## 3 Results and Discussion
### Simulations for Chain-Based Network
#### 3.1.5 Network Latency  
Using Equations (20) and (21), network latency of chain-based networks that separately uses AVG, EBDKF, and proposed statistical information fusion methods can be calculated. It can be assumed that for networks with proposed method and AVG that \(t_{qu}=0\) as there is always only one frame/packet waiting to be served. However, in EBDKF, there can be multiple frames/packets waiting to be served so that frame/packet waiting time has to be considered and we assume \(t_{qu}=0.1\) ms We substitute \(R=20\) kbps for Zig Bee, \(R=384\) kbps for WCDMA, \(l_{i}=50\) m for Zig Bee, \(l_{i}=5000\) m for WCDMA, \(c=3\times 10^{8}\) ms\({}^{-1}\) and \(P~{}=~{}20\)_bytes_ for Zig Bee (1 byte payload, 19 bytes for data link layer header and trailer), \(P~{}=~{}41\)_bytes_ for WCDMA (1 byte for payload, 40 bytes for TCP/IP header). \(K\) is set to 3,  
Figure 11: Network lifetime comparison with the proposed statistical, EBDKF and AVG information fusion methods when BER = 0.05 in a chain-based IoT platform.  
1 and 0 for AVG, EBDKF and proposed fusion methods respectively to achieve similar MSE values (close to 0.3). Fusion times (\(t_{fu}\)) are obtained from Table 2. Table 3 summarizes the network latency values calculated in this manner.  
As proved by the results in Table 3, when the proposed statistical method or AVG method is employed, the network latency is low when N low. However, on the other hand, EBDKF maintains a constant network latency independent of N. It can be shown that using results in Table 3 that AVG method and proposed method exceed the latency of EBDKF when N is greater than or equal to 5 and 14, respectively. Further, we can observe that the network latency of Average method is always almost 4 times that of that of proposed method in order to achieve similar accuracy.  
When obtaining the results in Table 2, we assumed that inter-node link length is constant. As the proposed method is targeted to be employed in HANs and FANs, we expect the total length of the chain to be less than 500 m and 500 km for HANs and FANs, respectively. Therefore, the value of N will be restricted to 11 nodes and 101 nodes respectively for HANs and FANs as \(l_{i}\) is 50 m and 5 km for Zig Bee used in HAN and WCDMA used in FAN. Therefore, the proposed method will have the lowest latency in a HAN so it is highly suitable to be used in a HAN compared to other two fusion methods standing tall in terms of network latency. For a HAN, EBDKF will have the highest latency when N is less than 5. When N is greater than 5, the AVG method will have the highest latency for a HAN using Zig Bee. When considering about FANs, the proposed method will maintain its dominance in terms of lowest latency until N is 14; but, after that, the latency of EBDKF becomes the lowest as the total length of the link exceeds 70 km. When considering about the Maximum tolerable latency of 300 ms for the SG applications intended in this context, the proposed method and diffusion technique will not violate the latency requirement for both HANs and FANs. That is because the proposed method will require at least 39 and 174 nodes for HANs and FANs, respectively, which are way above the limitations we assumed for N considering physical length of links for those networks. However, for the AVG method, it will require at least 11 nodes and 45 nodes to violate the latency requirement. Therefore, the AVG method will fail latency requirement in HAN by a small margin when N is 11 and it will also fail when the total length of the link in a FAN is high (exceeds 225 km in this case).