## 5 Results
### Simulation Model  
This simulation consisted of four edge devices and a varying number of mobile devices. The environment for the simulation was a 90 m by 240 m rectangle where edge devices are located at \((30,30)\), \((30,90)\), \((75,150)\), and \((25,210)\) coordinates. All mobile devices were positioned randomly with a uniform random distribution in a rectangle within the simulation environment. The simulation was repeated for two selection of rectangles for placing the mobile devices. First, mobile devices were concentrated in a rectangle of size 60 by 240 m in the bottom section of the simulation environment, as is depicted in Figure 1(left). Second, mobile nodes were concentrated in a rectangle of size 60 by 60 positioned at the vertical bottom and horizontal center of the simulation environment, as is shown in Figure 1(right). For the purpose of simplicity, the first model Figure 1(left) is referred to as \"uniform\" and the second model (right) is referred to as \"centered\". The reason for the asymmetry in the positioning of the edge and mobile devices is to better represent real world scenarios and to examine the efficiency of the provided methods in those settings. After the simulation started, mobile nodes moved around the designated rectangle for mobile nodes (centered or uniform rectangles) inside the simulation environment using the random waypoint model. In the random waypoint model, each mobile node selects a random destination to move to and a random speed, and moves towards that destination in a straight line. After the node reaches its destination, it chooses another random location and repeats the process. Edge devices remained in place for the entire duration of the simulation. The data rate between each pair of devices was modeled using Equation (5), with a random value of white noise used to calculate this value. The random value of white noise was calculated using a normal distribution. Additionally, the data rate for each task transmission was further randomized to a value in \([0.5,1.5]\) of the calculated connection data rate using a uniform distribution. The general configuration values for the simulation are shown in Table 1. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline simulation duration & 300 s \\ default task arrival rate & 0.5 \\ node state transmission interval & 1 s \\ ANN parameters transmission interval & 1 s \\ min task size & 0.1 MBit \\ max task size & 1.0 MBit \\ min floating point operation per tasks & 0.25 trillion \\ max floating point operation per tasks & 1.5 trillion \\ mobile power consumption per filops & 0.5 joules \\ mobile power consumption for transmission & 0.04 watts \\ mobile device antenna gain & 3 dBit \\ edge device antenna gain & 10 dBit \\ channel frequency & 2.4 GHz \\ channel bandwidth & 20 MHz \\ mean Gaussian white noise & \(-80\) dBit \\ standard deviation Gaussian white noise & \(-10\) dBit \\ mobile CPU core speed & 1 flops \\ mobile CPU core count & 1 \\ edge CPU core speed & 5 flops \\ edge CPU core count & 4 \\ learning rate & 0.001 \\ discount factor & 0.8 \\ training batch size & 200 \\ training interval & 5 \\ training buffer size & 10,000 \\ delay cost coefficient & 1 \\ power cost coefficient & 3 \\ simulation environment rectangle size & \(80\times 240\) m\({}^{2}\) \\ min mobile node velocity & 1 m/s \\ max mobile node velocity & 5 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 1: Two representations of the simulation environment where the distribution of mobile nodes is more uniform (**left**) and more centered (**right**). In this simulation, tasks arrive using a Poisson process for the duration of the simulation.