A critical look at power law modelling of the Internet

This paper takes a critical look at the usefulness of power law models of the Internet. The twin focuses of the paper are Internet traffic and topology generation. The aim of the paper is twofold. Firstly it summarises the state of the art in power law modelling particularly giving attention to existing open research questions. Secondly it provides insight into the failings of such models and where progress needs to be made for power law research to feed through to actual improvements in network performance.Comment: To appear Computer Communication

Dynamic Exploration of Networks: from general principles to the traceroute process

Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on a class of tree-like processes, such as those used to explore the Internet's topology. A general theory based on mean-field arguments is proposed, both for single-source and multiple-source cases, and applied to the specific example of the traceroute exploration of networks. Our results provide a qualitative improvement in the understanding of dynamical sampling and of the interplay between dynamics and topology in large networks like the Internet.Comment: 13 pages, 6 figure

Phase Changes in the Evolution of the IPv4 and IPv6 AS-Level Internet Topologies

In this paper we investigate the evolution of the IPv4 and IPv6 Internet topologies at the autonomous system (AS) level over a long period of time.We provide abundant empirical evidence that there is a phase transition in the growth trend of the two networks. For the IPv4 network, the phase change occurred in 2001. Before then the network's size grew exponentially, and thereafter it followed a linear growth. Changes are also observed around the same time for the maximum node degree, the average node degree and the average shortest path length. For the IPv6 network, the phase change occurred in late 2006. It is notable that the observed phase transitions in the two networks are different, for example the size of IPv6 network initially grew linearly and then shifted to an exponential growth. Our results show that following decades of rapid expansion up to the beginning of this century, the IPv4 network has now evolved into a mature, steady stage characterised by a relatively slow growth with a stable network structure; whereas the IPv6 network, after a slow startup process, has just taken off to a full speed growth. We also provide insight into the possible impact of IPv6-over-IPv4 tunneling deployment scheme on the evolution of the IPv6 network. The Internet topology generators so far are based on an inexplicit assumption that the evolution of Internet follows non-changing dynamic mechanisms. This assumption, however, is invalidated by our results.Our work reveals insights into the Internet evolution and provides inputs to future AS-Level Internet models.Comment: 12 pages, 21 figures; G. Zhang et al.,Phase changes in the evolution of the IPv4 and IPv6 AS-Level Internet topologies, Comput. Commun. (2010

Dynamic, Latency-Optimal vNF Placement at the Network Edge

Future networks are expected to support low-latency, context-aware and user-specific services in a highly flexible and efficient manner. One approach to support emerging use cases such as, e.g., virtual reality and in-network image processing is to introduce virtualized network functions (vNF)s at the edge of the network, placed in close proximity to the end users to reduce end-to-end latency, time-to-response, and unnecessary utilisation in the core network. While placement of vNFs has been studied before, it has so far mostly focused on reducing the utilisation of server resources (i.e., minimising the number of servers required in the network to run a specific set of vNFs), and not taking network conditions into consideration such as, e.g., end-to-end latency, the constantly changing network dynamics, or user mobility patterns. In this paper, we formulate the Edge vNF placement problem to allocate vNFs to a distributed edge infrastructure, minimising end-to-end latency from all users to their associated vNFs. We present a way to dynamically re-schedule the optimal placement of vNFs based on temporal network-wide latency fluctuations using optimal stopping theory. We then evaluate our dynamic scheduler over a simulated nation-wide backbone network using real-world ISP latency characteristics. We show that our proposed dynamic placement scheduler minimises vNF migrations compared to other schedulers (e.g., periodic and always-on scheduling of a new placement), and offers Quality of Service guarantees by not exceeding a maximum number of latency violations that can be tolerated by certain applications

Modeling Structure and Resilience of the Dark Network

While the statistical and resilience properties of the Internet are no more changing significantly across time, the Darknet, a network devoted to keep anonymous its traffic, still experiences rapid changes to improve the security of its users. Here, we study the structure of the Darknet and we find that its topology is rather peculiar, being characterized by non-homogenous distribution of connections -- typical of scale-free networks --, very short path lengths and high clustering -- typical of small-world networks -- and lack of a core of highly connected nodes. We propose a model to reproduce such features, demonstrating that the mechanisms used to improve cyber-security are responsible for the observed topology. Unexpectedly, we reveal that its peculiar structure makes the Darknet much more resilient than the Internet -- used as a benchmark for comparison at a descriptive level -- to random failures, targeted attacks and cascade failures, as a result of adaptive changes in response to the attempts of dismantling the network across time.Comment: 8 pages, 5 figure

Image scoring in ad-hoc networks : an investigation on realistic settings

Encouraging cooperation in distributed Multi-Agent Systems (MAS) remains an open problem. Emergent application domains such as Mobile Ad-hoc Networks (MANETs) are characterised by constraints including sparse connectivity and a lack of direct interaction history. Image scoring, a simple model of reputation proposed by Nowak and Sigmund, exhibits low space and time complexity and promotes cooperation through indirect reciprocity, in which an agent can expect cooperation in the future without repeat interactions with the same partners. The low overheads of image scoring make it a promising technique for ad-hoc networking domains. However, the original investigation of Nowak and Sigmund is limited in that it (i) used a simple idealised setting, (ii) did not consider the effects of incomplete information on the mechanism’s efficacy, and (iii) did not consider the impact of the network topology connecting agents. We address these limitations by investigating more realistic values for the number of interactions agents engage in, and show that incomplete information can cause significant errors in decision making. As the proportion of incorrect decisions rises, the efficacy of image scoring falls and selfishness becomes more dominant. We evaluate image scoring on three different connection topologies: (i) completely connected, which closely approximates Nowak and Sigmund’s original setup, (ii) random, with each pair of nodes connected with a constant probability, and (iii) scale-free, which is known to model a number of real world environments including MANETs