## 5 Numerical Simulation
In addition, the signal strength of our work is always than that of the control group, because the fiber link in the control group is ideal. In Figures 4 and 5, the hop number of wireless communication is 1. The distance from ONUs to OLTs is 10 km. The distance from OLTs to the Internet is 70 km. In Figure 4, the maximum available data-computing speed of OLTs and the Internet are both 1.6 GHz. The data-computing speed of servers at the place of ONU varies from 0.2 GHz to 3.2 GHz. In Figure 5, the maximum available data-computing speed of ONUs and the Internet are both 1.6 GHz. The data-computing speed of servers at the place of OLT varies from 0.2 GHz to 3.2 GHz. To show the difference between MEC-1 offloading and MEC-2 offloading, the total latency of all tasks was selected as an indicator. This is in accordance with Equation (17). In Figure 5, the total latency of our work is always smaller than that of the control group. The wireless sub-network is established upon multi-hop links. Through multiple hops, a user/human/machine can choose the most suitable path to the server via its nearest ONU or sub-nearest ONU. Meanwhile, for the control group, there is only one choice, i.e., the connected ONU. With the increase in the data-computing speed of servers at the place of ONU, the total latency decreases. When the data-computing speed increases from 0.2 to 1.0, the total latency decreases sharply. When the data-computing speed increases from 1.0 to 3.2, the total latency slightly decreases. In Figure 6, the total latency of our work has a crossover point with that of the control group: The data-computing speed of servers at the place of OLT is 1.6 GHz when two lines cross. The reason for this is that MEC-2 offload can provide a trade-off between shorting paths and increasing offloading locations. Before this point (\(\leq\)1.6), the total latency of our work is larger than that of the control group. After this point (\(\geq\)1.6), the total latency of our work is smaller than that of the control group. In addition, whether our work or the control group, the total latency decreases with the increase in data-computing speed. Combining Figures 5 and 6, the MEC-2 offloading may be more capable of MEC-1 offloading with the parameters we set in this simulation. In the control group, the service is modeled as a uniformly generated computing task in the range of [5; 30] Mobits. However, in the real production environment, the tactile internet service, such as remote robots, lasts for a long-term period with a relatively stable data rate. The amount of data in the tactile internet service is greater than that of the traditional service, due to the existence of high-definition picture or video transmissions. The same situation exists for the data transmission rate of tactile internet services. Each tactile service is seen as a long-lasting data stream with a uniformly distributed data rate in the range of [200, 500] Mbit/s. Figure 5: The total latency with MEC-1 offloading. The latency with different tactile services is shown in Figure 7. According to the 802.11 protocol cluster, the hop number in a wireless mesh network cannot be greater than 16. To demonstrate the variation in the latencies of multiple hop numbers, [1; 7; 15] hops were selected. The distance of each hop is 200 m. The distance between ONUs and OLT is 15 km. The distance between OLT and the Internet is 50 km. With the growth in the data rate of each tactile service, the latencies of different situations always increases. The control group has the largest values. The larger the hop number, the greater the latency of our work. The multiple hops in the wireless mesh network form a complex network with redundant paths. The existence of communication among ONUs makes the data transmission path short, from user-ONU-OLT-ONU-user to user-ONU-another ONU-user. This is the reason that the latency of our work with 1 hop is still smaller than that of the control group. The capacity of our work is shown in Figure 8. The network between ONUs and OLT is WDM-based.