# Intelligent Dynamic Data Offloading in a Competitive Mobile Edge Computing Market
## 6 Results
### Comparative Evaluation
#### 6.2.1 Different Learning Rates  
As we can see from Equations (6) and (7), the learning rate parameter \(b\) is an important factor regarding the convergence of the DO-MECS framework to the optimal stable state. Greater values of the learning rate would lead to faster convergence, however smaller ones allow the end-users to better exploit the available options and ultimately conclude to better states. To demonstrate the above tradeoff, a comparative evaluation between different values of the learning rate was performed. Table 2 shows the average execution time of our DO-MECS framework until convergence was achieved, while Figures 5 and 6 present the average MEC server's profit and the average end-user's utility for different learning rates, respectively. Indeed, it was observed that small values of the learning rate parameter \(b\) concluded to slow convergence of the DO-MECS algorithm, however, they allowed the MEC servers and the end-users to achieve higher average profit and higher average utility, respectively. Based on Figures 5 and 6, we can see that the the difference on the convergence state (i.e., average MEC servers' profit and average end-users' utility) between learning rates \(b=0.1\) and \(b=0.2\) was negligible, while the difference in the convergence time was significant. This was also evident from  
Figure 4: Pure operation of the proposed framework considering heterogeneous end-users: (**a**) end-users’ amount of offloaded data vs. time slots; (**b**) relative pricing of MEC servers vs. time slots; (**c**) number of end-users per MEC server vs. time slots; and (**d**) offloaded data to each MEC server vs. time slots.  
the execution times presented in Table 2, where for \(b=0.2\) the DO-MECS algorithm converged five times faster than in the case where \(b=0.1\), while, by using a higher value for \(b\) (i.e., \(b=0.5\)), we could achieve convergence times lower by an order of magnitude. Thus, a learning rate of \(b=0.2\) presented a good balance between optimality and efficiency. The convergence time of the DO-MECS algorithm could be further improved by adopting one of the following strategies and/or a combination of them: (a) Increase the learning rate \(b\). (b) Initiate the algorithm from an \"educated\" point of MEC servers' selection by the users, i.e., instead each user randomly selecting a MEC server at the first step of DO-MECS algorithm, they can use previous knowledge that would be available in a realistic environment after the initial interaction of the users with the MEC servers. (c) Utilize a more powerful machine with better computational characteristics.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Learning Rate** & **Execution Time (s)** & **Number of Timeslots** \\ \hline \(b=0.1\) & 147.2 s & 11053 \\ \(b=0.2\) & 27.5 s & 2959 \\ \(b=0.3\) & 11.6 s & 1357 \\ \(b=0.4\) & 6.4 s & 773 \\ \(b=0.5\) & 4.2 s & 504 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Execution time for different learning rate values.  
Figure 5: Average MEC servers’ profit vs. time slots for different learning rates.