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 non-parameterized, 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).
In @cite_51 , , presented an algorithm to create a random inhomogeneous node distribution based on a neighborhood-dependent thinning approach in a homogeneous PPP. The model, however, can not be used for generating BS-correlated UE patterns, as this is beyond the scope of that model.
@cite_51
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Most analysis and simulation of wireless systems assumes that the nodes are randomly located, sampled from a uniform distribution. Although in many real-world scenarios the nodes are non-uniformly distributed, the research community lacks a common approach to generate such inhomogeneities. This paper intends to go a step in this direction. We present an algorithm to create a random inhomogeneous node distribution based on a simple neighborhood-dependent thinning of a homogeneous Poisson process. We derive some useful stochastic properties of the resulting distribution (in particular the probability density of the nearest neighbor distance) and offer a reference implementation. Our goal is to enable fellow researchers to easily use inhomogeneous distributions with well-defined stochastic properties.