# Optimizing the Quality of Service of Mobile Broadband Networks for a Dense Urban Environment
## 4 Results and Discussions
### The Measure of Data Distribution
#### 4.3.2 Probability Density  
Equally important is the consistency in our measured data. Say an optimal RSRP, RSSI, and throughput value are found. What would be the probability of finding these values in the area where this experiment was conducted? Figures 14-19 present the normalized probability distribution function of the measured data. The probability of obtaining specific metrics values is also presented, and a normalized curve is used to show the congruence of the data. Figure 14 is the probability density function of the RSRP values for the three locations. Figure 15 highlights how the RSRQ values are distributed, with Oniru VI showing higher chances (about 0.9 pdf value) of obtaining the \(-7\) dB to \(-9\) dB range. Measured in decibels, the most probable RSSI values obtainable in the three locations can be seen in Figure 16. Figure 17 shows a probability density function (pdf) of the ratio of the packet component carrier (PCC) to the signal-to-noise ratio (SINR) for two locations. In terms of download speeds, Figures 18 and 19 show the most probable download speeds over the network at the three locations using the physical and logical links, respectively.  
Figure 14: Probability density function of the reference signal received power (RSRP).  
Figure 16: Probability density function of the received signal strength indicator (RSSI).  
Figure 15: Probability density function of the reference signal received quality (RSRQ).  
Figure 17: Probability density function of the ratio of the packet component carrier (PCC) to the signal-to-noise ratio (SINR).  
Figure 18: Probability density function of the packet component carrier (PCC) physical (PHY) downlink (DL) throughput.  
In line with the deductions from the histograms in Figures 8-14, the PDF graphs and curves provide more detailed information on the likelihood of sustaining various values for the different metrics considered. As expected, we observe that certain value ranges are more readily available, with corresponding higher probabilities of being obtained in the sample space (environment). For example, the PDF curve for RSRP in Unilag assumes an almost bimodal shape with two peaks, indicating that the data record a pattern where two ranges of values are more likely to be obtained in the environment. This confirms existing literature that wireless network parameters are not evenly distributed and may occur in clusters [44; 45; 46; 47; 48]. Although a similar graph is seen in the RSRP curve for Ikorodu, there is a significant disparity between the modal values. Additionally, it is important to note that the three graphs are skewed to the right, with fewer outliers found in the Oniru VI graph.  
However, the graph in Figure 15 is similar to a bell-shaped curve slightly tilted to the right, which is expected of real-world data. Describing the RSRQ values for the three locations, we can observe that the curve forms a kurtosis greater than three with heavy tails, especially in Ikorodu. This confirms that we have a normal distribution, even if the graph is slightly skewed to the right. The PDF functions for the PCC DL and the PDCP DL are almost identical in each case. This may indicate that the MNO has made efforts to provide hardware that can sustain similar physical and logical download speeds.