14,589 research outputs found
Reduction of Second-Order Network Systems with Structure Preservation
This paper proposes a general framework for structure-preserving model
reduction of a secondorder network system based on graph clustering. In this
approach, vertex dynamics are captured by the transfer functions from inputs to
individual states, and the dissimilarities of vertices are quantified by the
H2-norms of the transfer function discrepancies. A greedy hierarchical
clustering algorithm is proposed to place those vertices with similar dynamics
into same clusters. Then, the reduced-order model is generated by the
Petrov-Galerkin method, where the projection is formed by the characteristic
matrix of the resulting network clustering. It is shown that the simplified
system preserves an interconnection structure, i.e., it can be again
interpreted as a second-order system evolving over a reduced graph.
Furthermore, this paper generalizes the definition of network controllability
Gramian to second-order network systems. Based on it, we develop an efficient
method to compute H2-norms and derive the approximation error between the
full-order and reduced-order models. Finally, the approach is illustrated by
the example of a small-world network
Antitrust Analysis for the Internet Upstream Market: a BGP Approach
In this paper we study concentration in the European Internet upstream access market. Measurement of market concentration depends on correctly defining the market, but this is not always possible as Antitrust authorities often lack reliable pricing and traffic data. We present an alternative approach based on the inference of the Internet Operators interconnection policies using micro-data sourced from their Border Gateway Protocol tables. Firstly we propose a price-independent algorithm for defining both the vertical and geographical relevant market boundaries, then we calculate market concentration indexes using two novel metrics. These assess, for each undertaking, both its role in terms of essential network facility and of wholesale market dominance. The results, applied to four leading Internet Exchange Points in London, Amsterdam, Frankfurt and Milan, show that some vertical segments of these markets are extremely competitive, while others are highly concentrated, putting them within the special attention category of the Merger Guidelines
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