In this work, we are interested in the applications of big data in the telecommunication domain, analysing two weeks of datasets provided by Telecom Italia for Milan and Trento. Our objective is to identify hotspots which are places with very high communication traffic relative to others and measure the interaction between them. We model the hotspots as nodes in a graph and then apply node centrality metrics that quantify the importance of each node. We review five node centrality metrics and show that they can be divided into two families: the first family is composed of closeness and betweenness centrality whereas the second family consists of degree, PageRank and eigenvector centrality. We then proceed with a statistical analysis in order to evaluate the consistency of the results over the two weeks. We find out that the ranking of the hotspots under the various centrality metrics remains practically the same with the time for both Milan and Trento. We further identify that the relative difference of the values of the metrics is smaller for PageRank centrality than for closeness centrality and this holds for both Milan and Trento. Finally, our analysis reveals that the variance of the results is significantly smaller for Trento than for Milan.
For example, the authors in @cite_4 analyse an heterogeneous cellular network which consists of different types of nodes, such as macrocells and microcells. Nowadays a popular model is the one from Wyner @cite_0 , but it fails to fully capture a real heterogeneous cellular network because it is simplistic. Another approach is to use the spatial Poisson point process model (SPPP) @cite_9 , which can be derived from the premise that all base stations are uniformly distributed. However, a city can be classified in different areas, which have different population densities. These different areas can be characterised as dense urban, urban and suburban. To be able to classify the heterogeneous networks into these areas, the authors introduce SPPP for homogeneous and inhomogeneous sets. They show that the SPPP-model captures accurately both urban and suburban areas, whereas this is not the case for dense urban areas, because of a considerable population concentrated in small areas.
@cite_0 @cite_9 @cite_4
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In heterogeneous cellular networks spatial characteristics of base stations (BSs) influence the system performance intensively. Existing models like two-dimensional hexagonal grid model or homogeneous spatial poisson point process (SPPP) are based on the assumption that BSs are ideal or uniformly distributed, but the aggregation behavior of users in hot spots has an important effect on the location of low power nodes (LPNs), so these models fail to characterize the distribution of BSs in the current mobile cellular networks. In this paper, firstly existing spatial models are analyzed. Then, based on real data from a mobile operator in one large city of China, a set of spatial models is proposed in three typical regions: dense urban, urban and suburban. For dense urban area, “Two Tiers Poisson Cluster Superimposed Process” is proposed to model the spatial characteristics of real-world BSs. Specifically, for urban and suburban area, conventional SPPP model still can be used. Finally, the fundamental relationship between user behavior and BS distribution is illustrated and summarized. Numerous results show that SPPP is only appropriate in the urban and suburban regions where users are not gathered together obviously. Principal parameters of these models are provided as reference for the theoretical analysis and computer simulation, which describe the complex spatial configuration more reasonably and reflect the current mobile cellular network performance more precisely. We consider spatial stochastic models of downlink heterogeneous cellular networks (HCNs) with multiple tiers, where the base stations (BSs) of each tier have a particular spatial density, transmission power and path-loss exponent. Prior works on such spatial models of HCNs assume, due to its tractability, that the BSs are deployed according to homogeneous Poisson point processes. This means that the BSs are located independently of each other and their spatial correlation is ignored. In the current paper, we propose two spatial models for the analysis of downlink HCNs, in which the BSs are deployed according to @a-Ginibre point processes. The @a-Ginibre point processes constitute a class of determinantal point processes and account for the repulsion between the BSs. Besides, the degree of repulsion is adjustable according to the value of @[email protected]?(0,1]. In one proposed model, the BSs of different tiers are deployed according to mutually independent @a-Ginibre processes, where the @a can take different values for the different tiers. In the other model, all the BSs are deployed according to an @a-Ginibre point process and they are classified into multiple tiers by mutually independent marks. For these proposed models, we derive computable representations for the coverage probability of a typical user-the probability that the downlink signal-to-interference-plus-noise ratio for the typical user achieves a target threshold. We exhibit the results of some numerical experiments and compare the proposed models and the Poisson based model. The spatial structure of transmitters in wireless networks plays a key role in evaluating the mutual interference and hence the performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of wireless networks, it is not suitable for networks with repulsion. The Ginibre point process (GPP) is one of the main examples of determinantal point processes that can be used to model random phenomena where repulsion is observed. Considering the accuracy, tractability and practicability tradeoffs, we introduce and promote the @math -GPP, an intermediate class between the PPP and the GPP, as a model for wireless networks when the nodes exhibit repulsion. To show that the model leads to analytically tractable results in several cases of interest, we derive the mean and variance of the interference using two different approaches: the Palm measure approach and the reduced second moment approach, and then provide approximations of the interference distribution by three known probability density functions. Besides, to show that the model is relevant for cellular systems, we derive the coverage probability of the typical user and also find that the fitted @math -GPP can closely model the deployment of actual base stations in terms of the coverage probability and other statistics. Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. This paper proposes the use of the determinantal point process (DPP) to take into account these correlations, in particular the repulsiveness among macro BS locations. DPPs are demonstrated to be analytically tractable by leveraging several unique computational properties. Specifically, we show that the empty space function, the nearest neighbor function, the mean interference, and the signal-to-interference ratio (SIR) distribution have explicit analytical representations and can be numerically evaluated for cellular networks with DPP-configured BSs. In addition, the modeling accuracy of DPPs is investigated by fitting three DPP models to real BS location data sets from two major U.S. cities. Using hypothesis testing for various performance metrics of interest, we show that these fitted DPPs are significantly more accurate than popular choices such as the PPP and the perturbed hexagonal grid model.