## 5 Performance Analysis of Proposed Schemes: MRS-ST-BL and MRS-SD-BL
### Results
#### 5.3.2 Comparison of Average Number of Probes of Proposed Schemes with Others  
This section presents the comparison of average number of probes of our proposed MRS-ST-BL and MRS-SD-BL schemes with various relay selection schemes. The analysis is done for different social trust scenarios and different node densities. The key result from our analysis is that our proposed schemes probe less number of devices for selection of a relay compared to existing schemes. As a result, our proposed schemes significantly minimize total time spent for probing, which contributes for the enhancement of throughput in D2D communications. Figure 7 illustrates the average number of probes comparison of various schemes for different social trust scenarios in square network having width of 100 m. The average number of probes is on the y-axis and radius of search ring is on the x-axis in each of the graphs. Each of the schemes analyzed are represented by a line. Figure 7a shows that the average number of probes of MRS-ST-FB (blue line with squares) and MRS-ST-WFB (blue line with triangles) increase with the increase in search radius. From the observation, we can see that MRS-ST-FB and MRS-ST-WFB probe equally with the change in search radius. However, the our proposed scheme MRS-ST-BL (blue line with crosses) has less number of probes compared to MRS-ST-FB and MRS-ST-WFB. This is because MRS-ST-BL only probe those devices having battery level above battery threshold, from the list of devices in circular region that have social trust above social threshold. The reduction in probe number compared to MRS-ST-FB and MRS-ST-WFB contributes to increase throughput. However, the increment is not significant because  
Figure 7: Average probe number comparison of various schemes in different social trust scenarios  
this is a scenario where social trust among users in the network are very weak. Similar trend is observed when compared between HRS-FB (red line with squares), HRS-WFB (red line with triangles) and HRS-BL (red line with crosses). Figure fig:Average number of probes of different schemes NW100 mb depicts that the average number of probes of MRS-ST-BL (blue line with crosses) is less than that of MRS-ST-FB (blue line with squares) and MRS-ST-WFB (blue line with triangles). The difference in number of probes initially increases with the increase in search radius. This is because, with the increase in search radius more devices (within probe limit) are probed in MRS-ST-FB and MRS-ST-WFB. However, in case of MRS-ST-BL, it filters out the devices with battery less than battery threshold. When the search radius is further increased, the blue lines tend to converse as more devices are probed (up to probe limit) for MRS-ST-FB, MRS-ST-WFB and MRS-ST-BL. As there is no probe limit in HRS-FB, HRS-WFB and HRS-FB, these schemes probe more devices with the increase in search radius. MRS-SD-FB, MRS-SD-WFB and MRS-SD-BL probe least among all others because these schemes filter at most \(l\) (probe limit) devices which are nearest to the midpoint before filtering devices that have social trust above social threshold. This is a scenario when social trust among users in the network are weak. Therefore, less number of devices are probed, which helps to increase the throughput of D2D communications. Figure fig:Average number of probes of different schemes NW100 mc shows that the average number of probes for MRS-ST-FB, MRS-ST-WFB, MRS-ST-BL, MRS-SD-FB, MRS-SD-WFB and MRS-SD-BL are indifferent and have number of probes equal to probe limit, with the increase in search radius. This is because the social trust among the users in the network are high, all having social trust above social threshold. However, HRS-FB and HRS-WFB probe more devices compared to HRS-BL. The number of probes for HRS-FB, HRS-WFB and HRS-BL are significantly higher compared to our proposed schemes. Therefore, our proposed schemes have significantly higher throughput compared to HRS-FB, HRS-WFB and HRS-BL.