# A New Lightweight Watchdog-Based Algorithm for Detecting Sybil Nodes in Mobile WSNs
## 5 Simulation Results and Performance Evaluation
### Simulation Results
#### 5.3.2 Comparison  
In this section, we compare our algorithm with two methods in [24; 25] in terms of TDR and FDR. These works are chosen due to the similarities in the adopted attack models and approach.  
* **Comparison 1:** To compare our algorithm with PASID, we have to set the simulation parameters as per [24]. Therefore, in this part, we assume \(M=1\), \(max\ speed=0.2\) m/s, _wireless radio range_\(=10\) m, and the results are calculated at _movement step_\(=200\). Figure 12 illustrates TDR and FDR for PASID and our algorithm against the network size (herein called topography size as in [24]). To be consistent with results in [24], each point of the new proposed algorithm's results is an average over 240 combinations of \(N=5,10,25,40\), and \(S=5,10,20\), and \(W=\lfloor N/2\rfloor\) where the latter corresponds to the best case result reported in [24]. The results of PASID are extracted from [24]. The new algorithm performs better than PASID in terms of FDR for all network sizes. In terms of TDR, the new algorithm has a significant edge over PASID in large networks while slightly under-performing it in smaller ones.
* **Comparison 2:** In this test we compare our algorithm with another relevant algorithm in [25]. Our algorithm uses a somewhat similar information collection strategy as in [25] while using a completely different detection rule. To make our results comparable, we adopt the same values for our simulation parameters as those in [25].  
Figure 13 compares TDR and FDR variations versus time for different number of Sybil IDs. It should be noted that [25] provides the results just for a limited number of movement steps (time period) and no confidence interval consideration. Figure 13a suggests that initially TDR and its improvement rate in [25] is better than our algorithm. However, at some point our algorithm not only catches up but also starts out-performing [25]. Both algorithms expectedly show slightly  
better performance by increasing the number of Sybil IDs per malicious node (S). Regarding FDR, our algorithm starts significantly better and the difference in performance vanishes through time. Consistent with its definition, FDR in Figure 12(b) shows no sensitivity to variation of \(S\). The FDR of our algorithm is initially much better than the FDR of the algorithm in [25]. However, both algorithms perform asymptotically perfect in the long term. Time variations of TDR and FDR with varying malicious node population for both algorithms are illustrated in Figure 14. We observe almost the same trends as in Figure 13 with the following particularities. TDR in [25] seems to decline after some time as opposed to the new algorithm wherein TDR keeps improving constantly. Moreover, only TDR in the new algorithm and only FDR in the algorithm of [25] show sensitivity to the malicious node population in the transient state. To sum up:  
* Regarding TDR, although the detection process is slightly late in picking up due to its conservative approach (Equation (2) in step V) to somewhat compensate for erroneous receptions, it performs reliably and asymptotically better.
* Introducing the trap state (01/10) in the state diagram of Figure 13 and applying the detection rule of Equation (4) in step V result in an adequate FDR even in short term.  
Figure 12: Performance comparison of PASID and our new proposed method in terms of TDR (**a**) and FDR (**b**) versus the topography.  
Figure 13: Performance comparison of [25] and our new proposed method in terms of TDR (**a**) and FDR (**b**) versus number of movement steps for varying number of Sybil IDs.  
Finally, we would like to point out that the diagrams representing variations of TDR and FDR versus the number of normal nodes in Figure 10 of [25] are not usable for comparison purposes.