Remarks on Category-Based Routing in Social Networks

It is well known that individuals can route messages on short paths through social networks, given only simple information about the target and using only local knowledge about the topology. Sociologists conjecture that people find routes greedily by passing the message to an acquaintance that has more in common with the target than themselves, e.g. if a dentist in Saarbr\"ucken wants to send a message to a specific lawyer in Munich, he may forward it to someone who is a lawyer and/or lives in Munich. Modelling this setting, Eppstein et al. introduced the notion of category-based routing. The goal is to assign a set of categories to each node of a graph such that greedy routing is possible. By proving bounds on the number of categories a node has to be in we can argue about the plausibility of the underlying sociological model. In this paper we substantially improve the upper bounds introduced by Eppstein et al. and prove new lower bounds.Comment: 21 page

Critical market shares for investors and access seekers and competitive models in fibre networks

In this paper we consider and evaluate NGA architectures which meet the foreseeable future bandwidth demand and allow for highest bandwidth and quality for end-users and which no longer rely on copper cable elements. These are FTTH architectures only. From all available FTTH architectures we concentrate on the two most relevant architectures in Europe, Ethernet Point-to-Point and GPON. We assume the incumbent to be the investor in the NGA network infrastructure. If the NGA architecture is based on a Point-to-Point fibre plant we have modelled the competitors as using unbundled fibre loops as the wholesale access service. If the architecture is based on a Point-to-Multipoint fibre plant, we consider an active wholesale access (bitstream access) at the MPoP or at the core network node locations. Our basic modelling relies upon an engineering bottom-up cost modelling approach. We model the total cost of the services considered under efficient conditions, taking into account the cost of all network elements needed to produce these services in the specific architecture deployed. This approach is coherent with a Long Run Incremental Cost approach as applied in regulatory economics. Our modelling approach generates a broad set of results including the relative performance of the various network architectures, investment requirements and the degree of profitable coverage. In this paper, however, we focus on the results on the potential for competition and potential market structures in an NGA environment. --NGA architecture,cost modelling,FTTH,coverage,access models,unbundling

VDSL and G.fast Vectoring and the impact on VULA

VDSL and G.fast Vectoring are transmission technologies over copper access line pairs enabling the transmission of higher bandwidth to the end customers, but harm the infrastructure based competition using physical unbundled copper lines. Thus regulators have to decide between infrastructure based competition of physical unbundling against earlier broadband rollout meeting the DAE goals in time and bandwidth, while pure fibre based broadband networks will require more time and investment for serving whole areas, but then provide higher bandwidth. Thus VDSL and G.fast Vectoring each are an interim solution. This paper highlights the benefits of such solution and the regulatory challenges and options being faced. The Virtual Unbundled Local Access (VULA) is one regulatory tool forming a compromise between the advantages of physical unbundling and the need to early satisfy higher bandwidth supply targets