## 5 Cellular Network Analysis
### Temporal Analyses  
In general, a set of observations represents a given state of the network. As for their sampling, neither spatial nor temporal regularities are guaranteed. Thus, no assumption can be made about the state of the network between two measurements involving the same cell, especially if they are not close in time. As an example, it is not possible to establish whether a cell was not visible because it was not operating or simply because no device had made observations in its coverage area. In the following, under the simplifying assumption that the latter hypothesis holds, we outline some useful temporal analyses.  
Figure 16: Administrative areas in the Berlin area: urban (violet and pink polygons) and rural (green polygon) area. Orange polygons represent cell coverage.  
Figure 17: Distribution of microcells in the Berlin area.  
Cell coverage evolution.The presence of both transaction time and valid time dimensions allows us to easily track the evolution of the coverage of a cell over time. The idea is to exploit the transaction time of the involved instances to easily rollback the state of a cell. Figure 18 illustrates the coverage of a cell in the province of Bolzano (Italy) as it changes over time. Specifically, we report the resulting shape as new observations for such a cell are made. At the beginning, the coverage is just a single point, as only one observation is detected in such a cell. Then, the area progressively grows till it reaches the extension of the bright cyan polygon on 2017-03-12 at 08:50:38, i.e., when the last observation of the cell is added to the database. It is worth pointing out how the overall knowledge about the cell dramatically changed over a very short time interval.  
Cellular technology coverage evolution.Let us now turn to another practical scenario where the temporality of the data shows its usefulness: based on the valid time recorded for each instance, we can easily inspect the evolution of the coverage of the UMTS network in Germany at two different time points (2016-03-17 and 2017-03-17), as shown in Figure 19. Note how the coverage increased over time. Similar analyses can extract the evolution of the coverage of several mobile operators considering different technologies. In turn, those data may allow one to detect deficiencies in an operator's network, to compare competitors' coverages, and to build machine learning models able of predicting their future extension.  
Figure 19: Temporal evolution of the UMTS coverage in Germany: measurements were obtained from 2015 to 03-17 to 2016-03-17 (pink color) or 2017-03-17 (brown color). Only serving cells are considered.  
Figure 18: Evolution of the coverage of a cell as new measurements are added to the database over time. A brighter color denotes a more recent state.  
Cell renaming.Here we present the case of an actual cell that has been obtained after a renaming operation, detected thanks to the developed system. In such a case, it may still be useful to investigate how the network arrangement was before the renaming operation. Figure 20 depicts the coverage of a cell in the city of Polokwane (South Africa) as currently stored in the database. Thanks again to the support of valid and transaction times offered by the system, we can easily roll back the renaming operation, showing the previous situation where two cells are visible (red and blue polygons).