Loss network

Abstract: This article describes a novel method of achieving load balancing in telecommunications networks. A simulated network models a typical distribution of calls between nodes; nodes carrying an excess ...

Abstract: This paper proposes a mixed-integer conic programming formulation for the minimum loss distribution network reconfiguration problem. This formulation has two features: first, it employs a convex representation of the network model which is based on the conic quadratic format of the power flow equations and second, it optimizes the exact value of the network losses. The use of a convex model in terms of the continuous variables is particularly important because it ensures that an optimal solution obtained by a branch-and-cut algorithm for mixed-integer conic programming is global. In addition, good quality solutions with a relaxed optimality gap can be very efficiently obtained. A polyhedral approximation which is amenable to solution via more widely available mixed-integer linear programming software is also presented. Numerical results on practical test networks including distributed generation show that mixed-integer convex optimization is an effective tool for network reconfiguration.

Abstract: Network structures, such as social networks, web graphs and networks from systems biology, play important roles in many areas of science and our everyday lives. In order to study the networks one needs to first collect reliable large scale network data. While the social and information networks have become ubiquitous, the challenge of collecting complete network data still persists. Many times the collected network data is incomplete with nodes and edges missing. Commonly, only a part of the network can be observed and we would like to infer the unobserved part of the network. We address this issue by studying the Network Completion Problem: Given a network with missing nodes and edges, can we complete the missing part? We cast the problem in the Expectation Maximization (EM) framework where we use the observed part of the network to fit a model of network structure, and then we estimate the missing part of the network using the model, re-estimate the parameters and so on. We combine the EM with the Kronecker graphs model and design a scalable Metropolized Gibbs sampling approach that allows for the estimation of the model parameters as well as the inference about missing nodes and edges of the network. Experiments on synthetic and several real-world networks show that our approach can effectively recover the network even when about half of the nodes in the network are missing. Our algorithm outperforms not only classical link-prediction approaches but also the state of the art Stochastic block modeling approach. Furthermore, our algorithm easily scales to networks with tens of thousands of nodes.