motifs occur homogeneously or heterogeneously distributed over a graph. Therefore, we study triadic subgraph structures in each node’s neighborhood individually. In order to quantitatively measure structure from an individual node’s perspective, we introduce an algorithm for node-specific pattern mining for both directed unsigned, and undirected signed networks. Analyzing real-world datasets, we find that there are networks in which motifs are distributed highly heterogeneously, bound to the proximity of only very few nodes. Moreover, we observe indication for the potential sensitivity of biological systems to a targeted removal of these critical vertices. In addition, we study whole graphs with respect to the homogeneity and homophily of their node-specific triadic structure. The former describes the similarity of subgraph distributions in the neighborhoods of individual vertices. The latter quantifies whether connected vertices
are structurally more similar than non-connected ones. We discover these features to be characteristic for the networks’ origins. Moreover, clustering the vertices of graphs regarding their triadic structure, we investigate structural groups in the neural network of C. elegans, the international airport-connection network, and the global network of diplomatic sentiments between countries. For the latter we find evidence for the instability of triangles considered socially unbalanced according to sociological theories.
Finally, we utilize our TRGM to explore ensembles of networks with similar triadic substructure in terms of the evolution of dynamical processes acting on their nodes. Focusing on oscillators, coupled along the graphs’ edges, we observe that certain triad motifs impose a clear signature on the systems’ dynamics, even when embedded in a larger
network structure.
At the center of the Internet’s protocol stack stands the Internet Protocol (IP) as a common denominator that enables all communication. To make routing efficient, resilient, and scalable, several aspects must be considered. Care must be taken that traffic is well balanced to make efficient use of the existing network resources, both in failure free operation and in failure scenarios.
Finding the optimal routing in a network is an NP-complete problem. Therefore, routing optimization is usually performed using heuristics. This dissertation shows that a routing optimized with one objective function is often not good when looking at other objective functions. It can even be worse than unoptimized routing with respect to that objective function. After looking at failure-free routing and traffic distribution in different failure scenarios, the analysis is extended to include the loop-free alternate (LFA) IP fast reroute mechanism. Different application scenarios of LFAs are examined and a special focus is set on the fact that LFAs usually cannot protect all traffic in a network even against single link failures. Thus, the routing optimization for LFAs is targeted on both link utilization and failure coverage. Finally, the pre-congestion notification mechanism PCN for network admission control and overload protection is analyzed and optimized. Different design options for implementing the protocol are compared, before algorithms are developed for the calculation and optimization of protocol parameters and PCN-based routing.
The second part of the thesis tackles a routing problem that can only be resolved on a global scale. The scalability of the Internet is at risk since a major and intensifying growth of the interdomain routing tables has been observed. Several protocols and architectures are analyzed that can be used to make interdomain routing more scalable. The most promising approach is the locator/identifier (Loc/ID) split architecture which separates routing from host identification. This way, changes in connectivity, mobility of end hosts, or traffic-engineering activities are hidden from the routing in the core of the Internet and the routing tables can be kept much smaller. All of the currently proposed Loc/ID split approaches have their downsides. In particular, the fact that most architectures use the ID for routing outside the Internet’s core is a poor design, which inhibits many of the possible features of a new routing architecture. To better understand the problems and to provide a solution for a scalable routing design that implements a true Loc/ID split, the new GLI-Split protocol is developed in this thesis, which provides separation of global and local routing and uses an ID that is independent from any routing decisions.
Besides GLI-Split, several other new routing architectures implementing Loc/ID split have been proposed for the Internet. Most of them assume that a mapping system is queried for EID-to-RLOC mappings by an intermediate node at the border of an edge network. When the mapping system is queried by an intermediate node, packets are already on their way towards their destination, and therefore, the mapping system must be fast, scalable, secure, resilient, and should be able to relay packets without locators to nodes that can forward them to the correct destination. The dissertation develops a classification for all proposed mapping system architectures and shows their similarities and differences. Finally, the fast two-level mapping system FIRMS is developed. It includes security and resilience features as well as a relay service for initial packets of a flow when intermediate nodes encounter a cache miss for the EID-to-RLOC mapping.