# Value of Information Based Data Retrieval in UWSNs
## 5 Performance Measures, Simulation Setup and Results
### Results
#### 5.3.1 Valuation Ratio  
The first thing that we investigate is the valuation ratio. The valuation ratio is the ratio between the valuation of information of a high-priority event versus valuation of information of a low-priority event at \(t=\tau_{0}\), i.e., the ratio \(A_{H}/A_{L}\). In hindsight of the results for \(N_{HS}=0\), we found that if the VoI profile in a UWSN is similar or homogeneous, i.e., all the sensor nodes have almost a similar amount of VoI to offer, then a shortest path algorithm proved quite effective. This effectiveness is a result of distance minimization which results in minimization of time, and this time minimization helps to lock-in decaying VoI profiles at the earliest. However, so should be the case if \(A_{H}\approx A_{L}\), because, even though there are hot-spots, yet the VoI profile of the system is as if \(N_{HS}=0\). In such a case, there would be no real advantage of using a greedy planner. Therefore, there should be a particular range after which we can observe a performance gain for the greedy planners as compared to the shortest path planners. In this experiment, we determine the effective performance range for the lawn-mower, greedy and hybrid algorithms. The results for \(\Upsilon_{Acc}^{n}\) and \(\Upsilon_{L}^{n}\) versus \(A_{H}/A_{L}\) are shown in Figure 3. The superscript \(n\) implies that the results have been normalized with respect to RPP.  
\[\Upsilon_{Acc}^{n}=\frac{\Upsilon_{Acc}^{PP}}{\Upsilon_{Acc}^{RPP}}\,\Upsilon_{L}^{n}=\frac{ \Upsilon_{L}^{PP}}{\Upsilon_{L}^{RPP}} \tag{29}\]  
In Figure 3, the left two graphs are for the range \(A_{H}/A_{L}=[10^{0}\):\(10^{9}]\). The right two graphs are a magnification of the results between the range \(A_{H}/A_{L}=[10^{4}\):\(10^{5}]\). Also, the top two graphs are for \(\Upsilon_{Acc}^{n}\) (colored in tones of blue), while the bottom two graphs are for \(\Upsilon_{L}^{n}\) (colored in tones of red). We can observe that LPP performs better early on but once the ratio \(A_{H}/A_{L}\) becomes considerably large, the greedy algorithms start giving better performance. It is somewhere between a valuation ratio of \(10^{3}\) and \(10^{4}\) units that LPP loses its top spot on performance. At \(10^{4}\) GIPP, HPP, and HIPP start performing better. While at \(10^{5}\) GPP also starts performing better than LPP. LPP clearly performs best up to \(10^{3}\), while afterward, the greedy or hybrid algorithms start performing better. If we magnify the range between \(A_{H}/A_{L}=[10^{4}\):\(10^{5}]\), we find that the switch in performance takes place at \(A_{H}/A_{L}=3\times 10^{4}\).  
It is based on these results that we use a setting of \(A_{H}/A_{L}=5\times 10^{4}\) for the rest of this paper. This is a reasonable number for practical situations as e.g., it may imply a $1 versus $50,000 valuation. However, it is to note that the hybrid or intermediate node visitation algorithms perform better as early as a fiscal value of $10,000; as suggested by the performance improvement at \(A_{H}/A_{L}=10^{4}\).  
Figure 3.— The top two graphs (colored in blue) are for Y\({}_{Ac}\) while the bottom two are for Y\({}_{L}\) while the graphs on the left are for the valuation ratio range \([10^{6}\):\(10^{6}]\) while the graphs on the right are a magnification between \([10^{4}\):\(10^{5}]\): (a) The top-left graph is for Y\({}_{Ac}^{\prime}\) which is charted in the range \([10^{7}\):\(10^{6}]\): (b) The top-right graph is for Y\({}_{Ac}^{\prime}\) which is charted in the range \([10^{4}\):\(10^{5}]\): (c) The bottom-left graph is for Y\({}_{L}^{\prime}\) which is charted in the range \([10^{6}\):\(10^{7}]\): (d) The bottom-right graph is for Y\({}_{L}^{\prime}\) which is charted in the range \([10^{6}\):\(10^{8}]\).