# Performance Analysis of Time Synchronization Protocols in Wireless Sensor Networks
## 6 Conclusions  
In this paper, we presented a performance analysis of time synchronization protocols under the effects of different factors, such as message delay jitter, synchronization period, network topology, and packet loss. From the simulation, our conclusions are as follows:  
* Message delay jitter can be considered to be the primary factor affecting the performance of time synchronization protocols. In particular, it causes fluctuations in the clock skew through multi-hop flooding and reduces the accuracy of FTSP significantly. An extended version of FTSP (E-FTSP) was proposed to reduce the effect of message delay jitter and it demonstrated outstanding performance compared to FTSP and GTSP, especially in a large-scale network.
* Regarding network topology, the position of the reference node affects the convergence time and synchronization error of FTSP and E-FTSP. In detail, the hop distance from the farthest node(s) should be as small as possible to achieve a high performance in FTSP and E-FTSP. Meanwhile, the distribution of nodes, especially the number of links between nodes in the network, affects the convergence time of GTSP. In detail, the convergence speed of GTSP increases with the number of links. In a small-scale network, there is no significant difference between the aforementioned protocols in term of synchronization error and convergence time. However, in a large-scale multi-hop network, FTSP has huge synchronization error, and GTSP has very slow convergence time. Meanwhile, E-FTSP provides more accurate and faster time synchronization regardless of network scale.
* Changing the synchronization period (interval) does not reduce the synchronization errors of FTSP and GTSP. A short synchronization period slightly increases the synchronization error in FTSP. Interestingly, a short synchronization period reduces the number of rounds required to achieve convergence in GTSP. Time synchronization protocols require short intervals for fast synchronization and long intervals to save energy. Therefore, adaptive synchronization protocols should be further investigated.
* Packet loss clearly increases the convergence times and the synchronization errors of FTSP and GTSP. However, the network still achieves a synchronized status even when approximately one third of packets are lost. This proves the robustness of FTSP, GTSP, and E-FTSP.  
Apart from accuracy, convergence speed, robustness, and scalability, other attributes of a time synchronization protocol, such as energy efficiency and time complexity of algorithms, also need to be evaluated before implementing them in a real system. Thus, it is expected that studies on these attributes will improve the feasibility of real systems.  
Figure 14: (a) Number or rounds required to synchronize entire network for different packet loss ratios. (b) Network synchronization error of each protocol with different packet loss ratios.  
In our simulation, we did not evaluate the performance of FTSP and GTSP is mobile and the fast drifting environments. The mobility of the nodes in an ad-hoc network may generate unexpected results and problems. Although it has been claimed that FTSP and GTSP can operate well under dynamic topology changes, it is important to evaluate the performance of time synchronization protocols in a dynamic environment. These evaluations will be performed in future works. We believe that this study furthers our understanding of the performance of time synchronization protocols in real networks. Moreover, this work provides insights into the optimization of time synchronization protocols.  
Conceptualization, L.-A.P. and T.K. ([PERSON]); Software, L.-A.P.; Writing - Original Draft Preparation, L.-A.P.; Review & Editing, T.K. ([PERSON]) and T.K. ([PERSON]); Supervision, T.K. ([PERSON]) and T.K. ([PERSON]); Funding Acquisition, J.L. and J.-H.H.  
This work has been supported by the Small-scale Mobile Ad-hoc Network with Bio-networking Technology project of the Agency for Defense Development (UD170094 ED).  
The authors declare no conflicts of interest.