Abstract-A recent approach in modeling and analysis of the supply and demand in heterogeneous wireless cellular networks has been the use of two independent Poisson point processes (PPPs) for the locations of base stations (BSs) and user equipments (UEs). This popular approach has two major shortcomings. First, although the PPP model may be a fitting one for the BS locations, it is less adequate for the UE locations mainly due to the fact that the model is not adjustable (tunable) to represent the severity of the heterogeneity (non-uniformity) in the UE locations. Besides, the independence assumption between the two PPPs does not capture the often-observed correlation between the UE and BS locations.This paper presents a novel heterogeneous spatial traffic modeling which allows statistical adjustment. Simple and nonparameterized, yet sufficiently accurate, measures for capturing the traffic characteristics in space are introduced. Only two statistical parameters related to the UE distribution, namely, the coefficient of variation (the normalized second-moment), of an appropriately defined inter-UE distance measure, and correlation coefficient (the normalized cross-moment) between UE and BS locations, are adjusted to control the degree of heterogeneity and the bias towards the BS locations, respectively. This model is used in heterogeneous wireless cellular networks (HetNets) to demonstrate the impact of heterogeneous and BS-correlated traffic on the network performance. This network is called HetHetNet since it has two types of heterogeneity: heterogeneity in the infrastructure (supply), and heterogeneity in the spatial traffic distribution (demand).

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Wireless cellular network planning benefits from accurate and realistic, yet relatively simple and manageable, spatial traffic models. User locations in cellular networks are often modeled as homogeneous (uniform) Poisson point processes (PPPs). However, the real user distributions are seldom purely homogeneous. Network users are usually concentrated at social attractors such as residential and office buildings, shopping malls, and bus stations. Wireless spectral efficiency depends significantly on the users' spatial heterogeneity, and thus relevant spatial traffic generators and models are important. In future (5G) networks, for which device-to-device (D2D), millimeterwave (mmWave), and small-cell deployments in Heterogeneous Networks (HetNets), are promising technologies, it will become more important to have spatial traffic models which can represent the broad possibilities from completely homogeneous cases (e.g., a deterministic lattice) to extremely heterogeneous cases (e.g., highly clustered scenarios).In this paper, we study the spatial traffic heterogeneity of outdoor users in the denser areas of the city center of Paris, France. The building shape data is freely available from the OpenStreetMaps project. We measure the heterogeneity via a second-order statistic: the Coefficient of Variation (CoV) of two spatial metrics of the resulting point process: the Voronoi cell areas and the Delaunay cell edge lengths. The expected value of the CoV of these metrics allows us to study how the heterogeneity increases with the density of users. Moreover, we find that the statistical distribution of both these metrics is close to Weibull. Our results illustrate that the topology of the buildings in the city imposes a significant degree of heterogeneity on the spatial distribution of the wireless traffic.