# Evaluation of the Use of Compressed Sensing in Data Harvesting for Vehicular Sensor Networks
## 5 Evaluation
### Impact of CS in the Overhead  
We have proved that the improvement of CS-VDH compared with DB-VDG is notable. However, with this comparison, we do not have analyzed the benefits of the CS technology concerning the compression and size of the transmitted packets. For this purpose we have compared three variations of CS-VDH: two of them integrate CS, whereas, in the last one, intermediate nodes simply append their sensed information packet to be forwarded without applying any compression technique. On the other hand, the difference between the both CS variations consists of the two different operation modes, CS with and without accumulation, that we previously commented in Section 4. We refer to the first one as CSPure, to the second one as CSAccum and to the one without CS as NoComp.  
In Figure 12, we measure the amount of sensed values that nodes can carry in these operation modes without taking into account the packet size.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Density** & **DBVDG-sbss** & **DBVDG-dbss** & **CS-VDH-NOCS** & **CS-VDH-CS** \\ \hline
50 & 563,728.4 & 514,996.4 & 735.7 & 513.9 \\ \hline
45 & 712,439.3 & 592,476.4 & 274.5 & 243.7 \\ \hline
40 & 882,573.4 & 685,165.7 & 840.7 & 669.4 \\ \hline
35 & 786,394.4 & 597,975.6 & 2390.6 & 2080.1 \\ \hline
30 & 1,007,816.0 & 803,683.1 & 2261.3 & 2022.6 \\ \hline
25 & 1,127,205.2 & 878,429.9 & 2216.6 & 1924.2 \\ \hline
20 & 1,114,846.7 & 905,167.5 & 3239.5 & 2725.2 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Control overhead (total num. of generated messages) of both proposals.  
We consider the NoComp option the best possible solution in terms of the number of delivered packets due to its straightforward operation mode because new information is appended directly into the packet in case it does not exist.  
Regarding the compression variants, both CSPure and CSAccum take more time to comprise the information, being CSAccum the one with the most complex operation mode. Although by CSAccum, a node can insert more sensed values at once. The compatibility problem penalizes its performance. Despite that, its performance in terms of carried values is also good.  
In light of this graph, the NoComp approach can be considered as the ideal method, because it is the one which can carry more sensed values, improving the other CS options by 1 or 1.5 more carried values. Nevertheless, we still have not considered the overhead introduced in the whole network. Figure 13 compares this metric among the different options with respect to different vehicle densities. This way, now we are measuring the number of packets traversing the network.  
As we can see, the benefits of CS concerning the overhead are more notable as the density of vehicles increases. The reason for this is that under lowly dense scenarios, for a distant node, the probability of finding a way to reach the FC is low. So, since the timers of nodes close to the FC will expire with high probability, this reduces the possibility of combining data in CS. Thus, the performance is similar to the NoComp approach.  
On the other hand, in dense scenarios like 1/15, 1/10, and 1/5 \(veh/sec/route\), the results are different. Nodes communicate more frequently, i.e., the likelihood of finding promising nodes that can forward data packets to the FC before their delay timers expire is higher. Therefore, they are more likely to combine their information and thereby to reduce the network overload.  
Besides, overhead increases as the density does. This trend is less stronger in both CS strategies with a maximum overhead of about 12,000 messages for the highest density, whereas in the strategy without compression, the curve is more marked, reaching nearly 18,000 messages in the same scenario. This trend, therefore, confirms the better scalability of our approach in terms of control overhead.  
Figure 12: Number of sensed measurements carried in packets for CSAccum and CSPure for maximum time (TMAX) = 20 s. Density in x-axis corresponds to the name given to that density in Table 6.