# Task Migration with Partitioning for Load Balancing in Collaborative Edge Computing
## 4 Simulation Results and Discussion  
In this section, we verify the performance of the proposed method compared with other methods. It is assumed that the MEC system is deployed in a clustered area grouped by the units of administrative districts in the urban environments where MECSs are densely deployed and vehicles are not driving at high speed. We randomly distributed 10 MECSs within a MEC system. The capacity of each MECS was 10 GHz. Vehicles were distributed in a Poisson distribution on the road. All vehicles had mobility within a random walk model in an area of 1000 m \(\times\) 1000 m using the SUMO simulator [25]. The input size of the task followed a random distribution with 2-10 Kbits. The task graph used in the simulation was randomly generated, where the workload of each subtask followed a random distribution with 0.1-0.2 Gcycles. The mobility speed of the vehicle also followed a random distribution of 1-30 m/s. The parameters used in the simulation are summarized in Table 1 according to [26; 27; 28]. The path loss between the RSU and vehicle was modeled as \(128.1+37.6\log_{10}(distance(\text{km}))\). When vehicles offloaded their tasks simultaneously, the vehicles performed data transmission in different spectral bands via orthogonal frequency-division multiple access technology, and there was mutual interference among different subcarrier allocations. To demonstrate the reason for using task partition and migration in our method, we compared the _Proposed_ method with _No partition_ and _No migration_ strategies. The _Proposed_ method uses both task partitioning and migration. The _No partition_ method migrates an entire task without any task partitioning to the target MECS, and the _No migration_ method executes a task on the MECS in which the vehicle's task is offloaded without any task migration. The load variance among the MECSs is shown in Figure 4. It shows the load variance of each time slot when the vehicle arrival rates were 0.3, 0.6 and 0.9. In other words, it is an indicator of the distribution of the load among MECSs during the simulation. In the _Proposed_ method, the set of task subtasks in an overloaded MECS was migrated to underloaded MECSs. Under _No partition_ method, the all tasks in the overloaded MECSs were migrated to the underloaded MECS. Thus, the _Proposed_ method further reduced the load difference between overloaded and underloaded MECSs compared with the _No partition_ method. _No migration_ method had a large load variance, because vehicles were not evenly distributed geographically and had high mobility; thus, the loads may have been concentrated in specific MECSs. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline subcarrier bandwidth & 12.5 kHz \\ \hline transmission power of a vehicle \((P_{n})\) & 1 W \\ \hline received noise power \((\sigma^{2})\) & \(10^{-11}\) mw \\ \hline duration of a time slot \((\Delta)\) & 0.1 s \\ \hline delay constraint of a task \((t_{n}^{max})\) & 0.1–0.6 s \\ \hline radius of a MECS & 250 m \\ \hline waiting queue size of a MECS & 5 tasks \\ \hline computation queue size of a MECS & 5 tasks \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in the simulation. Figure 4: _Cont._  
The task completion rates within the delay constraints and task reliability rates are shown in Figures 5 and 6, respectively. The rate of task completion within the delay constraint is defined as the ratio of the number of completed tasks while satisfying the delay constraint to the total number of offloaded tasks. The task reliability rate is defined as the ratio of the number of completed tasks to the total number of offloaded tasks while receiving the result without the service interruption. The task completion rates within the delay constraints and task reliability rates are affected by the task execution delay. For example, for a congested MECS, the load of the MECS becomes overloaded. This can increase the waiting time of the MECS queue, resulting in an increase in a task execution delay.