## 4 Simulation Results and Analysis
### Simulation Scenario I  
In this simulation scenario of a small network, we consider a network topology of 30 edge data centers, which contains fifteen edge computational resource suppliers and two edge data centers for each. The number of AI services is set to 100, which consists of fifty users and two types of AI-distributed model training tasks. The backlog threshold of AI-distributed model training tasks in edge data centers is set to 50. A series of simulations in simulation scenario I of the small network are conducted to evaluate performance comparisons among different proposed DRL-based algorithms, MILPs, and benchmarks in terms of multi-objective optimization, profit, backlog, and running time.  
(a) Multi-objective optimization vs. number of AI services  
Figure 3 shows that the proposed DRL-based algorithm reduces by an average of 13.26% multi-objective than MILP, and the benchmark reduces by an average of 46% multi-objective than DRL as the weight coefficient ratio between profit and backlog is 100:1. As weight coefficient ratios between profit and backlog are 0.9:0.1 and 0.8:0.2, DRL-based algorithm reduces its respective average of 12.35% and 10.68% multi-objective than MILP, and benchmark reduces its respective average of 31.55% and 18.58% multi-objective than DRL. Thus, we find that the DRL-based algorithm achieves the most approximating performance as MILP, especially as the number of AI services is less than 60 when the weight coefficient ratio between profit and backlog is 0.8:0.2. Moreover, the benchmark reduces most multi-objectives by an average of 46% than DRL when the weight coefficient ratio between profit and backlog is 100:1. This is because under diversified types of AI service request and changing workloads on edge data centers, DRL can provide elastic computing resource scheduling strategy other than MILP with fixed accurate solution and benchmark with random assignment strategy. Another reason is that the proportion of profit is larger than the backlog of distributed model training tasks in multi-objective optimization.  
\begin{table}
\begin{tabular}{l l} \hline
**Parameters** & **Values** \\ \hline Learning rate & 0.01 \\ \hline Reward decay & 0.9 \\ \hline Memory size & 5000 \\ \hline Batch size & 32 \\ \hline Exploration rate & 0.9 \\ \hline \end{tabular}
\end{table}
Table 4: _Cont._  
Figure 3: Performance comparisons in small network in terms of multi-objective optimization, (**a**) \(\alpha\):\(\beta\) = 100:1, (**b**) \(\alpha\):\(\beta\) = 0.8:0.2, (**c**) \(\alpha\):\(\beta\) = 0.9:0.1.  
* Profit vs. number of AI services  
As shown in Figure 4, the proposed DRL-based algorithm achieves an approximating performance as MILP, especially as the number of AI services is less than 60, and the DRL-based algorithm outperforms the benchmark in terms of profit of AI service provider. Another observation is that the benchmark reduces the average to 44.7% less profit than the DRL-based algorithm. This is reasonable because the benchmark utilizes the random fit approach to assign the computing service request to the edge data center and consumes more computational resources with less profit compared with the DRL-based algorithm.  
* Backlog vs. number of AI services  
As shown in Figure 4, the proposed DRL reduces the average of 44.4% backlog of distributed model training tasks than the benchmark. Another observation is that although MILP can achieve the highest multi-objective among others, backlog performance under MILP is not stable due to the proportion of backlog being relatively small.  
* Running time vs. number of AI services  
It can be observed in Figure 4 that the DRL-based algorithm performs significantly better than MILP in terms of running time. Such performance advantage in time consumption is more obvious when the AI service number is large.