## 4 Result and Discussion
### Latency Characterization  
In haptic communication, QoS parameters are characterized by E2E delay, reliability, and synchronization [34]. The latency requirements for Tactile Internet applications depend on the type of application and dynamics of the remote environment. Some applications such as serious games (tele-soccer) demand latency value \(\leq\)10 ms and virtual reality-based teletherapy for phobia treatment E2E delay latency requirements (50 ms) with the packet failure rate (\(10^{-3}\)-\(10^{-7}\)). The latency and packet loss rate deeply impact QoE and the quality of task for haptic-driven applications. The work in [35] presents the role of the Tactile Internet in industrial applications. The authors explored the emerging tactile industrial services and compared their QoS requirements with conventional industrial applications. For example, remote control industrial applications including, process automation, monitoring, maintenance, and fault reporting demand cycle time (\(\leq\)50 ms), data rate (1\(\sim\)100 Mbps), latency (\(\leq\)50 ms) with packet loss rate around \(\leq\)\(10^{-7}\). Characterization of the latency for teleoperation systems is vital because it helps to provision QoS and QoE. Figure 7 depicts the analysis of the teleoperation system in terms of the E2E delay. To investigate the effect of network congestion with no external host and with multiple external hosts during haptic communication among the master and the slave, a simple haptic-enabled teleoperation system is developed and simulated for the number of external hosts = 1 to 20. The latency investigation with direct haptic communication without the external host, with the number of hosts = 10, 15, 20 is illustrated in Figure 7b-d, respectively. The analysis clearly shows that the trend with the increasing number of hosts increases the round trip time that a packet experiences from an average of 3.4 to 1159 ms. In Figure 7a, the direct haptic communication without an external host between master and slave, the packet latency is between 1 to 3.4 ms as compared to Figure 7c,d, where the average latency values are between 23 to 1159 ms. To demonstrate this latency analysis in-depth, Figure 8a-d depicts the histogram of the packet latencies. This analysis reveals the E2E delays of the haptic data traffic due to network load that induced congestion. Similar to Figure 7a-d, the result in Figure 8a-d indicates that the increase in the number of external  
Figure 7: Packet latency investigations for 3 Dof haptic data transmission; (**a**) master and slave direct communication (no external host are involved), (**b**) External Host = 10, (**c**) External Host = 15, (**d**) External Host = 20.  
host network experience congestion and lead the system to unstable and degrade the application performance. Figure 8a, indicates that most of the latency of the packet lies under 2 to 3 ms, and the frequency of the number of the packet under 4 ms is more than 95%. From Figure 8b-d, it can be clearly seen the latencies of the haptic traffic increase. In Figure 8b, most of the latency of the haptic packets centered between 20 to 60 ms, for Figure 8c it is between 600-1000 ms with an average of 849 ms and Figure 8d it is centered around 800 to 1500 ms with an average of 1159 ms. The packet interarrival times of teleoperation traces are also investigated and illustrated in Figure 9. The control signals as defined in the 3 DoF teleoperation dataset are transmitted as a packet to the slave and the slave backward the haptic force feedback in response. The packet interarrival times are calculated as follows:  
\[I_{i}^{c}=T_{i}^{c}-T_{i-1}^{c}, \tag{4}\]  
where \(c\) refers to the control signals, \(i\) is the sample that is transmitted, and \(T\) indicates the time instantly. In simple, it can be written the interarrival time of the packet \(I_{i}^{c}\) is the difference between the current sample \(i\) at the time instant \(T_{i}^{c}\) and the previously transmitted signals at \(T_{i-1}^{c}\).