# Adaptive BBU Migration Based on Deep Q-Learning for Cloud Radio Access Network
## 5 Simulation Results
### A Comparative Analysis with Some Time Series Methods  
In this paper, comparative results between the proposed DQN and two time series predicting methods which are simple exponential smoothing (SES) and auto-regressive integrated moving average (ARIMA) are reported. * **Simple exponential smoothing (SES)** To predict the near-term load (calculated as the number of linked virtual machines) for potential nodes in a BBU cloud environment, use simple exponential smoothing (SES). The objective is to proactively choose a node that, given its anticipated resource demand, is anticipated to be underutilized [48]. The key steps for the implementation of the method: \begin{table}
\begin{tabular}{l l l} \hline \hline
**Aspect** & **Statistical Methods (MAD, LR, and IQR)** & **DQN** \\ \hline Data Basis & Historical snapshot data & Real-time and historical combined data \\ \hline Adaptability & Static thresholds; require periodic updates & Continuously adapts through learning \\ \hline Multivariate Analysis & Typically univariate (e.g., VM count) & Incorporates multiple performance metrics \\ \hline Decision Proactivity & Reactive; based on past distributions & Proactive; forecasts future trends \\ \hline Complexity & Low computational complexity & Higher complexity; requires training time \\ \hline Scalability & May need reconfiguration with & \\  & new parameters & Naturally scales with high-dimensional data \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A comparative discussion. **Candidate collection:**  
The algorithm iterates through a set of eligible nodes and collects each node along with its current number of linked VMs. Each node's current value serves as an initial forecast since historical data or a previous forecast may not be available. **Forecast update:**  
For each candidate node, the forecast is updated using the SES formula:  
\[\text{forecast}=\alpha\times\text{current Value}+(1-\alpha)\times\text{previous Forecast} \tag{12}\]  
In this simplified implementation, the forecast is initialized with the current observation. **Thresholding:**  
A threshold is defined (e.g., 10 linked VMs) to distinguish underutilized nodes from acceptable ones. Nodes with a forecast below this threshold are considered underutilized. **Node selection:**  
If there are underutilized nodes, the algorithm selects the node with the smallest forecasted value. If no underutilized node exists, it selects from the acceptable nodes based on the minimum forecasted load. If no candidate nodes exist or if no node has any linked VMs, a fallback selection strategy (e.g., FCFS) is used. This approach allows for dynamic and proactive resource management by forecasting the load on each node and selecting the node that is most likely to be underutilized in the near future. **Auto-regressive integrated moving average:** Converts the IQR-based node selection method into one that leverages a time series forecasting model (ARIMA) to predict future resource usage (number of linked VMs) for each candidate node. The idea is to use historical data for each node to forecast its next time-step value, then apply a similar thresholding approach (using forecasted values) to identify underutilized or acceptable nodes [49]. The key Steps for the implementation of this method:  
**Data collection and forecasting:** For each candidate node, the algorithm retrieves its historical time series of linked VMs. An ARIMA model is applied to predict the next value for the number of linked VMs. If sufficient historical data are unavailable, it falls back to using the current observed value. **Threshold computation:** The forecasted values for all candidate nodes are sorted, and the first quartile (Q1) and third quartile (Q3) are computed. The interquartile range (IQR) is used to derive a lower threshold and an upper threshold (using the conventional 1.5 X QR rule). **Candidate filtering:** Nodes with forecasted values below the lower threshold are classified as underutilized. Nodes with forecasted values within the threshold are acceptable.