# Dependence Between Base Stations Deployment and Traffic Spatial Distribution

Background:

Base stations (BSs) deployment and traffic spatial distribution play crucial roles in network design and resource management. Actually, the BSs deployment and traffic spatial distribution are dually coupled, since BSs are built up to fulfill the traffic demand while data traffic is transmitted to mobile users through BSs. Thus it is imperative to fully understand BSs and traffic spatial distribution as well as statistical relationship between them.

Data Description:

The data used in this paper is obtained from a commercial mobile operator in China. The dataset, collected from two kinds of networks (i.e., 2G and 3G cellular networks), includes traffic and BSs information. The data traffic is measured in the unit of bytes that each BS transmits to the covered users in one-hour interval. BSs information mainly involves geographic location (i.e., longitude, latitude, etc.) and BS type (i.e., macrocell or microcell).  Specifically, we convert the longitude and latitude values of each BS to X, Y coordinates, and plot the actual geographic location on an 2D coordinate plane as shown in Fig. 1 and Fig. 2.

Spatial Distribution of BSs and Traffic:

Considering the real situations that heavy-tailed phenomenon does exist in BSs and traffic spatial distributions, we take α-Stable distribution as the fitting candidate. The parameters of α -Stable model are firstly estimated and the results are listed in Table II. Afterwards, we use the α-Stable model, produced by the aforementioned estimated parameters, to generate some random variable, and compare the induced PDF with the exact (empirical) one. Therefore, as shown in Fig. 3 and Fig. 4, after fitting an α -Stable distribution to BSs density and traffic spatial density in City A , they both better obey the α-Stable distributions obviously . In City B, α -Stable distribution is also applicable.

Linear Dependence Between BSs Density and Traffic Spatial Density:

To ease illustration, Urban1 is taken as an representative example. With the sampling window size being 3*3 km^2, 5*5 km^2, 7*7 km^2, then fitting results are depicted in Fig. 5. Evidently, BSs density and traffic spatial density exhibit strong linearity regardless of the BS type. Besides the visual observation, R- square value is also adopted as a performance metric to evaluate the goodness of fit. The closer is the value to 1, the better is the goodness of fit. According to Table III,  we find that linear regression model is reasonable to characterize the spatial correlation between BSs deployment and traffic spatial distribution, which can be stated as follows:

$${\lambda_{rm{BS}}} = {{k}{\lambda_{rm{TR}}+{t}}}.$$

Here, $${k}$$ is a linear slope value that represents the needed number of BSs per unit spatial traffic.

On one hand, linear regression model keeps better fitting effect no matter the sample region is urban or rural. On the other hand, the key parameter slope k is closely associated with the BS type, without dependence on the sampling window size. These findings indicate that BSs deployment is deeply influenced by the subscribers’s demand as well as the corresponding traffic dynamics over the space, and imply that BSs density and traffic spatial density have almost
identical heterogeneity feature.

Cellular Networks Evolution Trend:

By comparing the fitted parameters in 2G and 3G scenes carefully, we discover that the $${k_{2G,microcell}}$$ is greater than the $${k_{2G,microcell}}$$  regardless of region type. The computed results are listed in Table IV. These experimental results demonstrate that an upgraded BS in 3G own more capacity and higher transmission rate than that in 2G.

Generally, some technological bottlenecks would be inevitable in cellular networks evolution for each generation.Therefore, new and advanced technologies have been explored to solve the confronted problems, thus achieving success in network upgrading and optimization. Particularly, in view of the difference of slope k in various cellular network scenarios, a reasonable assumption can be stated as follows:

$${k_{2G}} > {k_{3G}}>{k_{4G}}.$$

In actual situations, however, with the increase of traffic load, it is impossible for the number of BSs to grow linearly and infinitely, due to the physical and performance constraints of each generation cellular network. Consequently, there should be a certain critical state for each generation cellular network. That is, the available service capability is pre-determined, and if traffic demand increases continuously, the network evolution would go through a network transition (i.e., upgrading from 2G to 3G, then to 4G). In that regard, an explanatory outline about how cellular network architecture evolves is illustrated in Fig. 6.

Whether it is a 2G era, 3G era or 4G era, linear dependence between BSs density and traffic spatial density always exists but with different slope k. Surely, the performance improvement of network expects BSs with larger capacity to supply more traffic demand meanwhile requires operators to implement less BSs to serve more subscribers in certain area.

PDF: On the Dependence Between Base Stations Deployment and Traffic Spatial Distribution in Cellular Networks
• Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, “The Stochastic Geometry Analyses of Cellular Networks with alpha-Stable Self-Similarity,” arxiv.org/abs/1709.05733v1, September 2017. PDF

• Zhifeng Zhao, Meng  Li, Rongpeng Li, and Yifan Zhou, “Temporal-Spatial Distribution Nature of Traffic and Base Stations in Cellular Networks,” IET Communications, August 2017.

• Meng Li, Zhifeng Zhao, Yifan Zhou, Xianfu Chen, and Honggang Zhang, “On the Dependence Between Base Stations Deployment and Traffic Spatial Distribution in Cellular Networks,” 23rd International Conference on Telecommunications, Thessaloniki, Greece, May 2016. PDF