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).
Understanding and solving performance-related issues of current and future (5G+) networks requires the availability of realistic, yet simple and manageable, traffic models which capture and regenerate various properties of real traffic with sufficient accuracy and minimum number of parameters. Traffic in wireless cellular networks must be modeled in the space domain as well as the time domain. Modeling traffic in the time domain has been investigated well. However, for modeling the User Equipment (UE) distribution in the space domain, either the unrealistic uniform Poisson model, or some non-adjustable model, or specifc data from operators, is commonly used. In this paper, stochastic geometry is used to explain the similarities of traffic modeling in the time domain and the space domain. It is shown that traffic modeling in the time domain is a special one-dimensional case of traffic modeling in the space domain. Unified and non-parameterized metrics for characterizing the heterogeneity of traffic in the time domain and the space domain are proposed and their equivalence to the inter-arrival time, a well accepted metric in the time domain, is demonstrated. Coefficient of Variation (CoV), the normalized second-order statistic, is suggested as an appropriate statistical property of traffic to be measured. Simulation results show that the proposed metrics capture the properties of traffic more accurately than the existing metrics. Finally, the performance of LTE networks under modeled traffic using the new metrics is illustrated. Future generation (5G and beyond) cellular networks have to deal not only with an extreme traffic demand increase, but also an extreme level of heterogeneity in the distribution of that demand in both space and time. Traffic modeling in the time domain has been investigated well in the literature. In the space domain, however, there is a lack of statistical models for the heterogeneous User Equipment (UE) distribution beyond the classical Poisson Point Process (PPP) model. In this paper, we introduce a methodology for the generation and analysis of spatial traffic which allows statistical adjustments. Only two parameters, namely, Coefficient of Variation (CoV) and Correlation Coefficient, are adjusted to control the UE distribution heterogeneity and correlation with Base Stations (BSs). The methodology is applied to cellular networks to show the impact of heterogeneous network geometry on network performance.