# Value of Information Based Data Retrieval in UWSNs
## 5 Performance Measures, Simulation Setup and Results
### Results
#### 5.3.4. Scalability with an Increase in Hot-Spots  
In the context of this discussion, a hot-spot is an anomalous event of probably catastrophic proportions and needs to be taken care of as quickly as possible. Such an anomalous event should be a rare occurrence and it would be a bit unlikely to find more than a few at the same time. However, then it can also be argued that the whole system is compromised if such a situation can arise. However, this scalability study is based on this hypothetical assumption that there might be a drastic increase in the number of hot-spots. Our goal is to see how the path planners behave when we vary the number of hot-spots (\(N_{HS}\)) across the range of nodes.  
The results are shown in Figure 7. The results are shown as heat-maps. Darker color tones imply better comparative performance in the heat-maps. We start from 5 hot-spots and ramp up to 95 hot-spots. We record percentage improvement in VoI accumulated (Y\({}_{ACC}\)% \(\uparrow\)), percentage reduction in VoI lost (Y\({}_{L}\)% \(\downarrow\)), percentage reduction in tour time (\(T_{Tour}\)% \(\downarrow\)) and a normalized measure of efficiency (\(\dfrac{\Omega_{PP}}{\Omega_{RPP}}\)). The percentages are calculated with respect to the RPP path planner performance:  
\[\text{Y}_{ACC}\text{\textasciitifontsize{\%}}\uparrow =\dfrac{\text{Y}_{ACC}}{\text{Y}_{ACC}^{RPP}}\times 100 \tag{30}\] \[\text{Y}_{L}\text{\textasciitifontsize{\%}}\downarrow =\dfrac{\text{Y}_{L}}{\text{Y}_{L}^{RPP}}\times 100\] (31) \[T_{Tour}\text{\textasciitifontsize{\%}}\downarrow =\dfrac{T_{Tour}}{T_{Tour}^{RPP}}\times 100\] (32) \[\dfrac{\Omega_{PP}}{\Omega_{RPP}} =\dfrac{\text{Y}_{L}^{RPP}\times T_{Tour}^{RPP}}{\text{Y}_{L} \times T_{Tour}} \tag{33}\]  
The first results we discuss are Y\({}_{ACC}\) and Y\({}_{L}\). As the number of hot-spots increase, the performance of HPP and LPP decreases drastically. GIPP and HIPP also experience a degradation in performance but the change is not that drastic. The performance of LPP remains the same at average. The reason for this is that an increase in hot-spots results in a map that is increasingly homogeneous in terms of VoI. When there are no hot-spots, there is a homogeneity in terms of VoI in the sensor map. In such a case, as discussed earlier, LPP performs best. With one and up till a few hot-spots, greedy path-planners perform better. However, at a certain tipping point in terms of \(N_{HS}\), the performance falls below than that of LPP. With a large \(N_{HS}\), the sensor map is similar to one with no hot-spots. This explains the better performance of LPP in such a scenario.  
In terms of \(T_{Tour}\), there is no effect in the performance of LPP, GPP or GIPP with an increase in \(N_{HS}\). However, the performance of HPP deteriorates to the level of GPP eventually and HIPP degrades to GIPP. The reason lies in the algorithmic construction of the hybrid path planners. They are designed in such a way that they switch to LPP once all the hot-spots have been visited. The time performance of hybrid algorithms is good because they incorporate LPP. Therefore, if there is a large \(N_{HS}\), there will be a lesser involvement of LPP in the path-planning process and this leads to an increase in the \(T_{tour}\) for hybrid path-planners.  
The measure of efficiency, normalized to RPP, has a very high value for hybrid algorithms at 5 hot-spots. However, onward 15 hot-spots, we see a very sharp decline in this performance measure. LPP is not affected in this regard. The reason is that \(\Omega\) depends upon Y\({}_{L}\) and \(T_{tour}\) and LPP is not affected in both regards by an increase in \(N_{HS}\).